The perils of blogging too much

So I just wrote the previous post. It's up. I'm proofreading it. It occurs to me that I once heard Mike Sexton make the same mistake (saying "reraise" when it was just a raise). I think that that would make a nice extra touch to add to the post. I start trying to see if I can remember which World Poker Tour event it was where I heard Sexton's gaffe. Then another thought starts creeping into the old noggin: Didn't I write a blog post about that when it happened? A quick search reveals not only that I did, but that I did a whole rant about the "reraise" thing back in May, 2008, in which I detailed the circumstances of his comment.

And now I just repeated myself, except that it probably wasn't as good the second time around.

On Sunday I was in a 14-player home tournament with Cardgrrl. I busted out and joined a cash game on the side, while she kept playing. (She won it, not too surprisingly, though she has so far been too modest to note that fact in her own blog.) I lost the biggest pot of the day (something like $70, which was massive, given that the stakes were $0.10/$0.20!) in one of the most annoying ways possible. Four of us checked it around on the river. I had top two pair, but didn't bet because the river put a fourth heart on the board, and I didn't have one. I showed my cards. Two of the others mucked. The last one made a dejected face and pushed his cards forward a few inches, face down, as if to muck. (This is a player-dealt game, and there was no clearly defined muck area.) Just then, a bozo at the far end of the table, not involved in the hand, said, "Nobody has a heart?" The fourth player, apparently not having noticed the four-flush on the board, then picked up his cards again, discovered that he had the ten of hearts, showed, and took the pot.

Why didn't I write a whiny blog post about this at the time? Because it was virtually identical to an incident I related here (fifth story) about a hand at Bill's, just over a year ago. I thought about recounting Sunday's hand in detail, complete with a rant about how such a stray comment egregiously violates the rule about not talking about the hand in progress, as well as the "one player to a hand" principle. (When you help one player in poker, you almost inevitably hurt another at the same time.) But why bother, when I've already done that post before? At least in that case I managed to remember having told the story before.

So this is one of the problems of having been blogging quite prolifically for a hair under three years now. (My first post was made on October 30, 2006. Happy early anniversary to me!) I have already tackled a hefty percentage of all the things I can think of to talk about. New things happen to me at the poker table with a much lower frequency than when I was first in Vegas. It's not exactly true that I've seen it all and done it all, but I've certainly seen, done, and written about a whole helluva lot more than I had back then. There are fewer novel thoughts and novel experiences to share with readers.

That leaves me the dilemma of repeating myself intentionally (figuring that not everybody has been reading all along), repeating myself unintentionally (as happened earlier today), just putting up pointers to an old post with a note like "this happened to me again," or just letting things go silently. I'm not sure that any of those is the optimal solution, though they'll probably all be deployed once in a while.

If you catch me telling virtually the same story a second--or even third--time, forgive me. It might be deliberate. Or it might be senility setting in.

It has to hurt

In the original Star Trek series episode "Mirror, Mirror," several members of the crew get switched, via one of those frighteningly frequent transporter malfunctions, into one of the many parallel universes which is almost but not quite like our own. In this one, doppelgangers of our heros are on a ship identical to the Enterprise, except that they are all selfish, power-hungry, violent, and cruel. Oh, and they tend to wear goatees and/or have facial scars, sure signs of all that is wicked.

In this mirror universe, each crew member is required to carry a small device called an "agonizer." In case of infraction of the rules of military conduct, a superior officer will take the offender's agonizer, activate it, and apply it to his body for whatever length of time is deemed appropriate to the occasion, resulting in unspeakable pain being inflicted. For the most serious offenses, such as mutiny or assassination, the guilty party was put into the "agony booth," which we must assume was unfathomably worse than the little agonizer device. See here and here for much more than any sane person would ever want to know about these instruments. What you see above is the unfortunate alt-Pavel Chekov receiving his torture for having staged a failed coup on board the mirror-universe starship. Tsk tsk tsk. As Mirror Spock coolly notes, "The agony booth is a most effective means of discipline."

Yes, there is a poker connection here. I've had more than my fair share of cold-deck situations over the past week, and it has brought back to mind a bunch of painful memories. I remember keenly:

--the first time I drew to the low end of a straight, got there, and only then realized what a bad spot I had gotten myself into.

--the first time I flopped trips and lost it all to a guy who had flopped a full house.

--the first time I had a full house and lost it all to a guy who had quads.

--the first time I had an ace-high flush and lost it all to a guy who had a straight flush.

--the first time I misread my hand, thinking I had the nut straight, when I actually had nothing, and called off all my chips, only to be thoroughly embarrassed when I turned over my cards and saw what I had done.

There is something about the pain of these moments that sears them into our souls. Mike McDermott observes in a rueful voiceover in "Rounders":

In "Confessions of a Winning Poker Player," Jack King said, "Few players recall
big pots they have won, strange as it seems, but every player can remember with
remarkable accuracy the outstanding tough beats of his career." It seems true to
me, cause walking in here, I can hardly remember how I built my bankroll, but I
can't stop thinking of how I lost it.

(Transcription taken from the imdb.com page here.)

I recall that once when I was a small child my mother was preparing to do some ironing. The iron was standing idle on the ironing board. She was out of the room. I wondered whether the iron was on or off, so I did what seemed like the logical thing at the time: I reached out and touched its surface with my index finger. It was on. I cried, of course. When mom came to see what the fuss was about, and I told her that I had burned my hand on the iron, she asked, "Why did you touch it?" I thought that was the dumbest question possible. "I wanted to see if it was on." Of course.

It must have been somebody with a similar childhood experience who coined the expression, "Once burned, twice careful."

Some things do get better with time and experience--and some build-up of scar tissue. These days I am never as shocked at the kind of situations I listed above as I was the first time they happened. (Fortunately, I still haven't experienced the really horrendous beats--things like quads being beaten by a straight flush, or the low end of a straight flush being squashed by the high end.) Just the other day at the Rio I had 6-7 offsuit in the big blind, so I took the flop for free. I loved seeing it come 8-9-10, two-suited. I bet, got raised by the button. It was early in the session, so I was relatively short-stacked, and moving all in was a no-brainer. Of course I knew that it was possible he had one of the two hands that had me drawing nearly dead (7-J or J-Q). But on the other hand, he would raise me and be willing to call my reraise, probably, with any two pair or trips, and maybe something like a pair and flush draw, or a combined straight draw/flush draw, or even just the nut flush draw with no pair. It was not one of those situations where my all-in raise would get called only if I was beat. But this time he did, in fact, have the J-Q. The only way I could win was with a runner-runner flush or split the pot with a runner-runner J-Q, neither of which happened. Sigh.

The point, though, is that I have become considerably more callused to this sort of thing, and because I anticipated the possibility of being shown the nuts, it didn't stun me and send me reeling the way that those earlier stories did when they occurred. It's not that it doesn't hurt. It does. But my skin is thicker than it used to be, and I have learned to expect the unexpected. With anything short of the nuts, I'm braced to take whatever hit may come, and even with the nuts I'm mentally prepared to see my opponent turn over the same hand for a chop, when that is a possibility.

Before I started playing in real-money games online, I spent quite a bit of time with Wilson Software's simulator. It was, I suppose, useful in getting me used to the mechanics of play, and giving me some feel for what starting hands were likely to end up winners and losers, but I honestly can't remember a single hand I ever played on it. I think it's because none of them actually cost me anything. If I got knocked out of a tournament, I could say, "Oh well," and be in another one ten seconds later, with nothing lost--and nothing learned, I'm afraid, whether it was a bad beat or a bad play.

Simply put, if it doesn't hurt, it's a lot harder for the lesson to sink in. I'm sure there's some biochemical reason for that, related to neurotransmitters powerfully stimulating certain loci in the nucleus-of-whatever deep in the brain. But you don't need to know the physiology to recognize the truth of it.

Of course, the magnitude of loss it takes to inflict the kind of pain necessary for a long-term memory of the event to form will vary according to your means and past experiences. I remember reading a poker magazine story about Phil Ivey (probably in this issue of Bluff, which has an interview with him available online, but not the feature piece I'm remembering). His wife was just learning to play poker and was doing microstakes online. Phil came home on edge because he had had an unusually deep loss--a few hundred grand, as I recall. His wife was upset at her day, too; she told him that she had lost something like 70 cents, which is a lot when you're playing $0.01/$0.02 games. Talk about different pain thresholds!

Mike Sexton said it well during an episode of the World Poker Tour a couple of years ago, when somebody got knocked out of the final table on a one-outer: "If you don't like a little pain once in a while, poker is probably not your game, because as you can see, you're gonna get it."

Who needs an agony booth when you have poker?

Does Mike Sexton really think this way?

I'm watching this week's "World Poker Tour" (as the previous post probably suggested). Mike Sexton just said one of the dumbest things I've ever heard come out of his mouth.

Two amateurs are involved. One of them, Andrew, won a huge pot with K-K on the "previous" hand. (The reason for the scare quotes will become clear later.) Now a guy named Robert is on the button and raises with J-J. Andrew is in the big blind and reraises with 7-7.

While we're waiting for Robert to decide what to do, Mike Sexton says, "Well, Robert knows that he [Andrew] had two kings the last pot. You're never gonna put a guy on aces, kings, and queens back to back."

Huh????

Why not?

Does Mike Sexton actually believe that the fact that a player had K-K on one hand makes it mathematically less likely that he has A-A, K-K, or Q-Q on the next hand? If so, how in hell has he managed to make a living at poker for the last 20 years or so, with such a fundamental distortion in his grasp of randomness?

The cards have no memory. The auto-shuffler has no memory. What a player had on the previous hand has exactly zero effect on the analysis of what he might have in this hand. He is every bit as likely to have K-K here as if you wait 200 hands and then try to figure out what he's holding. When the K-K hand was over, everything reset, and he became just as eligible to get K-K again as he ever was.

Yes, it's rare to get K-K (or any other combination of cards you care to specify) in consecutive hands. For any given two-hand sequence you name, them both being K-K will happen only once in 48,841 times, on average. But the probability of the second hand being kings is completely independent of the probability of the first hand being kings. Once you know that the first hand was K-K, you know nothing more or less about the likelihood of the next hand being kings than you did before. It is 1 out of 221, just as it was on the first hand, and just as it will be on every subsequent hand. In fact, even if somebody miraculously gets K-K 10 times in a row, the probability of getting K-K on the very next hand, to make 11 in a row, is still precisely 1 in 221 (barring some shady dealing going on, obviously).

I've talked about this common fallacy at least twice before that I can remember, here and here. I'm not really terribly surprised when I hear a recreational player fail to distinguish between a priori probabilities (e.g., the probability that two specified consecutive future hands will both be K-K) and conditional probabilities (e.g., the probability that the next hand will be K-K, given that the previous one was), which is the essence of the mistake here. After all, our public school systems are about as lousy as they can be in teaching kids to understand statistics and probability.

But how can a guy who has spent so much of his life playing, thinking about, and talking about poker as Mike Sexton has still hold on to such a simple, rudimentary error in understanding how randomness affects the game? It's kind of like an obstetrician still believing that babies are brought by storks.

The other possibility is that Sexton understands this perfectly well, but is being condescending towards Robert--saying, in effect, "This guy isn't smart enough to understand that what Andrew had on the previous hand should not be taken into consideration when assessing his range of hands here." If so, then he's being unfairly demeaning to the amateur player, with no reason to make such an unflattering assumption about him.

There's another factor making this statement even more stupid, if that's possible. Because of editing, this was clearly not actually the hand immediately following the one in which the player named Andrew had K-K. I went back and checked where the button was, and it had moved two seats. So there was at least one intervening hand not shown, and maybe 7 or 13 or 19 hands (beause there are six players at the table) that were not shown. This doesn't affect the probability, of course, but it means that both the factual basis and the theoretical basis for Sexton's statement are wrong.

To his credit, I don't recall hearing Sexton say anything quite this boneheaded before. But it was sure a doozy.

It's not a reraise, dammit!

I did a twofer tonight: I hit, first, Mandalay Bay, then hiked over to the Excalibur, taking advantage of them both being connected to the Luxor (which sits in between them) via indoor walkways. My original plan had been to play at all three places, Luxor last, but it was too late and I was too tired by the time I finished at Excalibur.

Anyway, I saw/heard the same mistake twice tonight, one in each casino. In each instance, somebody put in a bet on the flop, followed by another player announcing "reraise."

This is not a "reraise." It is simply a raise. In order to be a reraise, there first has to be a raise. The first bet on any round of betting is not a raise, because there is nothing to raise. So if the second person to act wishes to bet more than the first person did, it's a raise, not a reraise. The third player to act in a round of betting can put in a reraise; it is not possible for the second person acting to do so.

The World Poker Tour episode this week was their annual invitational "Ladies Night." Watching it reminded me that I never saw the one from last season (at least I don't remember having seen it, though with my aging brain cells, it's possible that I watched it 20 times and it didn't stick). I have all of the episodes from every season clogging up my computer's external hard drive, so I fired it up and watched the thing.

The lone amateur player, who won the qualifying tournament to earn a place at the table with the invited pros, does exactly the same thing at one point: she announces a "reraise," when she is simply putting in a raise. Well, not too surprising for an amateur to make that mistake. But I was shocked that Mike Sexton repeated it, saying, in his usual over-excited voice, something like, "Vince, she's not just calling, she's reraising!"

Mike Sexton definitely ought to know better.

And if you, dear reader, didn't know better before, now you do. It's one of those little goofs that, while not actually adversely affecting anything, reveals that one is rather inexperienced at live casino play.

Actually, nobody ever has to use the word "reraise"; simply "raise" works perfectly well, even if it's the fifth or tenth consecutive increase in the size of the bet. So if you want to avoid any possibility of ever making this faux pas, just delete the word "reraise" from your vocabulary entirely, and you'll be fine. For what it's worth, I think the word "reraise" sounds a tad silly, so I never use it. "Raise" does the job just fine.

Closely related is the error in which the first person to act in a given round of betting says "raise" before putting in his chips. Uh, no. You can bet, but it is logically impossible for you to raise, since there has not been any previous bet.

It's just as easy to get it right as to get it wrong, so please try to get it right, OK?

I can love the WPT again

If you follow such things, you've known for a long time that there have been loud and frequent complaints among both players and serious viewers that World Poker Tour final tables have been all-in luck-fests. The blind structure was such that usually half of the last six players came in very short-stacked and had to make shove-and-pray decisions. It was not the greatest display of poker skill.

Last night was the conclusion of the two-part Bellagio Cup III broadcast--a four-hour final table, the first using the WPT's new tournament structure, which made for much deeper stacks, and therefore much better poker.

It was like watching a whole new show. I cannot praise the change sufficiently. Even after two players were eliminated, even 2 1/2 hours into the 4-hour combined show, all four remaining players had more than 60 big blinds each! Deep-stack poker is a whole different animal than what we've become used to in these programs, and it was sweet.

I also noticed that Mike Sexton and Vince van Patten were going deeper in their analysis than they used to. They take a lot of grief for saying the same things over and over again, but frankly, these guys taught me the game. The first time it came on, I had no idea how to play, but I learned through watching. They understand that their audience has grown more sophisticated in its knowledge of the game, so their commentary is now stepping up a notch to accommodate that.

For example, at one point Danny Wong (who I thought was the most impressive talent at the table, with fewer missteps than anybody else, and astonishing feel for when to press and when to back off) flopped two pair and led out betting, rather than slow-playing it. He got no customers. In past episodes, I don't think that would have received any significant analysis. But this time they showed unimportant footage of him stacking up his chips (with four hours, they have the time luxury to do this sort of thing), while Vince came to his defense and explained why this non-obvious move was actually smart. (At the risk of breaking my arm while patting myself on the back, I appreciated this commentary because I was thinking that I would have played it the same way, and for precisely the reason that Vince noted.) Wong probably anticipated that his ultra-aggressive opponent, Kevin Saul, would view the bet as a steal attempt and raise with position. Wong would therefore win more chips than if he check-raised or just called, both of which would set off alarm bells in Saul and cause him to shut down. It's the reverse-reverse thing: betting out is the first-level obvious thing to do when you flop big, so the common ploy is to reverse that and check instead, which makes betting out look like you have a small piece of the flop, rather than a monster. I agree completely with the play and the analysis, and it just happened that Saul, this one time, didn't play as per his usual style. Anyway, I appreciated the time the show took to explain why the unconventional move may have been smarter than it looked at first glance.

I also appreciated what seemed to be the commentator's newfound willingness to be openly critical of bad plays. In the past, about the most scathing critique you'd hear from the ever-positive Mike Sexton would be something like, "Well, in my opinion, that was a questionable move there." But in last night's show, Mike Matusow, way behind in third place and getting pummelled by both remaining opponents, said that if he didn't win this event he was going to go kill himself. (To which Vince rather nastily remarked, "Promises, promises, Mike!") Mike Sexton said something like, "He's going to have to start playing better if he hopes to beat these two guys." Dead on accurate. I like the pull-no-punches approach, when it's justified.

I have to admit that I was disappointed not to see Matusow break down and cry like a baby when he got knocked out, the way he did in his only other WPT appearance back in season one. They showed a clip of that again last night, and again I laughed out loud at him. No wonder he and Phil Hellmuth are such good friends--they can cry on each others' shoulders. Not that there's anything wrong with that, if that's who they are....

I was surprised to notice that a guy I used to play with all the time at the Hilton is a Bellagio dealer and had a lot of time in the box on this episode. I didn't even know he was a poker dealer. There's probably not a chance in the world that he reads this blog, but just in case: Hi, Sal!

Now if they could just find a hostess that I like as much as Shana Hiatt, they'd have me completely hooked again.

A confession

When I'm in a hand, I often hear the voices of Mike Sexton and Vince Van Patten in my head, doing the play-by-play commentary.

**********

MIKE: Oh, look at this, Vince, Rakewell has flopped the nuts.

VINCE: Yes he has, Mike.

MIKE: He has top set with no straight or flush possible at this point.

VINCE: The "Star-Spangled Banner" is going off in his head.

MIKE: This could spell real trouble for his opponent's pocket aces. Let's see how he's going to play it. Well, he checked. He knows he has an aggressive opponent who will likely take a stab at it, so he's playing it slow.

VINCE: He's dug the hole, he's putting the twigs and branches over it.

[Etc.]

**********

I have a feeling I'm not alone in this little delusion.

Poker gems, #57

Mike Sexton, in a tribute to the late Chip Reese, in Poker Player newspaper, December 24, 2007, issue, p. 27.

Years ago, I was talking to Chip about another Hall of Fame poker player that we lost too early, Stu Ungar. I asked Chip if he thought Stuey was the most talented player he had ever seen. Chip said, "Natural ability-wise, yes. Certainly he was the quickest minded guy I've ever known. Stuey's problem is that he doesn't understand the 'object of the game.' The object of the game is to accumulate wealth, improve your lifestyle, and provide for your family, and Stuey will never get it." Chip did.

...

Poker players always admired Chip for his success, his demeanor at the table, his lack of ego, and that he never steamed or went on tilt. I'd suggest we remember him for one guy who truly understood the object of the game.

The worst hand in poker--are you sure?

A couple of weeks ago, while playing at the Hilton, I was in the big blind with 2-3 offsuit. The pot wasn't raised, so I got into the hand for no extra money. I got no help from the community cards, and at the end was playing the board, because all five cards out there were higher than mine. I got to the showdown because the action went check-check-check--it was one of those pots in which nobody made any hand worth betting on. I laughed as I exposed my cards, and said, "I don't think I win, since I have the worst possible hand."*

A player to my left said, "No, 2-7 is the worst possible hand."

I will cut him a bit of slack because he was referring to the worst starting hand, while I was referring to the worst possible hand at the end, given this particular set of five community cards.

But even after accounting for that misunderstanding of the context, the guy was wrong. Or at least he wasn't clearly right.

I first heard 2-7 (offsuit--and throughout this post I am granting that the hole cards are of different suits, because when they are of the same suit they automatically gain in potential value, due to the increased chance of hitting a flush) described as the worst starting hand in hold'em poker from Mike Sexton's commentary on one of the early episodes of the World Poker Tour, when I was just starting to understand how poker is played. And the observation stands to reason, because they are the lowest cards you can hold that can't make a straight. (That is, you can't make a straight using both cards--which means that in order to hit a straight you need help from four community cards, a considerably harder task than making a straight with just three of them.)

But anybody who makes the blanket claim that 2-7 is the worst possible starting hand just hasn't thought the matter through. In fact, next time I hear somebody say that, I think I'll test the strength of their belief by offering them a bet: "OK, I'll take 2-7 and give you 2-3, and we'll play out the hands, without any rounds of betting, just all five community cards at once. We'll do that, say, 100 times, and whoever has won the most hands gets $1000 from the other."

I sure hope somebody takes me up on that. Would you, dear reader? I hope not--because I hope my readers are smarter than that!

According to Card Player magazine's online poker odds calculator (http://www.cardplayer.com/poker_odds/texas_holdem), 2-7 beats 2-3 56% of the time, the 2-3 wins 26%, and they split the pot in 18% of hands. (All percentages in this post are rounded.) I like my chances for winning that $1000, if I can get anybody to agree to the bet.

As with nearly everything in poker, the answer to the question "What's the worst starting hand?" is "it all depends." Primarily, it depends on what you're up against.

Continuing with the 2-7 versus 2-3 comparison, let's see how they stack up against some sample opponents. I'm using two different tools for doing the calculation: the Card Player calculator and the application called Poker Stove (available for free download from http://www.pokerstove.com/). They come up with slightly different results, mostly because the latter doesn't spit out a separate percentage for ties, but takes the frequency of ties (e.g., the 18% above) and splits it between the hands being compared (in that case, it gives an extra 9% to each, and reports the result as 65% for the 2-7 and 35% for the 2-3). There are also probably differences in how the calculation is run, though I don't know the details of either one's operation.

In the table below, I show the results of pitting the 2-3 and the 2-7 against a variety of other hands, as shown. The results are, in each case, using the CP calculator first and Poker Stove second. The dollar sign shows which is superior (i.e., between the 2-3 and 2-7):

A-A versus 2-3: 86/13, 86/14 $
A-A versus 2-7: 87/12, 87/13

A-K versus 2-3: 65/34, 65/35 $
A-K versus 2-7: 67/33, 67/33

9-9 versus 2-3: 84/15, 85/15 $
9-9 versus 2-7: 88/12, 88/12

5-5 versus 2-3: 86/12, 87/13
5-5 versus 2-7: 70/28, 71/29 $

2-2 versus 2-3: 64/30, 67/33 $
2-2 versus 2-7: 65/30, 68/32

A-2 versus 2-3: 74/25, 74/26 $
A-2 versus 2-7: 74/25, 75/25

A-4 versus 2-3: 67/33, 67/33
A-4 versus 2-7: 65/35, 65/35 $

Which is kind of a long way of saying that against at least some other opponents' starting hands, 2-7 would be a better choice than 2-3, sometimes a far better choice.

(As an aside, neither the 2-3 nor the 2-7 is the worst hand to take up against somebody else's pocket aces. Top--or, rather, bottom--honors there go to the A-6 offsuit, which is a 94/6 dog in that race, which is the absolute worst scenario of any two hold'em starting hands. The point being, again, that what qualifies as the worst hand depends entirely on what one is up against. Or, to avoid ending that sentence in a preposition, it depends entirely on up against which one is. (Yuck. So much for grammar.))

Of course, we don't get to choose either our own hole cards or those of our opponents. So probably the best way of answering the question of the worst starting hand is by running the test against a random hand. This is a calculation that Poker Stove does easily, but isn't available from the Card Player tool. The answer is that the 2-7 beats or ties a random hand 35% of the time, the 2-3 only 33%. Matthew Hilger's book, Texas Hold'em Odds and Probabilities, gives these numbers, respectively, as 35% and 32% (pp. 235-237), a difference I assume is probably attributable to just rounding.

By that most general metric, then, 2-7 is a better place to start than 2-3. In other words, if what we're interested in is the likelihood of ending up with the best hand after all five community cards have been dealt out, the worst cards to have in your hand are what I had in the story that prompted this rant: a 2 and a 3, not the infamous 2-7.

So why does Mike Sexton say that the 2-7 is the worst starting hand? And since he's not exactly the first one to make that observation, why is it found in so many sources?

The answer is that nobody plays poker the way that the calculators do the math, or the way that I would propose to run my 100-hand bet.

Given the choice, I'd rather take a 2-3 than 2-7 into battle in any given pot, even though I know that 2-7 beats 2-3 a lot more often than it loses to it, and even though 2-7 will win slightly more showdowns than will 2-3 against random opposing hands. The reason is that I want to be able to make a strong hand against an opponent who has a hand that isn't quite as good but is good enough that he's willing to bet on it (and lose).

Considering the 2-3 and 2-7, they are equally likely to make one pair, two pairs, three of a kind, a flush, a full house, or four of a kind. But, as mentioned early in this post, they are not equally likely to make a straight. And that makes enough of a difference (because straights are relatively common) that I'd prefer to start with the 2-3. It is more likely that I will hit a straight. Of course, with the 2-7 any flush or full house I hit will be higher than making the same category of hand with the 2-3. But the increased probability of the straight easily outweighs that factor, in my view.

The probability of flopping a straight with the 2-3 is only 0.7%, according to Hilger (p. 189). But the probability of flopping either a straight or an open-ended straight draw is much better: 3.8% (Hilger, p. 194). With 2-7, it's obviously impossible to flop a straight. Hilger doesn't list the probability of flopping an open-ended straight draw with the 2-7, so I had to work it out myself: 1.6%.**

To make matters worse for the 2-7, having four parts of the straight on the board (as is necessary to make a straight with 2-7 in one's hand) is much more suspicious to an opponent holding, say, trips or two pair than is having just three parts of the straight visible. This translates to the 2-7 being less likely to win a big pot even when it does manage to make a straight. Furthermore, when you're relying on four parts of the straight being on the board, it's a lot more likely that an opponent will have a higher straight (or at least split the pot with you by holding the fifth card in common) than it is when that opponent has to have both of his hole cards exactly right to have a higher straight than yours.

In that sense, yes, the 2-7 is the worst starting hand, because it's the one I would least like to have to work with. I assume that most professionals have reached the same conclusion--hence the common observation about the poor, much-maligned 2-7. But now my readers can be among the cognoscenti, those who know that the answer isn't really that simple.

Now if I can just find that guy from the Hilton again, and offer him my little contest....



*Of course, any two unpaired cards in the hole that were both smaller than whatever the lowest card on the board was (I don't remember what that might have been) would actually be equally bad, since all such hands would split the pot, all playing the board. But I obviously had the lowest possible cards that fit that description.

** In case anybody wants to check my work: There are 19,600 possible flops (we don't care what order the cards come in), from the remaining 50 unknown cards (because C(50,3)=19,600). The flop has to be 3-4-5, 4-5-6, 5-6-8, 6-8-9, or 8-9-10 to give us the draw. Each of those has 64 different ways of hitting (because there are four cards of each rank), giving a total of 320 different flops that qualify. So the probability of hitting the draw is 320/19,600, or 1.6%.


Addendum, October 9, 2007:

After writing and posting the above, curiosity drove me to do a Google search on the phrase "worst hand in poker" to see what others have written on the subject. Along the way, I came across a table of percentage wins and pot equity of every hold'em starting hand, as played out (or so the author claims) in a computer simulation against a random hand in 2,000,000+ trials each: http://www.gocee.com/poker/he_ev_hand.html/

You've got to be careful what you say

This blog post was originally an overly long footnote in my post from a few minutes ago about "The Tournament Host." Upon re-reading, I think it deserves to be a separate entry. So first I'm going to repeat the paragraph to which it was appended (so the story may sound familiar, if you're reading things in chronological order of posting), then carry on with my related thoughts.


Also at today's tournament, in a hand I wasn't in, an early-position player raised. When the action got around to the guy on the button, he addressed the raiser and said, "I know you're raising with nothing. You have something like 8-2 of diamonds. I'm calling it right now." Then he threw his cards in the muck. It took me a couple of seconds to realize what had happened, but in retrospect what he apparently meant by "I'm calling it" was not that he was calling the raise, but that he was predicting what the raiser's cards were. But any competent dealer should have considered that a verbal, binding announcement of his action, and any floor person called to settle the inevitably resulting dispute should do the same. Again, their own rule #30 repeats the universal recognition that "[v]erbal declarations in turn are binding." Universal, that is, except in TH tournaments, I guess.

A very interesting incident along these lines happened at the final table of the World Poker Tour's "World Poker Open" at The Gold Strike Casino in Mississippi (season 5). Kido Pham, a well-known semi-professional tournament player, raised with K-7. An amateur, Gary Kainer, was short-stacked in one of the blinds, holding A-Q. He moved all-in, which constituted a big reraise.

Pham asked him, "Do you want me to call you?" He got no answer. Pham then told Kainer that he (Kainer) could decide--Pham would either call or fold, whichever Kainer wanted him to do. He said, "You call it--yes, no, whatever." This is an interesting ploy, one that I had never heard before. If Kainer took him up on the offer, it would make for an interesting question as to the rules, whether or not Pham's promise was binding. But it didn't come to that, because Kainer wisely just kept his mouth shut.

Finally, Pham apparently realized that he wasn't going to get any useful information from his opponent, and gave him a time limit for answering: "Three seconds. You call it." Still no response, so Pham counted down the time: "One. Two. Three. I call it." The dealer announced a call, and the announcer in the arena repeated that. But Pham quickly realized that he had been misunderstood; he didn't mean that he intended to call the bet, only that his offer to let Kainer make the decision for him was rescinded, and he (Pham) would make the decision for himself. Daniel Negreanu, also at the table, pointed out, "You said 'I call it.'"

The tournament director was called in to make a ruling, and he decided--correctly, in my view--that Pham's words "I call it" were binding, regardless of whether he intended something other than calling the bet. While they were awaiting the decision, commentator Mike Sexton observed, "Vince, he would have nobody to blame but himself if they make him put his money in and he loses this pot"--which is exactly what happened. After the ruling against him, Pham stated the obvious, that he never would have called with just a K-7. (Which raises the question of what he would have done if Kainer had taken him up on his offer and said, "OK, I want you to call.") That one little mistake may have cost Pham the tournament, and a few hundred thousand dollars in prize money.

A dealer friend once told me of an instance in which a player during a hand was telling the guy next to him a story about something that had happened long ago. The story included saying "All in," and this player said those words quite loudly (apparently recreating how it had happened). His opponent thought that the story-teller was declaring himself all-in, and immediately said "I call," and turned his hand up. The story-teller had had no intention of moving all in, but had just picked an unfortunate time to be saying those words loudly enough to be heard across the table. His words were ruled to be binding, even though he hadn't intended them that way.

It has to be so. Otherwise, you could have a scenario like this: Suppose I'm facing a large all-in raise from an opponent, and I've noticed previously that as soon as he gets called on his all-in bets, he instantly flips over his cards. (One should do this, of course, but not quite instantly. It's usually wise to take a few seconds to be absolutely sure that all the betting is over, that one's opponent really said he was calling, etc. I usually just wait for the dealer to instruct me to turn them over, because then any misunderstanding is the dealer's error, not mine.) I'm not sure what to do, so I say, "I'm going to call," kind of drawing out that last word, trying to induce my opponent to flip over his cards so I can see what I'm up against. Then, if I see that he has me in a bad spot, I complete the thought with, "...my mother on the phone at the next break." I then claim that my opponent jumped the gun, and I wasn't announcing my action.

Players have to be careful with the short list of words that sound like verbal declarations of action, particular when it's their turn.


Addendum, October 3, 2007:

By odd coincidence, I saw another example of this today while playing in the last-ever Hilton monthly freeroll tournament.

Before the flop, the player who was going to be second to act started to push his whole stack in when it wasn't yet his turn. He aborted the move before the chips crossed the betting line. (I don't know whether he was honestly mistaken or whether this was angle-shooting, but it doesn't matter for the point of this story.) The player under the gun noticed this, and asked him something like, "You're all in?" The dealer announced "All in." He heard clearly those last two words from this player, but not what went before it. The player protested that she wasn't moving all in.

The dealer called the floor person over and explained that the only thing he had heard clearly was "all in." The player confirmed that she had indeed uttered those words, but as part of a question to the other player. The floor person ruled that her words constituted a binding declaration of action. (Part of his reason was that one can't ask a player yet to act what he's going to do.) Presumably, if the dealer clearly heard the words "all in," other players might have heard them, too, and we can't have players trying to be weaselly by letting those words be heard, in order to see the reaction from other players, then retract them as having been accidental or misunderstood if it looks like somebody behind him--perhaps a player with pocket aces--welcomes that move. (I'm confident the player today was not trying to be tricky in such a manner. But the rule has to be enforced the same regardless of one's intentions, because intentions are impossible to know with certainty.)

Like the heading to this post says, you have to be careful what you say at the table, particularly when it's your turn to act.

Poker gems, #3

Mike Sexton, commenting on a bad beat during a World Poker Tour event:

"If you don't like a little pain once in a while, poker is probably not your game, because as you can see, you're gonna get it."

Wait until the action is complete, please

In limit games, the amount of every bet and raise is fixed by the structure of the game. Because verbal declarations of intent are binding, when a player says "raise," he must put in a raise, and it must be exactly the amount that the rules specify. The word "raise," therefore, determines what his action is on the hand, and the next player can safely and properly proceed with his own decision.

But in no-limit games, which is what I usually play, there's a crucial difference: a raise can be any amount between a defined minimum and all the chips that a player has in front of him. If he says "Raise to $20," or something like that, then that has the same effect as if he said nothing and pushed out $20 in chips. Either way, his decision for that turn is over, and the next player in line can act.

Lately, though, I've seen a lot of no-limit players muck their cards as soon as they hear the player on their right say the word "raise," even though no amount has been declared. This is in violation of the rules, because it isn't their turn yet. And, yes, it matters.

Suppose I'm one to the right of the button, and the first player to act after the flop puts in a bet. Everybody folds to me. I want to raise. My problem is that I don't know whether I'm going to have one opponent to deal with or two, because the guy on my left (with the button) hasn't acted yet. If I say raise, and he immediately throws his cards away, my decision just got easier. I might now put in a larger raise than I otherwise would have, because I know it's easier to get one opponent to fold than to get both of two opponents to fold. Or, alternately, I might put in a smaller raise than I otherwise would have, because I have a hand I want to play against just one opponent, and I was originally planning to raise enough to persuade the button to fold. Now, however, since I know he's folding, I want to coax the first-position bettor to call my very strong hand, so I can put in an irresistably small raise.

Either way, I have gained important information that I can use to make my decision, and it's information that I shouldn't have.

(There's an exception to the rule here. If, because everybody else has already folded, you are going to be the last person to act on the raise that has been announced, and you won't be calling even a minimal raise, then there is no problem with the insta-muck. This situation, however, will essentially only arise before the flop when it's down to the two blinds.)

Unfortunately, dealers tend to be pretty lax about enforcing this. My limited experience is that most players who commit this violation simply haven't thought about the implications, and once they understand how it distorts the rightful play of the game, they stop doing it.

So, dealers, could you please be more aggressive at putting an end to this? Every time it goes uncorrected, other players may notice, decide that it's perfectly OK, and start doing it themselves.

Addendum, August 30, 2007:

I’m watching an old episode of the World Poker Tour, specifically the first Mandalay Bay tournament from season 5, which I hadn't seen before. I was surprised to see this exact situation occur, and become the topic of discussion among both the players and the commentators.

Players are Brad Booth, Joe Tehan, and Burt Boutin.

Tehan has A-K and raises under the gun.

Boutin calls with A-Q.

Booth attempts a squeeze play with 10-2, and re-raises.

The action is back to Tehan, who announces “I raise,” and puts out chips to call Booth’s re-raise. He hasn’t yet decided on the amount of his raise.

Boutin apparently makes an honest mistake, thinking that the chips Tehan has put out are the raise. He presumably doesn’t care how much the raise is--he’s getting out. He folds and stands up from the table.

Tehan makes a face and says something I can’t hear, because over his words Vince Van Patten is saying, “Look at this, Burt has folded. He’s up out of his seat like a Pop Tart.”

Booth says, “You’re always supposed to wait for the amount to be raised there, Burt.”

Mike Sexton: “Brad makes a good point there.”

Boutin: “Oh, I thought he said raise and he raised it.” Apparently at this instant he realizes that the chips Tehan put out were just the call of Booth’s re-raise. “Oh, I didn’t see, I’m sorry.”

Sexton: “Joe said raise, and as soon as he said that Burt mucked his hand. But it makes a big difference. Does a guy raise the minimum raise? Does he move all in? He can bet any amount he wants there. You’re supposed to let him complete his bet before you fold your hand.”

The hand finishes playing out as Booth folds.

Sexton: “But the point is well made, though. You know, when you’re in a game, even if you know you’re going to fold your hand, courtesy dictates that you wait till your opponent make [sic] his raise before you muck your hand.”

Van Patten: “No doubt about it, and Burt knows that, but Burt just made a mistake there, and he apologized for it. So it does happen at the table. Burt, a veteran of the poker world, apologizes—no harm, no foul.”