A little lesson in law and politics for the Fourth of July

Warning: Zero poker content.

For a long time, I have wondered this: Suppose a U. S. president had as his highest poilitical priority reducing the federal deficit, but could not get Congress to agree with him. Could the president simply refuse to spend some significant percentage of the money that Congress allocated? E.g., the president has a cabinet meeting and tells the department heads that they are each ordered to spend, say, 5% less than Congress authorized for their departments, and if they didn't, he would fire them and replace them with people who would carry out this directive.

Can the president do that?

Well, as with many things, this turns out to be a lot more complicated than it might appear. I am looking into it today because several days ago while flipping through radio stations I caught a bit of conservative talk show host Mark Levin. I missed the context of why he brought this up, but he mentioned in passing that Richard Nixon had done exactly that, and Congress deemed it to be such an abuse of power that it was on the original list of proposed articles of impeachment, though in the end it was not included among the three articles the House of Representatives passed. I was floored. I had no idea.

So now that I'm home from visiting family in Utah, and have some free time, I decided to look into this more. I'm not going to try to make this a formal explanation, nor provide links to specific sources. (Unfortunately, most of the best sources would require me to go to the law library, and the question doesn't interest me that much.) Rather, this is just sharing the basic points that I have learned in the last few hours of reading. But the two most useful pieces of research I found online were these:

http://www.law.harvard.edu/faculty/hjackson/ExecutiveSpendingPowers_8.pdf

and

http://law.onecle.com/constitution/article-2/37-impoundment-of-appropriated-funds.html

It seems that this question goes all the way back to Thomas Jefferson, and has caused occasional legal and political skirmishes between the executive and legislative branches ever since. Most have been settled by negotiation and compromise without much by way of long-term consequences.

But it really came to a head under Nixon. He claimed that he had to refuse to spend several billion dollars in order to avoid exceeding the national debt ceiling. Whether that is true or not is disputed. But he was obviously not in particularly good standing with Congress anyway, and this act of defiance was kind of the straw that broke the camel's back. In response, Congress passed the 1974 Impoundment Control Act. ("Impoundment" is the general term for the president not spending funds allocated by Congress, while "rescission" is the formal process of giving the money back to Congress.) Nixon signed it (which I don't understand, since he had claimed that impoundment was an intrinsic constitutional power of the president). As a result, if the president wants to not spend money authorized by Congress, he has to follow certain procedures, which include getting Congress to agree.

You might guess that this doesn't tend to work very well. Congress has ignored or refused most of the rescission requests that have been subsequently made. It is viewed as kind of a slap in the face. It's the president telling Congress, "You're trying to waste taxpayers' money, and I don't want to let you." Congress doesn't like that. Reagan was the only president who had a sufficiently amicable working relationship with Congress that he could get away with it most of the time he tried it. When his successor, George Bush, tried to get Congress to take back $8 billion in what he considered unnecessary spending, Congress agreed to just $2 billion of the request, but also simultaneously withdrew $22 billion of funding for items that Bush had deemed priorities. He got the message, and never tried to get permission for impoundment/rescission again.

What do the courts have to say about this? There has been only one Supreme Court case on the matter, Train v. City of New York (1975), but it was decided on the grounds of the specific language of the appropriation statute in dispute. Neither side raised constitutional, separation-of-powers arguments, so the court did not address them. Lower courts, however, have said that the executive branch does not possess the authority to refuse to spend legislatively appropriated funds. (I am intentionally glossing over the difference between funds that have been allocated and those that have been appropriated, as well as the differences in how appropriations occur depending on the kind of spending involved.)

The 1974 law actually requires the Comptroller General (i.e., the head of the GAO) to sue the president to force him to spend appropriated funds if he is refusing to do so and is not following the rescission procedures the law mandates. As far as I can tell, that has never happened. That would be one strange court case, to be sure.

The executive branch does have discretion to move funds around within any particular spending appropriation, to the extent that Congress has not specified program-by-program allocations. But the president cannot move funds between departments on his own authority.

So what would happen if a president decided to disregard the rescission procedures Congress mandated, and just not spend some significant percentage of allocated funds? Well, somebody would surely sue--the Comptroller, or somebody who was supposed to get the money and didn't, or maybe a Congressional committee with oversight responsibility for the affected department. I really have no good sense of what the Supreme Court would ultimately decide. In addition, maybe Congress would initiate impeachment proceedings, as they did for Nixon.

In any event, it would clearly be, as Mr. Obama seems to like to say these days, a BFD, and would likely turn into one of the most momentous constitutional showdowns in history. It seems unlikely to me that any president would take the matter that far, as it would alienate nearly every member of Congress and make it impossible for him to get anything else passed. I would probably try it if I were president, because I would care more about righting the disastrous fiscal course we're on than anything about what might happen to me personally or politically. But nobody who thinks like me would ever get elected, so it's kind of a moot point.

OK, children, that's your Fourth of July lesson in American history, politics, and law. Class dismissed. Go set off some firecrackers.

Changing the rules

http://www.theatlantic.com/magazine/archive/2012/04/the-man-who-broke-atlantic-city/8900/1/?single_page=true

Really interesting article about the guy who won millions playing blackjack against the Atlantic City casinos. He did it not by counting cards, but by bringing a huge bankroll, playing perfectly, and--most importantly--literally getting the casinos to change the rules of the game. I had read a bit about how casinos will change the payout structures for whales in Double or Nothing, the book about the brief ownership of the Golden Nugget, but this article goes into more detail.

Betting stories

I just spent a pleasant hour or so reading this small collection of gambling stories: http://www.mcsweeneys.net/columns/fading-the-vig-a-gamblers-guide-to-life

Each tells the story of a single bet--on a horse race, a boxing match, blackjack, a chess match, along with reflections on life as revealed in the game in question. I like the author's writing style and hope that there will be more in this series.

Idiocy on display

I was at the Tropicana last night. I passed this guy at a video slot machine. As the electronic simulated reels were spinning, he would rub the glass over them, rapidly moving his hand up and down over each "reel" just before it was to come to a stop, thus moving his way from left to right.

I saw such behavior once before, at the MGM, and jeered about it here. Readers then assured me that this is actually fairly common. I spend no time playing or watching others play slots, so I wouldn't know, but I have never noticed it except for these two instances. As I wrote about the woman at MGM, I feel sure that this guy does it because he believes that it enhances his chance of winning. The reality, of course, is that the outcome of each game is determined by a microprocessor a tiny fraction of a second after he presses the "spin" button. He might as well spend the subsequent seconds splashing chicken blood on the machine, for all the good it--or his rubbing--will do.

I don't know why I am still able to be amazed by the level of stupidity people are willing to put on public display, but I am.

Talk about run-good

Check this out: http://blogs.forbes.com/halahtouryalai/2011/05/13/one-mans-blackjack-hotstreak-wipes-out-casinos-profit/

BetUnfair

Serious ugliness abroad. I had not heard of this elsewhere.

http://www.kickasspoker.com/blog/a-black-eye-for-betfair/

Why is Caesars lying to its guests?

I played poker at Caesars Palace this afternoon. On my way in, which requires a walk past the sports book, I noticed this sign. Actually, I've seen it there other times, too, but just not thought much about it.

If I had seen such a sign three years ago, it would not have surprised me. I remember the Hilton security people being absolutely fanatical about people being on cell phones in the sports book area, even if they were obviously just passing through quickly and paying no attention to the Big Board of Betting Lines.

But such a sign is out of place now, because the Nevada Gaming Commission repealing the regulation cited (22.135) in August, 2008. You can see the letter announcing this on the state's own web site, here.

That means that Caesars Palace, by continuing to have this sign out, is engaging in an ongoing lie to its patrons.

Why are you doing that, Caesars?

Blackjack players are idiots

I admit that I don't understand the whole gambling thing. For whatever reason, I'm just not wired to get any thrill out of playing games that I know will lose me money in the long run. I probably average about $20 a year total on non-poker gaming. Even that is just a few bucks in a machine with a friend while we're waiting for a show to start or for our names to be called for dinner, or the required contribution for one of those two-for-one coupons, which are +EV. I realize that this makes me something of a freak among the poker players of the world, but that's how it is.

I played blackjack for about an hour once while here on vacation, maybe 15 years ago, never before or since. So my knowledge of the game is truly rudimentary. Basically, all I know is little bits and pieces picked up from TV shows, overheard conversations, incidental mentions that come up in my poker reading, etc.

A couple of years ago, Vegas Rex mentioned in a post (and, sorry, but I spent about 20 minutes just now searching for the post in question but couldn't find it) that once in a while he likes to split 10s, even though he knows that this reduces his expected return. He does it because it increased the little thrill he gets from the game. His post was about the dirty looks and hateful comments that this move draws from the serious blackjack players at the table with him. My recollection (though my memory could be tainted by subsequent stories I've heard) is that he mentioned that sometimes people even get up and leave in a huff because they don't want to share the table with somebody who does that.

I didn't exactly doubt his veracity, but I sure wondered why anybody would have this reaction. However, since then, I have at least four times overheard conversations in which "serious" players have said that they can't stand playing at a table with somebody who doesn't know what he is doing, and will leave to find another table to continue playing at. I'm bringing this up now because the most recent of these conversations was just last night, while playing poker at Planet Hollywood.

These complaints have not all been about "bad" players splitting their 10s specifically, but more generally about players who hit when the math clearly favors standing. The complaint is universally the same: the "bad" player gets a small card that helps him, but results in the "good" player getting a high card and busting, when he would have received the small card instead.

Every time I hear this, I want to have the complainer sent for mandatory psychiatric evaluation. If they pass a battery of mental health testing by a panel of experts, then the least that they should have to endure is a remedial course in probability and logic.

In the long run, it makes no difference whether you play blackjack by yourself or with a full table, nor does it matter how anybody else plays. You could have somebody at your table who takes hits every single time until he busts, losing 100% of the time, and it still would not affect you. Furthermore, it makes zero difference where you are at the table, with the allegedly "bad" players to your right or to your left. (This isn't true in tournament-style blackjack, however, because there the amounts that others bet affect what your best decision will be. That's a special case not relevant here.)

Of course it is true that what other players decide will affect what card(s) you get on this hand, but it does so in a completely value-neutral way. Yes, sometimes the guy hitting on 18 will catch a 3 that otherwise would have made you a winning hand, and instead you take a king that busts you. But so what? Exactly as often, the king and the 3 in the deck will be reversed in order, and he will erroneously hit, taking the king that instead would have gone to you, and you get the 3. It seems that the idiot blackjack players I've heard whining have highly selective memories, and only remember cases where they get hurt by the "bad" player's decision, and either don't notice or don't remember the equal number of times that they are rescued by such decisions--even though the math says that the number of events must be exactly the same both ways.

Naturally, it works the other way, too--i.e., if the "bad" player stands where he should hit, the "good" player will get a card that would have gone to the "bad" player if he were playing optimal strategy. Sometimes that change of fate will work to his favor, sometimes to his detriment. But the cumulative effect over time must be exactly zero, with just as many of the former as the latter.

This basic truth is so simple and obvious that I'm stymied to figure out how somebody could spend hours honing their mastery of optimal strategy for every possible combination of cards, and yet fail to understand it.

Getting upset at another player for how his play affected your blackjack outcome is every bit as looney as getting upset because the dealer (or a player) cut the deck too high or too low. Of course it affects everything that happens thereafter, but it does so in a way that has no systematic positive or negative value. The only difference is that you can see the "what would have been" outcome for how another player affects the current hand, and you cannot know the "what would have been" for how the deck was cut.

In poker, all sorts of things affect what cards you get: how the cards are gathered after the previous hand, the dealer's precise shuffle method, where the deck gets cut, who leaves or enters the game just before the cards are dealt, whether there is a card flashed during the deal, whether there is a misdeal, etc. But they all affect the outcome in an absolutely neutral way over the long haul, even though the change will be either for good or ill on any given hand. It would be completely insane to bitch at a player for sitting down to your right just before the deal on the grounds that he just changed what your hole cards will be. It's definitely true that his arrival did change everything (including what the board cards will be), but not in a way that affects your long-run expected value by even one red cent.

The next time I overhear a "serious" blackjack player griping about how some novice player spoiled the game for him, I'm going to put in a call to the Moron Police and have him hauled away for public stupidity.


Addendum

While writing the above, I had a vague recollection that I had written something along the same lines before. Why didn't I check? First, it was because I thought it had just been an offhand couple of sentences as a tangent while writing about something else. Secondly, well, frankly, because if I'm repeating myself, I think that deep down I don't want to know about it.

But then I was just chatting with Cardgrrl, and she asked, "Didn't you do a rant on that same subject already?" Dammit. That meant I couldn't avoid checking. And, of course, it turns out that I did. See here for that post, as well as a lot of useful comments from readers.

Oh well. At least I'm consistent in what bugs me and in the conclusions I draw.

Automated craps table

Today I played for a while at the Rio, because they have suspended their daily freeroll tournament during March Madness days, meaning that the games there should be good again temporarily (and they definitely were).

I then headed to the Flamingo for a second session. I've been kind of neglecting Harrah's properties so far this year, and would like to make at least some effort toward maintaining my platinum status, though it really does me little good. I have found that it's much easier, when going to the Flamingo poker room, to park at Bill's and walk to the Flamingo than to navigate the Flamingo parking garage, which is one of the worst in the city.

While walking through Bill's, I noticed this new computerized craps table. Maybe they exist elsewhere (in fact, almost surely so, since it's hard to believe that Bill's would be the site chosen for a first installation) but I've never known of them before. I was intrigued.

As you can see, players can sit instead of stand. They each have a private monitor. There is obviously some means of loading money/credit into them. (I'm guessing that you just hand cash to the dealer, who enters the credit on his central terminal, but I didn't witness this happening.) There is still a physical table with actual dice and a shooter, but no chips are used. Bets are made from the computer screen.

There are obvious advantages. This must surely speed up the process of placing bets. It reduces dealer errors in payouts, as well as the ancient Vegas tradition of dealers helping themselves to part of the payout, as recreational players often don't know how much they're supposed to be getting and therefore won't notice that they got shorted. It also should eliminate what I understand are the most common forms of player cheating, such as past posting (altering bets surreptitiously after the dice have landed).

I stood and watched for a few minutes. The computer system did not seem to reduce the players' fun at all. They were hooting and hollering the same as at other craps tables. The shooter was on one hell of a hot streak, and everybody was loving it. Or so it appeared. From the very little that I understand about craps, I gather that you can make yourself very unpopular by betting against the shooter. In a regular game, it is openly apparent that you have done so. But with the monitors, I assume that your bets are private (unless somebody is looking over your shoulder), so you can bet "don't pass" all you want, and nobody will know, unless you cheer when everybody else is dejected.

I wonder how the system affects dealer tips. I overheard enough to know that there are mechanisms built into the machine for tipping dealers from your credit and for posting bets for the dealers. But perhaps the social pressure to tip is reduced when nobody knows if you won or lost and the dealer isn't the one pushing you the winnings.

Another interesting feature is that the central monitors display information such as how many times in a row the shooter has won, and the highest number of times in a row a shooter has won since the table opened. If you're dumb enough to believe that certain numbers on the dice are "overdue," the screen helpfully tells you exactly how many throws it has been since various combinations hit.

I still have zero interest in playing craps, and have never put a single bet on the dice--a situation which is likely to continue for the foreseeable future. But I like seeing how technology changes gaming. If I were to decide to play, I think I'd seek out one of these tables. I think it would both speed up my learning curve about the multitude of betting options and enhance my enjoyment of the experience if I didn't have to be reaching down onto the table and figuring out which chips were mine, where to put them, when to pick them back up, and so forth. And secretly betting contrary to the rest of the table would satisfy some facet of my misanthropic tendencies.

Incidentally, while I was watching, one of the players' girlfriends rejoined him after having been off doing something else. He told her, "You should play this. You would win right away. Girls are always lucky at craps." I got the impression that he genuinely believed this, rather than that he was trying to butter her up in some way. Sigh. My campaign to make the world think rationally is a massive failure. Some people are just bound and determined to believe moronic things, and can't be educated out of it.

Interesting new game from Shuffle Master

While waiting for a seat in a game at the Luxor tonight, I picked up the only reading material they had available: the awful "Gaming Today" rag. For once, I was glad I did. I found this review of a new game from Shuffle Master.

You have to know that Shuffle Master's latest table shuffler reads the cards as they are shuffled, and therefore knows the exact position of every card in the deck. (The current versions do not do this.) The new game takes advantage of that knowledge in an interesting way.

Here's how the company describes it in a press release:

Dealer Bluff Six Card Poker™. Featuring head-to-head play against the dealer and
an optional bonus bet, Dealer Bluff Six Card Poker™ is the first table game to
incorporate the card-reading capabilities of an automatic card shuffler into
game play. Players and the dealer each receive six cards to make their best
five-card poker hand, and when the dealer pulls his hand from the i-Deal®
shuffler, the shuffler reads his hand and makes a bet based on the strength of
that hand which is reflected on an LCD display embedded in the table. If the
dealer’s hand is good, he bets a large amount, and occasionally the dealer will
bluff and slow-play.

But read the review for a lot more detail on how it works. It's still a fixed house edge, of course, but having a computer that knows the cards and makes wagers based on the strength of its hand--but with random variability built in to make guessing harder--makes it, I think, one of the most interesting table games ever to come along, and a whole lot more like actual poker than anything else I've heard of.

I'm assuming that the computer doesn't know the players' hands, because there is presumably no way to input how many players are being dealt in on any given hand. And even if the computer "knew" opponents' cards, as long as the betting algorithm doesn't take that into account, it's irrelevant. (Superstitious and/or paranoid players may not see it that way, however.)

Just thought maybe you'd like to know.

A small mystery resolved

I occasionally get "match play" coupons. For any even-money table-game bet of $5 or more (that's the usual stipulation, anyway), they match the bet amount. For example, you can use it on odd/even or red/black at roulette, which is my usual approach. It's definitely a +EV (expected value) thing to do.

The question I have wrestled with, though, is exactly how much EV is there in, say, a $5 coupon? This should be a completely straightforward question, but I had difficulty with it. My instinct at first was to say, "Well, it adds $5 to the bet, but only pays half of the time, so the EV is $2.50." (For present purposes, I'm assuming it's exactly an even-money payout and odds, disregarding the small chance of 0 or 00 on roulette.)

But when I did the math, I kept coming up with it being a $5 EV. Suppose we have two such coupons, and we bet $5 plus the coupon on red both times. The ball lands on red once, black once. When it hits red, the payout on a $10 bet is $20. I.e., you get the $10 bet back plus $10, net gain of $15, after investing $5. When it hits black, you lose $5. The sum of these two events is +$10, so the EV of each coupon is $5--in conflict with my first conclusion.

Hence my conundrum.

Today I had lunch with Cardgrrl at the Orleans, where she is staying. She was given one of these coupons on check-in, so I explained my dilemma. She wasn't sure of the correct resolution, either.

So we took the coupon to a table, put a $5 chip and the coupon on black, and the ball fell on 22 black. The woman placed two more $5 chips on our winning spot, and we walked away.

It took us a bit of thought to realize what had happened. The payout was smaller than expected--$15 rather than $20. And, once it dawned on us, the reason was obvious: They don't replace the coupon with a $5 chip before spinning the wheel. That makes it different from making an actual $10 bet in this crucial way: With a $10 bet, you get your original $10 back plus the $10 win, or $20. With a $5 bet and a coupon, you get back your original $5 plus the $10 win, or $15.

In fairness, I had seen this happen a couple of other times that I used these coupons and won, but I left wondering why the payout was less than I had thought it would be, without ever stopping to think through it all the way.

When you win, your net gain is $10. When you lose, your net loss is $5. Those two things happen with equal frequency, so the EV for the coupon is $2.50.

On the rare occasions that my gestalt sense of what should happen in a gambling situation conflicts with what the math is telling me, it's usually the math that is right and my subjective sense that is wrong. Here, though, I had the math set up incorrectly, which led me astray, and my original thought about the value of the coupon was correct. I suppose that's reassuring in some way, but, on the other hand, it's a bit embarrassing and distressing that I made such a fundamental error in how to evaluate the situation mathematically.

Can you tell that, aside from poker, I really don't gamble much?

Blackjack question #2

Once again the disclaimers about the shallowness of my grasp of blackjack, blah, blah, blah. Still, I wonder things.

Video blackjack machines exist. I have seen them. I have played them at the MGM Grand while waiting for a show to start, at Ellis Island while waiting for a seat in their excellent barbecue restaurant, and at Terrible's in Primm, again while waiting for a show.

But what always puzzles me is how few and far between these units are. I was discussing this with Cardgrrl over dinner at the cafe at Harrah's the other day. She didn't seem convinced, so we wandered all over the casino floor in search of a video blackjack machine, never finding one. Perhaps there are one or two tucked off in a corner somewhere that we missed, but I'm not sure. We passed dozens upon dozens of video poker machines and slot machines (reel and video) of every variety. I checked as many of the multi-game units as I could, because I know that sometimes those have blackjack as a game option--but not at Harrah's. No video blackjack.

I don't understand this. If I were inclined to play blackjack, I would prefer a video machine to a live dealer, all else being equal. I'm assuming here that the payout schedules are the same. That may or may not be true, but it should be true that the video blackjack machines don't have worse payout than live games, because the casino logically should want to encourage people to play the version of the game that costs the casino less to provide, which is surely the electronic one. So if there is any difference, the payout schedule should favor the machine over the dealer. Still, I'm assuming that they are equal, without having put even one minute into ascertaining whether this is so. (Why would I bother with actual facts when I can form opinions without them?)

If that assumption is correct, then the video version seems to me obviously superior to the table game, if making more money (or losing less money) is your goal. You get a lot more hands per hour, and you don't lose anything to dealer tips.

But it's perfectly obvious from the scarcity of video blackjack machines and the large number of blackjack tables that very few players prefer the machines to the dealers. My question is why that would be so.

One possibility is that people counting cards can't exercise this skill at the video game. But surely that's only a small fraction of all blackjack players.

Another possibility is that people like the social interaction with the dealer and/or with the other players. I don't suppose I can say that that is clearly irrational, but it seems odd to the misanthrope in me to put that factor ahead of the financial one. Maybe if you know that you're going to lose money over the long run, spreading the loss out more slowly makes sense so you can enjoy it longer. But that frame of mind is completely foreign to me--if you know you're losing money, why play in the first place?

My best guess, though, is that the main reason that people choose the table version of blackjack is that they don't trust the machines to be playing fair. When you happily stand pat with your two 10s, and the dealer is showing a deuce with a 10 in the hole, then catches a 9 to hit 21, my hunch is that most people just chalk it up to bad luck when the pretty young lady is turning over those cards in front of her. But if the same thing happens electronically, they think they're being cheated by a crooked machine that deliberately dealt itself the perfect card.

Naturally, I can't prove that the casinos and video machine manufacturers do not conspire to make the loss rate higher than it would be if the game were fair, but I'm inclined to think that they're legit, in the absence of pretty compelling evidence to the contrary. Then again, when I see contrails from jets overhead, I think that they are what they seem--condensation from the heat of the engines in cold air, rather than seeding the sky with mind-control chemicals to enslave the population, or whatever.

So for those of you who play a lot of blackjack, enlighten me: Do you pick the dealer variety primarily because, (A) you're counting cards and you can't do that at the machines, (B) you know you're losing money and you want it to leak away more slowly, (C) you like the social atmosphere and would miss it at a machine, (D) the payouts are somehow more favorable at the table game, (E) you can't bring yourself to trust that the cards are genuinely being dealt randomly in the video version, or (F) some other reason I haven't thought of?

Blackjack question #1

I never play blackjack. Well, that's not quite true. I think I have played video blackjack machines three times in my almost three years here, all while waiting for a show to begin or my name to be called to a restaurant. I think I lost $5 once, $2 once, and made about $1 once. That's me, Mr. Big-Time Professional Gambler.

Oh, and I played it live once, too. That was when I was here on my honeymoon--we're talking 1984 here, so long ago that I literally can't even remember which casino it was.

But being immersed in the world of casinos, one hears things about games one doesn't play. Something I keep hearing about blackjack that has me perplexed is the complaint by better players that they hate sharing a table with people who don't know what they're doing. As far as I can tell, the gripe is simply this: A player taking a hit when he shouldn't means that the next player gets a different card than he otherwise would have. If that card is a 10 and he busts, it is apparently common to get upset at the player who took what "should" have been his card. The complaint seems to be lodged even by people who are making no attempt at card counting, so that is apparently not part of the issue. As I hear it, many "serious" players will even get up and leave the table because of their fury at the guy who is playing "incorrectly."

If I'm right that this is what the complaint boils down to, it is madness.

Of course it is the case that a player's decision to hit or stand affects what cards will be given to subsequent players. But it does not do so in any systematic way. If Player 1 takes a card, it means that Player 2 gets Random Card B instead of Random Card A. But Random Card B is just as random as Random Card A, which means that it is just as likely to be good or bad for Player 2's situation as Random Card A would have been.

It seems that this is purely a case of selective attention and memory. Player 2 notices when, e.g., Player 1 hits on 17 and catches a 4, which would have proved to be a winning card for Player 2, who instead now busts when a queen comes his way. But he does not mentally attend equally to the situation in which the reverse happens, and Player 1 takes the bust card when he "should" have stood, and Player 2 instead now gets the baby card that gives him the winner.

If the game were played with the dealer (or even the player) selecting a card randomly from somewhere in the deck, instead of always the top card, then this complaint would presumably vanish, because one would no longer be able to determine what would have happened if the offending player had stood instead of hit, or vice-versa. The same would be true if the rules specified that the deck be reshuffled after each player. But there is no mathematical difference between these hypothetical changes and the way the game really is. A random card is a random card. No player can systematically cause either benefit or harm to subsequent players' situations. The effect a player's decision will have on the other players will be unbiased--sometimes favorable, sometimes unfavorable, but with a long-term net effect of exactly zero, with the good precisely balancing out the bad.

Consider a poker analogy. Last night at the Imperial Palace a player recounted how the heart royal flush jackpot had been hit at his table at about 3:00 a.m. that day. He said that it only came because he got up and went to the restroom, thus shifting what cards every player left at the table received. The player who got the royal would have received either one or two different cards than he actually did (depending on their relative table positions) had my storyteller not been absent on the crucial hand. This is the case every time a player leaves the table, joins the table, changes seats, sits out for a few hands, etc.--it changes the cards for everybody else. But nobody complains about it, for three reasons. First, you only rarely figure out what would have happened had the last player/position change not happened. Second, there is nothing "wrong" with any of the actions that result in the alterations, so there is little temptation to lodge any sort of accusation. Third, everybody is still getting two random cards; whatever change is made is just as likely to be helpful as harmful to any given player.

As far as I can tell, the blackjack complaint, though frequently enough voiced that I have heard it from multiple sources despite paying essentially zero attention to the world of blackjack, is utterly irrational. It is based on a combination of superstition, lack of understanding of the nature of randomness, and selective attention to unfavorable versus favorable outcomes.

The purpose of this post is to query my readers and see if I'm missing something. Do I have it right? Is there something actually rational about this complaint that I'm not grasping? It would hardly be the first time I'm confronted with evidence of human irrationality on a large scale, but it would make me happier to hear that there is something genuinely sensible about the situation that I have overlooked, and it is not just another example of masses of people being stupid. Please use the comments to enlighten me.

I have another blackjack question about rationality and irrationality. I'll post it here in the next day or two.

Casino roulette is TOTALLY rigged

I was walking through Binion's toward the poker room a few days ago when this roulette history board caught my eye. Hitting the "0" four times in a row? Please. It's so obviously rigged. Such things cannot happen by chance alone.

Fyodor Dostoevsky's novel The Gambler has a section about an unusual string of roulette hits, including more "0" than would ordinarily be expected. You can hear my friend Shamus read that portion of the book in the Hard-Boiled Poker Radio Show, episode 4, which you can download from here. The pertinent section runs from about 17:00 to about 27:00.

How do they get these writing jobs?

Gaming Today/Slots Today is a dual-named publication because they print the two parts on opposite ends of each issue, each upside down with respect to the other. I don't pick it up or read it regularly, but once in a while I'm bored and take a look, because occasionally it has some interesting tidbit of news of the gaming industry that I had missed elsewhere--mostly (1) stuff about regulatory and licensing issues, and (2) casino promotions. A previous time that I read it prompted a lengthy two-part screed against one of its columnists (see here and here).

In the issue of GT/ST that I have in front of me (May 27-June 2, 2008), I find evidence that other columnists are just as stupid and/or willing to deceive their readers as the one I wrote about previously, Ms. L.J. Zahm.

But let's start with her, since she remains the paradigm of how unbelievably moronic you can be and write a column for this rag.


Zahm again

I covered all of this in my previous posts, but as a quick refresher, Ms. Zahm's columns--and even a book she published--always center around her two primary theories about video keno: (1) You have to pick numbers in groups or clusters, because that's how they tend to hit--in fact, her column is called "Cluster Keno." (2) The machines tend to hit big soon after starting a session, so she advocates frequently "resetting" the machine by taking your card out, then reinserting it and re-entering your numbers, even if you are going to pick the same ones you were previously using. Of course, she has zero meaningful evidence that either of these things actually turns a -EV game into a +EV game (or even into a slightly less negative one). But she writes about the same two things, week after week after week. Easy work if you can get it, I guess.

But in this issue she outdoes herself in stupidity. Here's her gem of insight: "I've always believed that gambling is based in large part on luck."

Wow! Quick, write that down before you forget it!

She again reviews her machine-resetting theory (I suppose by now she has a macro on her word processor that lets her spit out those oft-repeated paragraphs with just a couple of keystrokes). She concludes this week's column with this brilliant advice: "By following your system, whatever that happens to be, you give yourself a chance to overcome, the odds of the game." (Yes, there really is an extraneous comma in there. I didn't make that up.)

I see. So if you don't follow your system, then you don't give yourself a chance to overcome the odds of the game. And apparently it doesn't matter what your system is, as long as you have one. Every system is as good as every other, I suppose. Each one gives you "a chance" to overcome the odds. She doesn't specify how big your chance is. I have never seen even a shred of mathematical analysis in any of her columns--for example, estimating how much she thinks you improve your odds or reduce the house edge by employing one or both of her theories. My guess is that numbers make her head hurt too much to fiddle around with them.


Larry Edell

Speaking of systems, this guy Larry Edell has a column in this issue about a betting system for craps. It has nothing to do with selecting which bets to make--only about the quantities.

His system is based on the famous Fibonacci sequence, in which each number in the series is the sum of the two previous ones: 1, 1, 2, 3, 5, 8, 13, 21, etc. He translates this into a system for altering one's bet sizes depending on the number of consecutive wins or losses one has incurred.

He says that "craps professionals use the Fibonacci to increase their profits." Yeah, right. First off, I don't believe for a second that there are any "craps professionals." You can't make a sustained living from a game that has a fixed house edge. Naturally, he produces no actual evidence that that this system makes the game profitable. That might be because it doesn't. It can't.

Over a lifetime, the only thing that determines the predicted amount of loss from playing craps is (1) the total amount bet, and (2) the odds for each kind of bet made.

One of my favorite David Sklansky books is Fighting Fuzzy Thinking in Poker, Gaming, and Life. In the first chapter of the book, he presents the story of three imaginary brothers who each have a system for playing craps, changing bet sizes depending on wins and losses. He then asks the reader to determine which of the three brothers will have the smallest or biggest expected loss or win over many years of playing every day.

I have to admit that the first time I read this I couldn't guess the answer. But it's painfully simple, once you have your eyes opened. The system that results in the fewest number of total dollars being wagered is the one that will have the lowest expected long-term loss. (In his story, they all bet on the pass line, so the odds were the same on every bet.)

For purposes of long-term results, it makes no difference whatsoever whether you bet the same amount every time, use a Martingale type of system (which involves doubling bets), this idiotic (and way more complicated than necessary) Fibonacci-based method, or use a random number generator to size your bets. Your lifetime EV is still based purely on the total amount you wagered over the years, and the odds offered on each of the dollars bet. A bet-sizing system can help control the range of wins or losses for a session (though any reduction in possible loss is necessarily offset by a reduction in possible gains, and vice versa), but it cannot change the long-term outcome. It cannot turn an intrinsically -EV game into a +EV one. It is just a fancy way of implementing a stop-loss measure.

Mr. Edell says that "The Fibonacci can be very profitable to a crapshooter." Well, sure. But it would be equally true to say, "The Fibonacci can be very costly to a crapshooter." His assertion is no more meaningful than saying that "gambling can be very profitable." Of course it can. But it usually isn't in the short run, and never is in the long run, if you're playing against a mathematically irreducible house edge.

Mr. Edell never quite tells the lie that his system will make the game profitable, but it certainly appears to this critical reader that that's the message he wants to convey, without saying so explicitly. In other words, he depends on his readers not being bright enough to see through his careful language. He also apparently assumes that they won't care that he provides not an iota of mathematical or real-world proof that this works.

It would be a pretty simple thing to rig up a computer simulation, run it through a few million iterations, and see what the net profit or loss would have been from using his Fibonacci system. I think we all know why Mr. Edell doesn't do that: he would have to report that the loss was pretty close to what would have been predicted for the total amount wagered at the odds of whatever type of craps bet he was testing. That's not the kind of fact he would want to have to give his readers. And, slightly in his defense, it's probably not the kind of hard, ugly truth that his readers want to hear. They want hope, the fantasy that they have a system that can beat the casino, and Larry Edell is selling it. He's the modern equivalent of a snake-oil salesman, but he presumably has an audience that positively adores snake oil.


Rob Singer

This is another puzzling column. It is ostensibly about video poker, but on each of the few occasions that I've read it, the guy doesn't actually describe what to do in particular situations to optimize gains. (Clearly there are better and worse strategies for playing; a source I deem reasonably reliable asserts that the optimal strategy gets approximately 99% payback, and can actually be slightly profitable, once you take into account the incentives and bonuses offered by casinos on players' club cards. The casinos are relying on the fact that only a small percentage of players deploy a strategy anywhere near optimal. If all players did so, they would probably have to lower the payout schedule to keep the machines profitable to the house.) Rather, all he does is brag about the fact that he is a long-term winner at the game.

In this week's column, as with the other couple I've read from him, he says that he is always being attacked by critics he disparagingly refers to as "the math people," who don't believe he could be as successful as he claims to be. He says that he has records to back up his claims, and, of course, the critics can't prove him wrong. He claims to be a "professional video poker player."

To be sure, I haven't examined Mr. Singer's personal win/loss records, nor am I interested in doing so. Let's assume, for the sake of argument, that he could upon request produce records showing a substantial profit over many years of playing in quantities approaching the hours of a full-time job. Would that convince me that he has found a system of play that turns video poker into a +EV game (neglecting here any points-based incentives offered by the casinos)?

Nope. I would consider it far more likely that his record-keeping was deficient, either through intentional misrepresentation or the kind of selective neglect that is a temptation to any record-keeping gambler: Faithfully record every win, but leave out losses now and then, with a whole litany of excuses why they shouldn't be counted. (I am proud to report that although my poker playing has plenty of faults and holes, my poker record-keeping has been scrupulous. I have not even once yielded to the temptation to omit the results of a session on the excuse that it was an atypically bad or unlucky day, or that I wasn't really trying that day, or whatever. I have definitely felt such pulls, but have managed to force myself to include every painful loss.)

The problem is much like trying to disprove alien abduction. Of course, for any individual story of such, it is possible that the alleged victim really was paralyzed and taken by a tractor beam up into an alien spaceship and given anal probes. (I saw it on the very first episode of "South Park," so it must be true!) I can't prove that it didn't happen. But the alternative explanations are, in my opinion, just a whole lot more plausible. They include, variously, people seeking attention and/or financial gain, delusions and hallucinations, and manifestations of poorly understood but natural physiologic states of sleep, influenced in their subjective interpretation by cultural norms and the experiences reported previously by others. (In other words, the same phenomenon that in previous generations would have been reported as a visitation from a succubus, say.)

In Mr. Singer's case, I find it just as implausible that video poker game manufacturers have designed the games in a way that can turn them into your own personal ATM if you just follow the simple strategy (whatever it is; he doesn't seem to talk much about it) claimed by Mr. Singer to be a winning one, as that every night thousands upon thousands of people are being abducted and experimented upon by aliens.

Look at it like this: If you were a casino owner or manager, would you purchase for your casino a machine that the manufacturer told you could be easily exploited by players to be profitable? I sure wouldn't. That would kind of defeat the basic idea on which casinos are built.

That consideration leaves us with only four possibilities: (1) The machine designers and casinos are knowingly building, purchasing, and installing games that they know can be beaten by anybody who follows the Singer strategy. (2) He has stumbled upon a loophole that has not been noticed by anybody in any of the various manufacturing companies, nor by any of the casinos that install the machines and monitor their profitability performance. (3) He is either intentionally lying or somehow unintentionally deceiving himself about his actual long-term results. (4) He is the luckiest S.O.B. ever to walk the planet, with results many standard deviations from the mean.

I find #1 and #2 impossible to accept, absent extraordinarily strong evidence (which no one person's results could provide). I have no objective way of distinguishing between #3 and #4, the only other remaining possibilities. But #3 strikes me as by far the less improbable one.


I am, in a sense, envious that these hacks can get paid for writing complete bullshit and passing it off as helpful gaming advice.

I'll leave you with this thought: If winning at gambling were as easy as these worthless columnists portray it, the casinos would all go bankrupt overnight. Casinos love players who are convinced they have a system that reverses the odds--because they're all wrong, no matter what some lying or self-deluded GT/ST columnist has written.

Poker Grump, master sports handicapper

I claim to have the highest winning percentage of any sports bettor in history.

I know next to nothing about sports, a level of knowledge that exactly matches my interest in the subject. Following Warren Buffet's advice about investing in what you know, I have never previously bet on the outcome of a sporting event.

That changed this week. I finally signed up for a Planet Hollywood player's club card. I didn't bother with one before, because PH is one of the few places that don't track poker players' hours and/or reward them with comps. But I decided that my card collection was woefully deficient, so Wednesday I stopped by the "A-List" club and got myself one. (It's another one with the hole in the wrong spot -- see http://pokergrump.blogspot.com/2007/12/casino-club-cards.html -- so I had to punch another one in it when I got home. So annoying.)

Along with the card they gave me two gambling coupons. The first was an added $25 payout to a win at any even-money bet of $25 or more on a table game. So I headed to the first roulette table I saw. I was going to bet on black, but another player put out several chips on the black spot just before I reached for it. I didn't want to crowd the spot and confuse things, and I really didn't care where I put the money, so I took red instead. And we have a winner! 12, red. I get paid $75 for my bet of $25 and the coupon.

The other coupon was for an extra $5 on a sports bet of $5 or more. Never having placed a sports bet before, I didn't know the procedures--like what to say to the guy behind the counter. That made the whole business a little intimidating, so I took a couple of days to think about it. I was back at PH last night (Friday), and decided to give it a go. After all, any straight bet is close to a 50/50 proposition, but with a nearly 4:1 payoff. Like the coupon-enhanced table-game bet, this was a +EV situation. I'm not a gambler at heart, but this is basically free money.

College basketball seemed an easy way to go. I pulled a list of the weekend games from PH's rack of betting information. I quickly settled on Minnesota, up against Wisconsin. This was based on an intensive study of the players, the records, scouting reports, injury lists, statistical analysis of recent trends.... OK, I'm lying. I moved here from Minnesota, and that seemed like good enough reason. Also, a friend of mine is the Gophers' team physician. If that isn't a clear sign from the gambling gods as to where to put my money, I don't know what is.

I gave the guy at the counter my $5 and my coupon. I may have detected a hint of disdain in his tone and facial expression. If so, I suppose that's because this was, like, the biggest bet he had ever had to be responsible for, and he was feeling the pressure to get it written up correctly. But I ended up with my ticket, Minnesota +10.

Today after I get up and showered and got dressed, I click into Yahoo Sports to see what happened. (You see, we big-time sports bettors can't be bothered with wasting time to actually watch the games.) And there it is: Wisconsin 65, Minnesota 56, a 9-point difference. The Gophers beat the spread by 1! Woohoo! My ticket says I will get paid $19.05 for my $5 investment.

And so I now retire from my career in sports betting, with a perfect 100% track record, with a lifetime payout of nearly 400% of my lifetime bets placed.

I am a legend.

A blue moon in your eyes (non-poker content)

About the title of this blog post--you either get it or you don't. You either excitedly thought, "Cool, a post about the Sopranos!" or you thought, "What the hell is 'blue moon in your eyes' about?"

There was a big gaming expo here a month or so ago. The only news from it that caught my attention was the announcement of a Sopranos-themed slot machine. Now, I could easily go the rest of my life without touching a slot machine and not feel the loss. But with the best television show in history now off the air, anything new related to Tony and the gang will get my heart beating a little bit faster. Upon hearing the news, I vowed that I would deviate from my usual abstinence from the slots and give David Chase et al. one dollar of my hard-earned money when I first found one of these beauties.

And tonight it happened. While playing poker at the Silverton, I noticed a banner announcing that the Sopranos slot machines were here. When I was done playing, I went looking for them. As you can (maybe) see from the blurry pictures (some day I have got to upgrade to a phone with a better camera), they are arranged in banks, with a big TV screen overhead. The screen rotates between playing the show's famous opening (the drive from New York to New Jersey, with the song, but without the credits rolling), the current jackpot amounts, and photos of the Soprano crew with quotations.

The machines use mechanical reels rather than video-simulated ones, but don't bother with an arm to pull--just a button to press. In addition to more traditional slot-machine symbols on the reels, there are photos of the main characters, plus a few locations, like Barone Sanitation and Satriale's Meats, that can line up.

As with most modern slots, there is a bewildering variety of ways the symbols can line up in various combinations to win, and if you really want to understand them, you have to crouch down and read about 30 paragraphs of fine print. I didn't bother. I inserted my $1, selected one winning line and ten credits (at $0.01 each) per line, which meant I would get ten shots at winning, for ten cents each. That's me, Mr. Big-time Gambler.

The first seven times I pushed the "spin" button, the only outcome was 10 fewer credits in my bank. But then....

I have no idea what combination I hit. It didn't look particularly special to me, but the machine started going crazy. In addition to racking up some credits, it gave me eight free spins. Unlike any machine I've played before (which admittedly isn't many), however, it started doing the free spins for me right then, just one after another, and it seemed that every one of them was hitting something and adding more credits and more free spins, which it also ran automatically for me. It felt vaguely like watching a nuclear chain-reaction in slow motion, and I was just hoping that it would spit out a "pay" ticket before it went all China Syndrome on me.

This went on for about two minutes. When it finally stopped ringing and dinging and spinning, it showed me having accumulated 430 credits.

Well, I know that this is as good as it's likely to get, so I cashed out my big $4.30 ticket and took it to the cashier's cage for my cash. I was willing to give the gang $1, but when they were nice enough (probably because I've been such a loyal fan of the show) to make me a winner by quadrupling my money, I didn't want to insult their generosity by just losing it back.

So I did what any good "wise guy" would do: I took the money and ran.

Thanks, T!

How to write a gambling column, part 2

You don't really have to read part 1 of this two-parter (http://pokergrump.blogspot.com/2007/12/how-to-write-gambling-column-part-1.html) to follow what I have to say here. In part 1, I was railing about the particular two theories that a keno-playing columnist touts as being the keys to winning play. The larger point that I had intended to get to, but never did, was the process of writing a regularly published column about a game that is 100% luck, 0% skill, and always a negative expected value on every play.

I'll try to keep on topic better this time around.

I was talking with a friend a couple of weeks ago about Linda "L.J." Zahm, the keno columnist for "Slots Today." As hard as it is to come up with new and different things to write about poker a few hundred times in a row, it would be vastly more difficult to write about strategies for games in which there cannot be any rational strategy. Or at least that's what I opined to my friend.

She, though, being wiser than I am and more in tune with the way that most of humanity thinks, immediately pointed out that I was wrong. In fact, as she noted, it's much easier to come up with material, because it doesn't have to be verifiable!

I quickly realized that she was right, and found myself awash with jealousy. Dang! I want to be writing a blog about playing video keno or slot machines instead of poker! Poker is just too complex, and, besides, there are theories and ideas and strategies that are actually testable, that can be proven to be correct or incorrect, net winners versus net losers, and I would hate to be wrong about them.

But for keno, slots, lottery playing, etc., there is no strategy that is right or wrong!* That gives you enormous flexibility and freedom in what you write, and nobody can ever prove you wrong!

"Today's column is about standing on your left foot while throwing the dice in a craps game. I've tried this several times, and have won enough that I think I'm on to something here!"

Then for your next submission you can write, "Today's column is about standing on your right foot while throwing the dice in a craps game. I've tried this several times, and have won enough that I think I'm on to something here!"

Two weeks later, when your next column is due, you can have another new discovery: "Today's column is about having your girlfriend blow on the dice before you roll them. I've tried this several times, and have won enough that I think I'm on to something here!" And, of course, the one after that would explore the no-blowing theory, with your evidence of several trials.

The possibilities are limited only by your imagination.

Along the same lines, I'd like to offer Ms. Zahm some topics for her video-keno columns, since she may be short of ideas, as evidenced by the fact that the two I've read from her covered basically the same two bogus theories.** There's no charge for these, Ms. Zahm; you may use them without paying me royalties, because that's just how nice of a guy I am:

--Using a $5 bill versus five $1 bills to charge the machine.
--Playing in the morning versus afternoon versus evening versus middle of the night.
--Playing on weekends versus weekdays.
--Showering versus not showering before you play.
--Wearing green versus blue versus red hats while you play.
--Picking your nose while the machine is spitting out the winning numbers versus non-picking.
--Selecting numbers based on family members' birth dates versus the birth dates of Hollywood celebrities.
--Using astrology versus consulting a psychic as methods of predicting the winning numbers.
--Praying to Jesus versus Buddha for your selected numbers to hit.
--Pressing the "play" button really forcefully versus pressing it very lightly, just enough to make it go.
--Sacrificing a live chicken and smearing its blood on the video keno machine before playing, versus smearing the blood on your face and arms, versus no smearing at all (cuz you've always got to have a scientific control group, ya know).

With each of these you could write a column about why you think it should work, along with a description of what happened when you tried it "several times" (which Ms. Zahm unquestionably believes is all you need to test a gaming theory). However, with the chicken-blood thing, you may have to move to a different casino for each trial, because security will probably 86 you fairly soon after the squawking ends.***

Of course, anybody with a lick of rational thinking ability already knows that any of these things would have exactly the same long-term expected value as Ms. Zahm's nutty ideas about number clusters and machine resetting. But clearly her readership is not composed of people who think very hard about the plausibility of the material they're presented. If they were, Ms. Zahm would be out of a job real fast.

In fact, it's safe to say that anybody who enjoys, appreciates, and/or puts stock in what Ms. Zahm has to say about how to beat keno must, by definition, be just as stupid and clueless about the nature of randomness as Ms. Zahm proves herself to be every time she sits down to write her next installment.

I suppose it's easy work, if you can get it.


*That's not quite true. In most casino games, some ways of betting have larger or smaller house edges. With most slot machines, e.g., your expected return is at least a little bit larger (or, more accurately, a little bit less negative) if you always put in the maximum allowable bet, because this entitles you to a proportionately larger jackpot if you hit the miracle combination. But all such basic strategy can fit onto a 3 x 5 card, and once you've stated those facts, as a columnist, you're out of advice that can actually help or hinder "winning" play.

**Incidentally, I should be something of an expert at keno, because I was once, long ago, actually married to a woman whose maiden name was "Keno." Yep. Absolutely true. Apparently a French ancestor, with a name something like "Quineau," had it phonetically Americanized by a bureaucrat upon his entry at Ellis Island. I submit that that history give me just as much authority and credibility to write about keno as Ms. Zahm has.

***Have you ever wondered where the term "86" (for expelling and banning a person from a business establishment) came from? I've wondered that every time I've heard it. I just now tried looking it up, and found that there are many theories, apparently none of them with conclusive supporting evidence. See http://en.wikipedia.org/wiki/86_(number), about halfway down the page.

How to write a gambling column, part 1

Most of everything is crap. Most food is crap. Most movies are crap. Most books are crap. Most journalism is crap. Most web sites are crap. Most blogs are crap. Most TV and radio is crap. Most cars are crap. Most clothes are crap. Most nations are crap. Most games are crap. Most of the mail is crap. Most politicians are crap. Most magazines are crap. Most music is crap. This is just the way the world operates. Because most people are undiscerning and have no taste in what they eat, buy, wear, drive, and entertain themselves with, the market supplies mostly crap, in large volumes and at low prices.

It's the same with poker publications, both books and magazines, and, as an extension, with gambling publications generally. Most of what's out there is crap.

But sometimes I'm stuck in a poker room waiting for a table, and the only things to read are issues of the worthwhile publications that I've already read, and the crap. So I pick up the crap, and hope that maybe today it will be a little less crappy than the last time I looked at it. Hasn't happened yet, but hope springs eternal.

One of the worst rags is a dual tabloid, with "Gaming Today" in one half and "Slots Today" in the other half. They actually have columnists specializing in how to play slot machines and other casino games. I feel kind of sorry for these writers, because, really, your first installment in the series pretty much has to be, "Playing this game is like flushing your money down the toilet, except that you'll probably lose it a little bit more slowly than you would to the sewers." And then what do you say after that?

The keno columnist

The first time I perused this paper, I was particularly struck by an apparently recurring column on how to play keno, written by one Linda "L.J." Zahm. Turns out that she has also published a book of her ideas.

The other day I picked up the latest issue of GT/ST, and there she was again. She said pretty much the same things that she did the other time I read her column, at least as I recall it. I was going to try to check the online archives of her writing, but I discovered that this nasty little rag actually charges you a membership fee to look at their past stuff, even though they give the thing away at every casino in town. This I don't get: the credible, professional, helpful periodicals, like Card Player and Bluff, have free access to their past material online, but one of the lowliest, crappiest, most worthless pieces of trash in the industry thinks people will pay to see it?

Anyway, Ms. Zahm has two central tenets of playing video keno. First, the winning numbers tend to fall into clusters on the screen, so you should pick your numbers in clusters, too. Second, you're more likely to make a big win shortly after you sit down at a machine or, failing that, cash out and then log back on to one.

The machine re-setting strategy

Let's look at the second premise first. Here's how she states it in the current column:

[T]here's no secret that part of my strategy in playing video keno is the
notion of "re-setting" the game frequently, as virtually all of my big jackpots have come within the first few plays of re-setting the machine.

Once again, "re-setting" means cashing out the EZ Pay ticket and beginning over again, or going back to the starting screen menu (on the Game King machine), then returning to the game....

Oftentimes people ask why this works, if in fact it does work. First, let's look at the opposite strategy: staying on your numbers without a break, that is, playing the game as if it were a live keno game by letting the numbers "come to you."

I know this doesn't work because I've testing it several times--usually at great cost in time and mostly money!

For whatever reason, the keno machine often slips into a cycle in which the numbers simply won't "come to you," no matter what.

Thus, it makes sense that if you feel this is occurring then you should cash out and start again.

She freely admits that she doesn't know how this works or why it should work: "I simply don't know, not being privy to how the keno program works." There is not one speck of evidence or statistical analysis in the column, beyond the claim that she has tried not "resetting" the machine "several times" and has lost money by doing so. QED.

Now, I'll readily admit that, like Ms. Zahm, I have no insider information as to how video keno machines' software works. But I would readily wager my entire net worth on the proposition that her observation is pure hogwash--that is, that over a number of trials large enough to even out random statistical fluctuations, there would be absolutely no difference in a given set of numbers hitting a winning combination on the first game after sitting down (or resetting a machine) and the 100th game.

How can I be so confident? Well, look at it from the perspective of the owners of the casino. They will, within allowable regulatory parameters, set up games to reward the kind of player behavior that makes them the most money. They would much rather have a player stick his ID card in the machine, charge it up with cash, then sit there and play uninterrupted until all the money has gone into the casino's coffers. The last thing they would want is for it to be both true and widely known that a player's odds of winning are greatest within the first few games, because then customers would respond by playing a few times and walking away. If nothing else, the time that the player spends logging off then checking in again, as Ms. Zahm advises, is time that that player isn't gambling. From the point of view of the casino, that customer is wasting space during those seconds.

There is just no way that a casino would choose to purchase machines that were programmed to operate that way, which means that there is no way that a manufacturer would design them that way.

So what explains the author's perception? That's easy. Look at her own language: She tried the opposite "several times." She obviously plays a lot of video keno, which means that all except "several times" she has employed her frequent-resetting strategy. It is therefore no surprise that nearly all of her big jackpots have come within the first few games after resetting, because all (or nearly all) of her games are within the first few games after resetting! If you buy a lottery ticket every week, and always pick 2-4-6-8-10, then if you ever win, it is guaranteed that your winning numbers will be 2-4-6-8-10. It will have nothing to do with whether that particular combination is really more likely to hit than any other, and everything to do with the fact that that's all you ever tried.

If Ms. Zahm had an identical twin in a parallel universe who, for whatever reason, stumbled upon the opposite strategy, she would write her book and columns to encourage people to stick it out for long sessions, having learned from experience that virtually all of her big jackpots came that way. She would write that she had tried the frequent-resetting strategy "several times" and it never worked for her. And her claim would be just as valid as Ms. Zahm's is. In fact, although it's unlikely that the machines have any built-in bias for or against picking winners based on duration of play, just thinking about how casinos want to reinforce players' behavior, you'd have to guess, in the absence of any hard data, that the alternate-universe columnist is at least slightly more likely to be correct.

The cluster theory

What about the central tenet of the Gospel According to Zahm, that of playing keno numbers in clusters? Well, this, too, is clearly just a figment of her imagination.

It's certainly true that if you look at a typical completed keno board (traditional or video), you can spot several clusters of numbers. To understand why, just think about what would have to happen for that not to be the case: The numbers would have to be quite evenly distributed. Even distributions are statistically rare. Randomness is "clumpy" by its very nature. Let me give you three examples of this phenomenon from three completely different fields.

First, a while back I took the time to figure out how many different possible Texas Hold'em boards of five cards did not make a possible straight for the lucky player holding the right two hole cards: http://pokergrump.blogspot.com/2007/10/doyle-brunson-is-wrong.html. I discovered that of all the full, unpaired boards, 1206/1287, or 93.7%, have a straight possible, given the right hole cards. That is, the great majority of the time the cards are "clustered" closely enough together in rank that you can make a straight. It is quite difficult for a random shuffle to produce the relatively few combinations of cards in which the spacing is so dispersed that no straight is possible.

Second, people are always reporting to various government health agencies their fears of a cancer "cluster." Typically this happens when somebody becomes aware of, say, three kids on one block all developing leukemia, or a few co-workers all being diagnosed with brain tumors in some relatively short period of time. But, again, that's just how randomness is--it doesn't spread things evenly. Random things tend to have more clumps or clusters than one would be inclined to think. There are lots of governmentally sponsored web pages that try to explain this to people so they won't leap to the conclusion that there's some scary external force that is behind the cancer clusters--for example, this one: http://www.cancer.gov/cancertopics/factsheet/Risk/clusters. It doesn't help much, though. People see a cluster and immediately convince themselves that it's the electrical lines or the flu vaccine or something in the water or the nuclear power plant a mile away that's the culprit. It isn't, the vast majority of the time.

Finally, consider why people make very poor random number generators. If you ask people to write down a long string of random digits, the result will almost always fail statistical tests for randomness, and almost always for the same reason: there aren't enough clusters. That's because a person will think that something like 4-4-4-4 is too obviously non-random, so even if he puts down "4" twice in a row, he's unlikely to write it a third and fourth time. But real random digit strings are chock-full of sequences that look distinctly non-random. Of course, over several million digits, the occurrence of any particular suspicious-looking string won't be any more than would be predicted. But there are lots and lots of digit sequences that, in isolation, look artificial. The human digit-generator will tend to filter those out, and the results are much more "smooth," statisically, than actual randomness produces. The human thinks, "Hmmm, I haven't written a "9" in quite a while now," so he throws one in. The true random number generator has no memory for what has come before, and nothing in it that is trying to "look" random, so it has no bias to spit out a "9" just because there hasn't been one in the last 20 or 30 digits.

All of which is a long way of getting to this point: When Ms. Zahm sees clusters of numbers on a keno board, they really are there. But the knowledge that they tend to come in clusters is of exactly zero helpfulness in predicting the winners.

Everybody who has played poker even once has seen that some players go on streaks of unusually good luck, while others go on streaks of unusually bad luck. Again, that's the "clumpiness" of statistical variance at work. But knowing that that will happen doesn't help you. Unless you know in advance which seat at the table is going to be hitting the lucky streak, and exactly when that streak will begin and when it will end, the theoretical knowledge that streaks will occur is useless.

It is precisely the same for Ms. Zahm's cluster-keno theory. Her telling you to pick numbers in clusters is just as pointless as if she told you, before sitting down in a poker game, "Be sure to sit down in the seat that is about to get hit by the deck." Gee, thanks for the hint!

Until Ms. Zahm figures out a way to tell you exactly which clusters, of all of the hundreds of possible clusters one could define on a keno board or card, are going to be the ones that hit, her observation is meaningless. I think it's safe to say that if Ms. Zahm possessed this information, she would (1) be so rich that she wouldn't need the income from writing for a cheap, pathetic tabloid, and (2) she would keep that secret very, very quiet.

I wonder if she keeps complete and detailed records as to her wins and losses. It would be interesting to see if she is actually a winning keno player over the long run. I kind of doubt it.

Wrapping up

Well, to my chagrin, I see that I have rambled unforgivably here. This post is already about twice as long as I had envisioned it, and I haven't even gotten yet to the main point suggested in the title! That's a clue to end it here, and start a new entry, I think.

Casino bingo is RIGGED! (non-poker content)

I have virtually no interest in any form of gambling other than poker. But once in a while I am curious about something and have to try it.

Recently when I was at Palace Station for the L.A. Comedy Club show, I noticed that they had a bingo hall. I commented to the friend that I was with that it might be fun to try that sometime. She has played several times before and quickly offered to go with me whenever I wanted. So last night we did it.

My family had a board-game version of bingo when I was growing up. There was a large stack of cards, and you'd place little plastic disks on the cards you were playing to mark the numbers that had been called, so that you could use them over and over without messing them up permanently. That was basically my whole framework for visualizing bingo, other than occasional scenes in movies and TV shows that take place in nursing homes or Catholic church basements on bingo nights.

Well, that's not exactly how things work at a modern casino, as I was to learn.

We went back to Palace Station. There was a bewildering variety of ways to buy into the session. The nice lady behind the counter tried to explain the options, but the lingo meant nothing to me. The signs and brochures didn't help much, either. With people waiting in line behind us, we finally bought what appeared to be the most basic package: $9 each for a ten-game card. It took just under an hour to play the ten games. It got even more complicated, in that some games used the free space in the middle, while others didn't; some games required just one completed row, while others required two or three, and the final game required every number on the card to have been called. I sure don't remember those variations from the old home game.

I was suprised--though perhaps I shouldn't have been--at how computerized the whole process has become. Maybe half of the people there were actually using automated devices, so that they didn't even have to bother finding the numbers on the cards and marking them. Talk about lazy! But even those of us going old-school had serial numbers on the pages, so that verifying a winner didn't involve rechecking what balls had been drawn, as I've always pictured the process. Rather, an employee just reads off the serial number of the player's page of cards, and another enters it into a computer, which instantly checks whether it's a winner or not. There is maybe 30 seconds total down time between when somebody yells "Bingo" and when the next game is going. Very efficient.

But not nearly as efficient as it could be. Assuming they keep track, by serial numbers, of which cards were sold for a given game, and link the sale to one's player's club card, an entire game could be played in less than one second. They hit a button, the computer randomly picks numbers until it detects that one of the cards sold for that session has hit a bingo, and it announces that the winner is Thelma Stanberg. Done. On to Game 2. Employee hits a button, and beep-boop-bop, a tenth of a second later we have the next winner announced. Repeat ten times, and we're all out of there in maybe two minutes tops, ready for dinner.

Of course, that takes away all of the suspense of being close to a bingo and feeling nervous about whether you'll hit the last number you need before that old witch across the aisle hits hers. The outcome would be the same, however. (Well, maybe not quite. It would eliminate the possibility of somebody failing to win because they overlooked marking a spot. But that's already being taken care of by those who use the computer-terminal thingies.)

From my perspective, it wouldn't be any different at all, because I never came even remotely close to winning. I never had fewer than two open spots left to fill in a regular game, and never less than four spots to fill on a double or triple game, before somebody obnoxiously yelled out "Bingo!" There was no adrenaline rush, except from the mild frustration of wondering why every number set everybody in the room madly daubing at numbers on their cards, while I looked in vain for any matches on mine. I ended up quite confident that they sold me the packet with the lowest number of matches to what was being drawn. I think they were mocking me for being pretty much clueless as to what was going on.

There is only one logical conclusion: Casino bingo is totally rigged! You probably have to bribe either the clerk who sells the cards, or the guy drawing the numbers, or both, in order to win.

Now if you'll excuse me, I have to go write my letter of complaint to the Nevada Gaming Commission, to have them look into this obvious malfeasance.