Saturday, October 18, 2008

This week's ESPN scoreboard

I just finished watching this week's WSOP coverage on ESPN. Once again, they fed us two "poker facts" which need checking. (For the earlier ones in this series of posts, start here and work backwards following the links, or just type "ESPN" in the search box at the top of this page.)

Here's the first alleged fact:

Let's assume that their inelegant wording means three of a kind on the flop, rather than after the flop, for the sake of clarity. I'm also going to cut them a little slack and assume that "full house or better" actually means "full house or four of a kind." That is, I'll assume that they did not intend to also include straight flushes, the probability of which would vary a lot depending on the exact cards in question. They just didn't phrase their query very precisely.

Once again, this is easier to check by figuring out the probability of not making a full house or quads on the turn or river. Suppose we start with A-K and see a flop of A-A-Q. That's five cards gone from the deck, leaving 47. Seven of those will make a full house or quads on the turn (one ace, three kings, and three queens), so the probability of not doing so is 40/47. If we don't make it on the turn, then 10 out of 46 remaining cards could make such a hand on the river (the same seven as before, plus the three pairs to the turn card), so the probability of not making it is 36/46. Multiply those two fractions together and we get 0.6660, or 66.60% as the probability of not making a full house or quads after having flopped three of a kind. Therefore, the probability of making it is 33.40%.

Hey, that's what ESPN said! Amazing!

OK, maybe they can get both right this week. Here's "fact" #2:

So far in this series, all of their facts have been specifically about hold'em. Sadly, ESPN is wrong here, as far as hold'em is concerned.

The number of possible ways to pull seven cards from a deck of 52 is given by C(52, 7), which Excel will instantly calculate for you as 133,784,560. We don't care what order they come in. Let's look at just the probability of getting a specific royal, such as in clubs. Of the seven cards, five are specified to be the royal, leaving two slots that can be filled by any other cards. There are 47 cards left that could fill one of those slots, then 46 left for the other. That makes a total of 47 x 46 = 2162 seven-card hands that contain a club royal flush. Now multiply that by four so that we encompass all four suits, and there are 2162 x 4 = 8648 seven-card hands that contain a royal. With 8648 hands containing a royal, there are 133,784,560 - 8648 = 133,775,912 that do not contain a royal, so our odds are 133,775,912:8648, or 15,469:1. Those are the odds against hitting a royal flush on any hold'em hand if you see all seven cards--actually a lot better than ESPN is reporting.

So where is ESPN getting its number? It appears that they are working with a five-card poker hand, such as five-card draw. Alternatively, they could have intended to figure the odds of flopping a royal flush, or seeing one come on the board of five community cards. If that is the question, then they have it almost, though not quite, right:

The number of five-card poker hands is given by C(52, 5), which is 2,598,960. Of those, obviously only four are royal flushes, and 2,598,956 are not. That makes our odds 2,598,956:4, which is 649,739:1. ESPN said it was 649,740:1. This is not a rounding error on their part. Instead, they probably forgot to subtract the four royal hands from all possible hands before taking the ratio, so they figured it erroneously as 2,598,960:4, which would be 649,740:1. Close, but still an error.

More importantly, though, since every previous poker "fact" has been about hold'em, and they are adding this little feature into a broadcast hold'em event, I think the viewer has a reasonable expectation that the "facts" presented are about hold'em, when the answers would differ among the various forms of poker. That means that ESPN needed to do the math with a seven-card hand, rather than a five-card hand. (That's slightly sloppy language on my part. I realize that even when one has seven cards to choose from, one's final "hand" is made up of only five. There isn't really anything such as a "seven-card poker hand." But I don't know any other reasonably compact phrase for describing what I'm meaning, so please forgive the slight imprecision.) For example, the first "poker fact" discussed above has to be hold'em; the answer would be different for Omaha, even though both use a flop, turn, and river.

Since ESPN erred both in using a five-card hand rather than seven (or not specifying a different game), and got the math wrong even assuming a game such as five-card draw, I have to score them a zero for this one.

ESPN's score for this week: One hit, one miss.

Friday, October 17, 2008

Buncha stories

Last night I did the MGM-Mirage trifecta: Played at Mandalay Bay, Luxor, and Excalibur (which I think are the only places in the city where you can hit three poker rooms without ever going outside in between), and scored a "W" at each one. Picked up a few stories along the way.

Hooray for sanitation

The first photo above shows a hand sanitizer dispenser at the cashier's desk at the Luxor. The second one shows a similar device in the poker room at the Excalibur. These have been there for a while, but it didn't occur to me until last night to make a point of them.

These things are an excellent idea and should, in my ever-humble opinion, be added to every poker room in the city. Hey, poker room managers--do you really want your place to be known as less interested in cleanliness than the Excalibur? If that isn't motivation enough, consider this: If you get your dealers to use them religiously, you will probably cut down on them calling in sick due to respiratory illnesses they pick up from customers.

It's good to be recognized sometimes

As I was heading to my seat at Mandalay Bay, I was greeted by a guy I had met at a get-together of denizens of Within a few minutes he was leaving, but came over to my table to pass on a hint: "Get yourself moved to table 7." He said there were some weak calling stations there and it was an easy spot to make money.

This was welcome news, because within the first three hands it had become apparent to me that I had drawn an unusually difficult table. One player had about $1000 in chips, one about $800, one about $600. The only way a table gets stacked like that in a $1-2 game is if they are gambling big-time, going all-in with low thresholds. And sure enough, there had already been big raises on every hand I had watched in my first couple of minutes. One can certainly make a lot of money in a game like that, but it's also high-risk, high-volatility, high-variance. I'm still in conservative mode, rebuilding the bankroll from the dreadful August, so if there are easier, lower-risk pickings to be had nearby, count me in.

I followed his advice and was glad I did. He was exactly right. Playing purely textbook, zero-imagination, value-betting poker, I made $240 in 90 minutes, with never a single difficult decision on my hands. Like taking candy from a baby, as the saying goes.

Which is worse--being stupid or being a liar?

Early in my time at that second Mandalay Bay table (they got me moved within just a few minutes), I watched this hand play out: Before the flop, Player A raises and B calls. Flop is 2-5-7. Player A bets $20. B raises to $70. A calls. Turn is a jack. A checks. B bets $100. A check-raises all-in for almost $300 more. B calls. A has K-K for an unimproved overpair with no redraw. B, predictably, had flopped a set with pocket deuces.

What made the story worth telling was that as soon as A saw B's cards, he said (repeating it three times for emphasis), "I knew that's what you had all the way."

I've heard this sort of thing many, many times, and I can never understand it. I mean, in one sense I get it--the guy is trying to save face by making a retrospective claim about what he knew. Apparently he thinks that this will cause others to think that he's a smarter player than he just showed himself to be. I don't know why people care so much what others think of them, but it seems to be an endemic characteristic of you humanoids.

But the actual effect--on me, anyway--is the opposite, because there are only two possibilities:(1) He really did know that the other guy had him crushed, and threw away $400 anyway, in which case he's a completely moron, or (2) he did not know it, and is lying to say that he did. In reality, it has to be (2), because it's always a lie to say that one "knew" what an opponent had, unless you have somehow seen his cards flash, or something along those lines. So all his little speech did was convince me that he's not only a bad player, but incapable of being honest with himself. That's a great combination to find in an opponent, not such a great one to find in oneself.

What's going on in that marriage?

At the Excalibur, I was surprised to see a massage therapist wandering around looking for customers. If they have been there before, I had never noticed. So now I can add Excalibur to the list of places that I know offer massages while you play poker.

One player at the table was from Boston, in town for some sort of convention. He was interested in getting himself a massage. But he did something I've never seen before: He first called his wife in Boston to ask permission.

That was strange enough. What was stranger was that she said no! He had to apologize to the massage therapist, who was standing by waiting for the go-ahead, and admit that his wife wouldn't let him get a massage.

This completely baffles me. In what kind of marriage does either partner feel obliged to seek permission from the other for a fully-clothed neck/shoulder massage from a licensed massage therapist, taking place in the middle of a public casino while sitting at a poker table? And in what kind of marriage, when that call is made, does the answer come back "no"? What is his wife thinking--that it's actually a secret cover for prostitution, and that "massage" is a euphemism for sexual favors? Or perhaps that he was actually at a strip club instead of a poker room, and what he had in mind was a lap dance? But if that were the case, would the guy be calling to ask permission?

Maybe it was him calling to ask that made her more suspicious than necessary--after all, why would he call and ask unless it were something to which she might reasonably object?

Whatever the explanation, there's something seriously peculiar going on in that relationship.

Stratosphere adds a bad rule

I played at the Stratosphere the other day for the first time in several months. They had just recently added a button straddle, a rule I dislike. As far as I know, they thereby become the third joint in town with this option available (after Rio and Hard Rock, though Hard Rock's works somewhat differently from the others).


On Wednesday night's "Poker After Dark," Gabe Kaplan made a bet on the river when the board was showing Jd-Ac-2d-Qs-6h. His sole remaining opponent in the hand, Dee Tiller, folded.

Doyle Brunson pointed to Kaplan and said, "Mark that one down. I'm predicting a cold, stone bluff."

Kaplan's actual cards? Kc-10d, the cold, stone nuts.

Highly amusing.

Stupid and/or prejudiced judges

It's 5:30 in the morning, and I kind of need to go to bed pretty soon. But I just finished reading the idiot Kentucky judge's decision, and have to comment.

Some things I think he gets right (such as that the domain names are property), some wrong. But to my mind the most obvious thing that he got wrong is the conclusion that the domain names do, in fact, fulfill the definition of "gambling devices" found in Kentucky statutes. See my previous post here on the question.

Here's the definition on the books:

(4) "Gambling device" means: (a) Any so-called slot machine or any other machine
or mechanical device an essential part of which is a drum or reel with insignia
thereon, and which when operated may deliver, as a result of the application of
an element of chance, any money or property, or by the operation of which a
person may become entitled to receive, as the result of the application of an
element of chance, any money or property; or (b) Any other machine or any
mechanical or other device, including but not limited to roulette wheels,
gambling tables and similar devices, designed and manufactured primarily for use
in connection with gambling and which when operated may deliver, as the result
of the application of an element of chance, any money or property, or by the
operation of which a person may become entitled to receive, as the result of the
application of an element of chance, any money or property;

It's highly doubtful whether a domain name can reasonably be considered a "device" at all. It's also doubtful whether it makes sense to say that a domain name was "manufactured." But what's most troubling to me is that the judge didn't even bother to discuss the rest of the definition. Even if a domain name is a device that was designed and manufactured primarily for use in connection with gambling, there is no way that it fulfills the rest of the definitional requirements.

Specifically, when a domain name is "operated," all that happens is that a web browser connects to a specific server. That's it. "Operating" the domain name does not involve any application of any element of chance. Operating the domain name does not deliver any money or property, nor entitle the operator to receive any money or property. Those things might happen after one downloads software from the web site, establishes a money account, and plays a game. But those steps in the process are not operating the domain name in any meaningful sense.

It's rather as if the judge is treating the key to the door of a gambling den as if it were a roulette wheel. Sure, the key may give one access to the gambling devices inside, but that does not make the key itself a "gambling device" as defined by the statute. The state could seize the roulette wheels, but it would have no authority to seize the keys to the building.

On this ground alone, I would be flabbergasted if this ruling withstood an appeal. Of course, there's going to be a lot of disruption in the meantime--state appellate procedures tend to take many months to play out.

I know nothing of this judge, but my guess is that he is personally strongly opposed to gambling. To my eyes, the entire decision reads as if he detests gambling, thinks it a scourge on society, and was willing to find whatever facts necessary and twist the law in any which way in order to make the decision come out as it did. For the definitional question, he pounded a round peg into a square hole. He trimmed the edges of the jigsaw puzzle pieces with scissors in order to force them to fit the way he wanted.

What the affected property owners needed was Al Pacino yelling at the judge, "You're out of order! You're out of order! The whole trial is out of order!" (From "And Justice for All." See the amazing courtroom scene below.)


After a few hours' sleep, I'll add a bit here. Kentucky, like most states, employs the judicial doctrine of the rule of lenity, or strict construction of penal/criminal statutes. That means that the conduct prohibited must be unambiguously defined in the statute, and if there is any reasonable doubt about whether the conduct in question violates the statute, the benefit of the doubt must go to the defendant. The statute is construed strictly against the state. For example:
The use of "injure" following "to kill" evidences a limitation on the type of
injury to physical injury, not economic, etc., injury. See Thompson v. Bracken
County, 294 S.W.2d 943, 946 (Ky. 1956) ("Simple words when considered in a
statute are generally accorded their ordinary and accepted meaning
."). The
limitation of "injure" to physical injury only is further evidenced when
"threat" is viewed in context of KRS 524.040, "by use of physical force or a
threat directed to a person . . ." (emphasis added). See Department of Motor
Transp. v. City Bus Co., 252 S.W.2d 46, 47 (1952) (whole statute may be
considered in interpreting meaning). This conclusion is consistent with another
principle of statutory construction, the "rule of lenity", which requires, in
construing an ambiguous penal statute, to give to the appellant the benefit of
the doubt
. Roney v. Commonwealth, 695 S.W.2d 863, 864 (Ky. 1985). See also,
Woods v. Commonwealth, 793 S.W.2d 809, 814 (Ky. 1990); Commonwealth v.
Lundergan, 847 S.W.2d 729, 731 (Ky. 1993); Commonwealth v. Colonial Stores,
Inc., 350 S.W.2d 465, 467 (Ky. 1961). "Penal statutes are not to be extended by
construction, but must be limited to cases clearly within the language used
Woods, 793 S.W.2d at 814.

Godby v. Commonwealth, 187 S.W. 3d 857 (Ky. App. 2005); 2005 Ky. App. LEXIS 289, at *11-12. (Emphasis added.)

The statutory definition of "gambling device" quoted above is part of a penal statute. It is used both to define the crime (unlawful possession of a gambling device, in Kentucky Revised Statutes 528.080) and to describe what the state may seize (in KRS 528.100). Therefore, courts are required not to go beyond the literal language of the statute. Judge Wingate's reference to the "spirit of the law" is simply not applicable in penal cases. If a domain name is not "clearly within the language" of the statute--and it is not--then it cannot be read as if it were there by interpretation of the judge.

Technically, what is being invoked here is a civil forfeiture rather than a criminal one, because there has been no conviction of a crime. However, it would be preposterous to apply one set of rules for reading the definition of "gambling device" where a conviction was in question and then a different set of rules for reading the same words when a forfeiture was in question. That is, since the owners of the domain names could not possibly convicted for possession of a gambling device, given the rule of strict construction of the statute, it would stand logic on its head to tell them that the "device" in question must still be forfeited. "We can't convict you because the domain name does not fall within the statutory definition of a gambling device, but we're going to seize the domain name because it falls within the statutory definition of a gambling device."

Wednesday, October 15, 2008

I voted today

My little spit in the wind.

So much for secret ballots, eh?

Poker gems, #173

Crandell Addington, in Des Wilson's Ghosts at the Table, as excerpted in Poker Pro magazine, September, 2008, p. 53.

In heads-up play, you must outplay your opponent and that's why it's called poker and not just catching cards. If you want to know what to do in these positions, read the books written by field marshals and generals because no-limit poker is crystallized aggression, and you have to be willing to sacrifice some troops in a battle to win the war. Most people are unable or unwilling to do that, and that's why they're not good players.

Why I might be good for your game

The other day I was playing at Bill's. I moved from one table to the other because I wasn't making any progress where I was. But not too long after moving, a bunch of people left and we all got moved back to the first table. A guy that had been across from me at the second table ended up on my right after the consolidation.

I was puzzled when he told me that he had been glad to have me join his table. I was even more puzzled when he said, "In fact, I wish you'd follow me around everywhere I play poker." I didn't understand this comment--I wondered if he was trying to tell me that I was a fish from whom he'd easily be able to make money.

Nope. He cleared it up for me with the next sentence: "Having you around keeps me from making stupid moves, because I don't want to have to read about it the next day."

Incidentally, I think I finally convinced him of the amazing power of the mighty 4-2. He saw me take a decent pot with it by backing into a flush, then followed my example and won an even larger pot himself, bluffing at an ace-high flop, then hitting a 3 on the turn and a 5 on the river to back into the nuts with my favorite junk hand.

I'd better stop telling these stories. Don't want everybody to know about the secret power!

Tuesday, October 14, 2008

Not too slow

On last night's "Poker After Dark" a hand played out between Howard Lederer and Doyle Brunson. Lederer flopped a set, Brunson a flush draw. Brunson led out on the flop with a bet. Lederer raised and Brunson called. On the turn it was check/bet/fold.

When the hand was over, Brunson began complaining about how long Lederer had taken, and said he would have to start calling the clock. Lederer wasn't sure he was serious at first and asked if he was talking about the hand they had just played. Brunson said yes, because Lederer had taken "ten minutes" of stalling before acting. Lederer was clearly annoyed by this complaint, feeling it unjustified, and retorted that he had taken only "ten seconds." At this point, it wasn't clear that either man was meaning the claimed time as literal. Both were likely knowingly exaggerating.

Still, Lederer pointed out that he had won a speed poker tournament in Australia, and would be perfectly willing to play with a time constraint (I assume that this would be only if everybody were equally limited). He asserted that he would not have "busted the 30-second clock" in the previous hand. Brunson replied, "Oh yes, oh yes." Gabe Kaplan weighed in, too, agreeing with Brunson and saying that Lederer had taken a full minute, though a few seconds later he revised his best estimate to "53 seconds." This prompted Lederer to propose a prop bet--whether his action on the turn took over or under 45 seconds. Eli Elezra inserted his opinion that it was over 0:45, but under a minute. Kaplan didn't take Lederer up on the bet, but Elezra did, for $5000. Brunson said that he thought it would be over 0:45, but that it may be "real close." Lederer's final guess was that he took "about 20 seconds," at which estimate Elezra scoffed.

So I went back and checked. It did not appear that the hand was edited; everything appeared continuous, as far as I could tell. I clocked Lederer right between 0:29 and 0:30 to make his raise on the flop and 0:28 to make his bet on the turn. Brunson, meanwhile, took 0:22 to call Lederer's bet on the flop and 0:37 to fold on the turn, after Lederer's bet was in. (I haven't finished the show yet, and so far the producers haven't announced an "official" time after checking their replay, but I suspect that will be coming up later.) [Edit: On the next day's show, the official time was given at 29 seconds, and Lederer won his bet.]

In other words, their combined thinking times were within a second or so of each other (I'm disregarding Brunson's initial decision on both streets, since he had one more decision than Lederer both times), though it appears that Brunson probably took one tick more than Lederer. (This is hard to score precisely, because it's a little fuzzy exactly when one should start and stop the clock, so it's easy to be off by a second or so either way.) Moreover, Lederer was correct that he would not have been burned by a 30-second clock for either of his decisions. Most striking is that the complainer, Brunson, easily took the longest time for any decision in the hand, and would have been in trouble with a 30-second limit!

It's really difficult to keep even the remotest track of time when thinking about a difficult poker decision. Sometimes the time is distorted to be faster than reality, sometimes slower. Can't really blame either participant in this argument for being off in their estimates, though when it came down to a clearly factual assertion (more or less than 30 seconds), Lederer was correct and Brunson incorrect.

Maybe this is already obvious, but anytime in this blog that I describe how long somebody in a poker hand took to make a decision, there is no timepiece being consulted, and any number I give is pretty much a wild guess, distorted not only by the psychological forces acting in the moment, but by the passage of time between the occurrence and the writing--so they are all to be taken with a grain of salt. I wouldn't knowingly falsify what happened, but as the televised incident demonstrates, we're all highly fallible when it comes to estimating elapsed times, particularly when distracted by the puzzle-solving task of the hand and its emotional overlays.

By the way, Brunson's hand-reading radar was as far off as his internal clock; when another player opined that Lederer had held a set, Brunson bitterly countered that he must have only had "some kind of old phony-ass draw."