Yesterday Kathy Liebert learned the power of the Mighty Deuce-Four the hard way at the WPT Borgata Winter Poker Open. I couldn't find a way to link to the specific live-update post, so I took a screen shot:
I just read this post from my friend Josie. She had been planning to play in her first-ever World Poker Tour tournament at Borgata. She arranged for time off work and somebody to care for her son, then flew from Boston just for the event. Got to Borgata, found that she couldn't register for the tournament without getting a Borgata player's card, and couldn't get a player's card because their own internal policy wouldn't accept her official Massachusetts-issued ID card (she doesn't have a driver's license). Nobody she talked to would even consider making an exception.
I'm just watching the World Poker Tour Bay 101 Shooting Star event broadcast earlier this month--the one in which Phil Hellmuth collapsed on the floor after being knocked out on a bad beat. (Hee hee hee!)
In the second part of the episode, the eventual winner, Mclean Karr, took the Mighty Deuce-Four up against Hasan Habib's pathetic little Kc-10c. Habib flopped a flush draw and check-raised, but Karr shoved with his trips. Habib called and was shocked, SHOCKED, to see Karr's hand.
Naturally the 2-4 made a full house on the turn, and Habib was reduced to hoping for a chop with one of the two remaining jacks.
Nope.
The card with maximal rub-it-in value came: not just a club to make Habib's useless flush, but the four of clubs, the deck showing obvious solidarity with the deuce-four. In effect, Karr had two full houses (deuces full of fours and deuces full of jacks) from which he could at his leisure select to trounce a mere flush.
Such is the power of the Deuce-Four. As you can see, WPT champions understand this.
(Yes, I wrote about this when it first happened, here. But I didn't have the nice screen shot to put up with it.)
(Image from here.)
I was just reading in a poker magazine a wrap-up of the Bay 101 Shooting Stars WPT tournament held in March. I had not followed it as it took place. I was intrigued when I noticed how Hasan Habib was knocked out by the eventual winner, McLean Karr. Here's how the WPT live bloggers reported it (here):
Hand #113: Hasan Habib Eliminated in 4th Place ($234,300)
Level 26: 15,000-30,000, 5,000 ante
McLean Karr raises from the button to 75,000, and Hasan Habib calls from the big blind. The flop comes J22, Habib checks (it may have been in the dark before the flop), Karr bets 115,000, Habib check-raises to 300,000, and Karr thinks for about 15 seconds before he says, "I'm all in."
Habib thinks for about 45 seconds before he says, "Alright, I've gotta call you, man." Habib shows K10 for a club flush draw, while Karr turns over 42 for trip deuces. Habib needs to improve to stay alive.
The turn card is the J, the river card is the 4, and McLean Karr wins the pot with a full house, deuces full of jacks, to eliminate Hasan Habib from the tournament.
In November I spent an inordinate amount of time obsessing over what appeared to be phony money piled on a poker tournament table. See here.
Tonight I was catching up on this season's World Poker Tour events, and caught another instance of the same thing. This is from the Borgata Poker Open. The episode was actually the first half of the final table, and the screen shots below are from the previews to the finale, which is why they have credits rolling over them.
If you look closely, you can see that the obverse of the bills is not good ol' Ben Franklin on the hundred, nor is the reverse even close to a real C-note. However, they are both suspiciously similar to the images on the fake 100s seen about halfway down the page here, a site that was pointed out to me by an astute reader in the comments section of that November post. I am nearly certain that these fake bills are the ones being piled on the Borgata table.
I'm glad to know this, actually. Now I will never enter a WPT event because, unlike most of the participants, I know their dark secret: They pay the winners in counterfeit money!
I feel like I need to shout this discovery to the world, like Charlton Heston trying to warn everyone, "Soylent Green is people!"
Addendum
Now watching the end of the tournament rather than just the previews, there is this better shot of the front of one of the bills, making perfectly clear that it is not Ben Franklin:
"Fraud!" cried the maddened thousands, and the echo answered "Fraud!"
(Bonus points for knowing where that line comes from without Googling it.)
I haven't been watching the World Poker Tour this season. I'm feeling like I've been neglectful, so today I started with episode 1, the Bellagio Cup. Just a few hands in, I spotted this horrendous incident.
As Vince Van Patten calls the action, "Gabriel Thaler looking down at a four-deuce, won't play that mess." Thaler folds.
That mess? THAT MESS???
And these are your supposed expert commentators? They seem not to know that Deuce-Four can take down pocket kings in its sleep.
Never mind the ensuing action. Just look at the final board and what won:
Thaler's Deuce-Four for the straight was way good. Even better, there was no betting on the flop, so he would have made the nuts on the turn for free. But this allegedly great player threw it away. And the commentators apparently didn't even notice that he folded what would have been the winner. If they were more attentive, they might have said something like, "You know, Thaler's hand would have taken that pot, and nobody would have ever suspected what a monster he was holding until it was too late."
But no.
*sigh*
It's so hard to convince people to change their already-made-up minds, no matter how much evidence you put in front of them.
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.
Ted Forrest, interview on World Poker Tour, season 6, Foxwoods Poker Classic, aired August 11, 2008.
Everybody has their breaking point. You can just watch the wheels come off, so to speak, and players kind of crumble one by one, and if you can be the last one to crumble, then you're gonna be there at the end to win it.
Hey, it's not a WSOP story for a change!
There's a World Poker Tour event going on at the Bellagio, and a bit of a controversy came up Friday between Barry Greenstein and David Williams. This is interesting for a couple of reasons. First, it's rare that Greenstein gets involved in a dispute of any sort. Second, it's rare for the events underlying a tournament dispute to be caught on camera.
You can read the blog post and watch the video of the incident and the floor decision here. (Caveat: That URL may not be stable as they add more pages of posts to this event, and there doesn't seem to be any way to point you to the specific post. You're looking for a post titled "Floor to Table 61," so if you don't see it on this page, you may have to move forward or back a couple of pages to find it.)
A few thoughts:
First, it's good to see that Greenstein, true to form and true to how he describes himself in his book, remains calm and rational through the whole thing. He never apologizes (since he believes he didn't do anything wrong), but also never gets accusatory towards Williams, as he easily could have ("Hey, pal, my chips were right here, it's your own fault for not asking for a count!"). Williams, on the other hand, is agitated and even drops an f-bomb on the floor guy, which isn't the best way to sway a decision in your favor.
Second, I think Greenstein's explanation fits perfectly with what we observe. He seems to be recounting things both subjectively and objectively accurately.
Williams, on the other hand, I'm not sure is being completely forthright. He says that he wouldn't have called if he had known the correct amount. Well, in the first place, he never called anything. He raised both times the action came to him. He moved all in, and Greenstein called him. Maybe he just got flustered, but he is definitely not describing what occurred accurately.
More significantly, though, he claims that he would not have "called" (or, presumably, moved all in) if he had known Greenstein's stack size. This seems implausible to me. The discrepancy is only one 10,000 chip, so, essentially, whether Greenstein had about 50,000 or about 60,000. There's nearly 60,000 in the pot when Williams shoves. At that point he allegedly thought that Greenstein had only another 15,000 left, and is trying to assert that if he had known that Greenstein actually had 25,000, he would have done something different. What, folded? The notoriously aggressive and willing-to-gamble David Williams folding pocket jacks preflop in that situation strikes me as pretty dubious. And what if he had just called? The flop came 10-7-2, so he definitely would have either pushed all in or called Greenstein's all-in bet after the flop anyway, with the same result.
Williams had to know that Greenstein was absolutely pot-committed. Greenstein had raised to 35,000, so whether he had another 15,000 or 25,000 left, either way Williams had to know that Greenstein was not only willing but probably eager to get it all in. Williams had no fold equity. So when Williams had his decision to make, he thought he would be putting in about 23,500 (to call Greenstein's raise) plus 15,000 (to put Greenstein all in), or a total of 38,500 to try to win the 60,000 already in the pot plus the additional 15,000 that he figured Greenstein had behind, or a total of 75,000, for pot odds of about 1.95:1. The actual situation is that he had to put in 48,500 to win 60,000 + 25,000, for pot odds of about 1.75:1.
In other words, I think Williams was either lying or just hadn't fully thought out the situation when he claimed that he would have done something different. (He doesn't specify what different action he would have taken, but as I said before, if he just calls Greenstein's raise at that point, all the money is going in anyway when the flop comes out; folding would have been smart, but out of character for Williams.) I refuse to believe that he would have been willing to commit that much money when being offered 1.95:1, but not when being offered 1.75:1. With pocket jacks against two opponents, both out of position and both clearly willing to shove it all in, that's just asking for trouble. It was a bad move on Williams's part, just about any way you analyze it, and failing to ascertain in advance exactly how many chips he was putting up was really just a minor part of his overall problem in that spot.
Frankly, Williams's trouble began with his outlandishly sized reraise. We don't know what the blinds and antes were at this point, but we are told that the first player raised to 1475 as the opening action. Williams reraised him to 11,500, a nearly 8-fold raise! That's just silly. It's one of those raises that will only get called (or, in this instance, reraised) if he's beat. Yes, of course he was trying to isolate the original raiser, perhaps sizing his bet to be about what that player appeared to have left. But if so, it was a serious error, not taking into account that there were two players yet to act between him and his target (the blinds). Had he raised to only, say, 5000, then it might have been easier to at least stop and think about getting away from the hand when (1) Greenstein came charging over the top of him, from out of position, with the third raise, and (2) the player under the gun pushed all in. That would tend to tell me, were I in Williams's position, that J-J might be in deep doo-doo.
I think the floor decision was the correct one. There was not even an accusation, really, that Greenstein had tried to hide high-denomination chips. And Williams didn't take the simple precaution of asking for a count of Greenstein's chips before pushing. He could even have just asked Greenstein to move his hands to get a clearer view, and that would have done it. In fact, I suspect that if he had done that, so that Greenstein knew he was contemplating an all-in, Greenstein would have accommodated him and counted (or at least estimated) his remaining stack. Greenstein's bet of over half of his stack was obviously a signal to Williams that he wanted to get it all in, and he would be happy to help Williams realize that he didn't have much left behind.
Back in April I groused about The Toothpick People, guys who sit at the poker table sucking/chewing on toothpicks. It's stupid and makes the person doing it look stupid.
Even worse, though, is doing it on national television. Look at this bespectacled moron, Brett Faustman, who was on the World Poker Tour last week. (I'm just getting around to watching it now.) He chewed on his pointy little pacifier through the whole final table.
I think that when he was preparing for his television debut, he thought, "How can I show the world what a country bumpkin Southern redneck hick backwoods hillbilly inbred half-wit imbecile I am? [Light bulb clicks on over his head.] I know! I'll chew on a toothpick! Everybody recognizes that as a symbol of pure good ol' boy idiocy!"
And whaddaya know--it worked. It projected exactly the image he was shooting for. Next best thing to growing out a mullet.
Congratulations, you dweeb.
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?
This is Kofi Farkye, a 19-year-old college student who got to the final table of the North American Poker Championship (season 6, episode 5 of the World Poker Tour). In addition to the humiliation of being knocked out on a kind of dumb play, he has to live with having neglected to wear a belt when it might have done him the most good.
Don't they have any sort of dress code for this show?
Not only does this guy not how to wear pants, he is apparently an online poker cheater who has been banned from Poker Stars for multi-accounting. See story here.
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 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/
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.
From the best poker dictionary in existence, by Michael Wiesenberg (http://www.poker1.com/mcu/mculib_dictionary.asp):
slow roll
(n phrase) The practice by some players, at the showdown, when they have the best hand, of waiting till the last possible moment before showing that hand. This is usually done for one of three reasons: to see everyone else's cards first, to needle one or more of the active players, or just out of pure orneriness.
slow-roll
(v) To knowingly have the best hand at the showdown but expose it only after the losers' hands are shown, leading another player to think he has the winning hand. See slow roll.
By odd coincidence yesterday, I was both the intentional victim and unintentional perpetrator of a slow roll of unbeatable four-of-a-kind hands in one session at the Venetian.
Perpetrator:
I'm in late position with suited Q-9 and call a largish raise from one of the blinds. It's heads-up between us. The flop is 9-8-8 rainbow. My opponent hesitates, looks at his chips, looks at me, seems quite nervous, then puts all his chips into one big stack and pushes it forward. It's $103. This is well over twice the size of the pot--a huge overbet. Before that, I thought it most likely that he had a big pair, something between jacks and aces, and I was frankly just hoping to catch a lucky flop, but expecting to have to dump my hand if I didn't hit something strong.
His hesitation, nervousness, and the peculiar size of the bet made me re-think this, however, and suggested to me that he actually had A-K, missed the flop, and really, really, really didn't want a call. At this point, I had only $110 in front of me, so the call is for essentially my whole stack. I finally convinced myself that hitting my 9 actually did put me ahead, so I call.
Then several things happen basically all at once. My opponent turns over his cards, and I see that I was dead wrong in my post-flop read of him: he had pocket aces. Oops. Oh well. So without even watching the dealer put out the turn and river cards, I start counting out what I'm going to have to pay him.
While I'm doing that, I glance up at the now-completed set of community cards. The last two cards have come 9-9, giving me quad 9s, but it doesn't register that way with me. For some reason I can't explain, my brain reads the board as 9-8-8-8-9, instead of the actual 9-8-8-9-9. Just at this moment, I get more confused because the dealer announces my opponent's hand as "nines full of aces." I'm frozen like a deer in the headlights, simultaneously trying to figure out (1) how he can have nines full when there are only two 9s on the board (or so I think), and (2) whether my full house is bigger or smaller than his. I haven't turned over my cards because I'm a little embarrassed to have twice called big bets from a guy with aces when I was so far behind.
It takes me probably five seconds to clear my head and realize why I'm so confused. Then I see that I got just obscenely lucky to turn my measly pair into quads. So I sheepishly flip over my hole cards. Several people at the table gasp. My opponent--to his credit--didn't whine or complain, just let his head roll back for a second, then stood up and walked away.
The dealer seems to understand my situation, and quietly says, "You didn't see it, did you?" No, I didn't.
So to the guy I beat, I apologize for the slow roll. I'm well aware of how rude it is. I swear it was completely unintentional. I thought for sure I was dead. All those 8s and 9s blurred in my visual cortex, and I just didn't grasp what had happened for a few seconds. I would never do that on purpose. You left the table too quickly for me to explain, though I did attempt to tell the other players at the table what had happened, once it became clear to me in retrospect.
Victim:
Earlier in the evening I had A-J. The flop was A-K-x. A guy in the big blind checks, I bet, he calls. The turn card is another K. This makes me think he probably doesn't have a king and my ace is probably good. I only have in front of me about the same amount that's in the pot, so I move all in after he checks again. He calls. The river is a blank. I turn over my A-J.
He looks at my cards, looks at me, nods, but doesn't move. Then oh-so-slowly he turns over first one king, then another one. He has all four of 'em.
I suppose that if I were a generous soul, I would give this guy the benefit of the doubt and assume that somehow he got confused about his hand the same way I did. But, frankly, this seems pretty damn unlikely. Pocket kings are the second-best starting hand, and I think everybody who looks down at them gets a little jolt of excitement at the prospect of winning the hand. Then upon hitting a third one on the flop, the excitement builds, because you're a virtual lock to win the hand. When the fourth one hits the turn, and an opponent pushes all-in, it's like having an orgasm.
It's just not plausible that this guy didn't know what he had, given the sequence of events. It played out in a completely different way from the hand in which I made quads on the turn and river after all the money went in on the flop. With about 99% certainty, this guy was just being a jerk. I have no idea why, other than a personality disorder. It happened within the first five or so hands of my session; I had just sat down, and so hadn't had any kind of history with him that would make him want to retaliate.
On one of the first seasons of the World Poker Tour (season 2's "WPT Invitational," to be exact) Harry Demetriou accidentally gave an opponent a slow roll. He had put in a pre-flop raise with pocket aces. The short-stacked opponent (I don't remember who it was) moved all-in. Harry didn't realize that a player between the all-in guy and him had folded; that is, he didn't know the action was back to him. He just sat quietly for maybe 30 seconds. Finally he realized that everybody was waiting for him to act. He obviously was going to call.
What was impressive is that he apologized over and over and over again. He would never intentionally slow-roll anybody; he just didn't realize it was his turn.* He was mortified that anybody would think he had done that deliberately. He's a classy guy.
I think most players are delighted to show their winning hands as quickly as possible. It's rare to run into a player who takes some sort of sick pleasure in slow-rolling with the absolute nuts. I don't recall ever before being the one to have done it (however unintentionally), nor being on the receiving end (though perhaps I have been, and don't remember it). It was very strange to be on both sides of it in one night.
To the guy who slow-rolled his quad kings: a pox on you, sir.
*In this case, it would be a slightly different kind of slow-roll than described in the definition above. If at any point in the hand one has the nuts--the best possible hand--so that a call of an opponent's all-in bet is eagerly and automatically given, delaying that call any longer than necessary is another version of a slow-roll. Now, sometimes there is a strategic reason to take one's time about it--most commonly to seduce another player into also calling, by acting as if it's a difficult decision. There's nothing unethical about that. But in Demetriou's case, he was the last one to have a decision to make. He would surely have acted instantly if he had known it was his turn.
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."
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.”
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