First watch the video below. The dark haired guy, Booth, has just made a big bet. He is claiming to have three-of-a-kind (fours). If he does he would win the hand, but he might be bluffing. The other guy, Lingren, has to decide whether to call the bet and he does something unexpected: he asks Booth to show him one of his cards:
The strategic subtext is this: if Booth has the third four then he wants Lingren to call. If not, he wants him to fold. Implicitly, Lingren is offering the following mechanism: if you do have the third four then you won’t want me to know it because I would then fold. So show me a card, and if it’s not a four I will call you.
What is left unsaid is what Lingren would do if Booth declined to show a card. The spirit of the mechanism is that showing a card is the price Booth has to pay to have his bet called. So the suggestion is that Lingren would fold if Booth is not forthcoming because that would signal that he is hiding his strong hand.
But in fact this can’t be part of the deal because it would imply exactly the opposite of Lingren’s expectations. Booth, knowing that it would get Lingren to fold, would in fact hide his cards when he is bluffing and show a card when he actually has the three-or-a-kind (because then he gets a 50% chance of having his bet called rather than a 100% chance of Lingren folding.)
So what exactly should happen in this situation? And did Booth really play like a genius? Leave your analysis in the comments.
Visor visit: the ever-durable Presh Talwalker.
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August 18, 2010 at 3:42 am
Innovative Poker Strategy « Cheap Talk | Jeux Poker En Ligne|Regles Poker|Poker Gratuit
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August 18, 2010 at 6:25 am
Anonymous
I’m not an experienced poker player but in my opinion, Boothe knowing that he has a four should probably have not shown his cards. He would probably had increased his chances of winning from 50% to say, whatever Lingren perceives Boothe’s likelihood of bluffing his. By not showing the cards, Boothe can use this perceived likelihood to his advantage to have Lingren call the bet? Especially, the video shows that Lingren thinks that Boothe likes to bluff so that the winning chances for Boothe by not showing would most probably be higher than 50%. So hm, hm, hm, true geniuses should work on improving their play next time?
Mi.
August 18, 2010 at 6:26 am
miyu
I’m not an experienced poker player but in my opinion, Boothe knowing that he has a four should probably have not shown his cards. He would probably had increased his chances of winning from 50% to say, whatever Lingren perceives Boothe’s likelihood of bluffing his. By not showing the cards, Boothe can use this perceived likelihood to his advantage to have Lingren call the bet? Especially, the video shows that Lingren thinks that Boothe likes to bluff so that the winning chances for Boothe by not showing would most probably be higher than 50%. So hm, hm, hm, true geniuses should work on improving their play next time?
Mi.
August 18, 2010 at 9:56 am
asha
not show, as showing, by the analysis offered above implies that Boothe is trying to get Lingren to call (i.e., if Boothe is willing to reveal a card, it must mean he believes he’ll beat Lingren’s hand even if the King is revealed and Lingren calls – therefore, by this deduction, Boothe’s offer to reveal a card implies that he has the four); resting on the assumption that Lingren would interpret Boothe’s willingness to reveal in this way (which, is of course an important assumption), then Boothe should not show. Not showing still implies that Boothe may be bluffing.
However, of course, you could keep applying this logic recursively and depending where you land either move (reveal or not reveal) could be interpreted to mean a bluff or not…
such is the beauty of the game!
August 18, 2010 at 10:07 am
anon
based solely on where the video picks up, and looking strictly at this street (no games of iteration):
from lindgren’s eyes there’s a 2/45 chance booth has a 4. it is $1600 to win a $4200 pot. assuming lindgren’s only intention is to call or fold reading ONLY the 4, the price is way too high for lindgren, even under booth’s offer.
additionally, there are a number of other hands that could dominate top pair: 56,77, 88,9T,J8, J7,78, and QQ-AA.
extending the analysis a little bit back to the beginning:
preflop
booth easy called his small blind for 100, in the pot of 700. lindgren could probably rule out a range of hands here unless booth is the type to play passively.
flop
booth quick checks. lindgren does not have to worry. the remaining players quick check. lindgren probably still does not have to worry.
turn
booth bets quickly, slightly more than half the pot. lindgren quick calls because a 4 does not pose a likely threat.
river
booth bets quickly, slightly more than half the pot. based on action on the prior streets, 56 should come to lindgrens mind as a possibility, more so than the other dominating hands mentioned above. (connecting hands calling in the small blind is a very typical poker play). 9T is also possible, as such a strong hand would be more inclined to check the flop like booth did, and tempt lindgren on the turn and river.
but lingren puts him on solely a 4 and makes a terrible offer.
ive spent too much of my morning on this…but id be happy to continue later.
August 18, 2010 at 10:14 am
anon
this is an iterative game, afterall. lindgren might have placed $value on information for future hands as well. if lindgren thought about the hand preflop, he shouldve realized that players in the small blind will usually have a very wide range of hands.
perhaps he paid $1600 to confirm this information.
August 19, 2010 at 10:50 am
David Eil
I think it’s ok to model this game as similar to the canonical “AKQ” poker game. Erick’s hand is pretty much face up as a bluffcatching hand like the one he has, even at the time Brad is making his bet. He can beat a bluff, which Brad can have given the flop and turn action, but nothing that Brad would be betting for value (i.e., betting in hopes of getting called). To simplify things, I’ll take Brad’s bet size as given. He bets 1600 into the 2600 chip pot. In order to deter Brad from bluffing all the time, Erick has to call 1600/2600 = 8/13 of the time (unless you think Brad doesn’t have enough weak hands that he would check the flop and bet the turn with, in which case you probably haven’t seen Brad play very much). If he called any less, then Brad would have a higher expected profit from betting all of his bad hands than checking them. And we have already assumed that Brad has enough bad hands such that if he bets all of them, the posterior probability that he has a bad hand given that he bets is greater than 1600/5800, the probability with which Erick needs to have the best hand in order to make the call. Erick has to be calling with this probability whether Brad decides to reveal a card or not – otherwise Brad would have a strict preference over whether or not to reveal a card, a preference which would also reveal his hand, as said in the original post.
Assume that if Erick does pick a random card when Brad decides to reveal (Brad disputes this later in the video). Also assume that the only value hands Brad has include a 4 (this is clearly not the case as Brad could have T9 or 56 for instance, but close enough for now). Then given that Brad does have a 4, half the time he will reveal it and Erick will fold. Half the time he will not. This is clearly worse than not showing and getting called 8/13ths of the time by Erick.
So it can’t be any NE for Brad to show (given his bet size…could be different if he had bet a larger amount before this conversation took place). But then again we’re at a table full of people who play symmetric zero-sum games for a living, so they’re used to the idea of people not playing NE strategies at the table, and therefore may also play non-NE strategies themselves because they are best responses.
As a side note, Brad Booth is famous in poker circles for, among others things, living in the Bellagio hotel and casino for a year. Living there as in never going outside. For an entire year. It’s not by accident he’s that pale.
August 23, 2010 at 9:45 am
Jonathan Weinstein
The bird’s-eye view is that under equilibrium play in this zero-sum situation, it’s impossible for the card-showing shenanigans to change the value of the game in any way, since they can both easily opt out. (For Booth, opting out means always refusing to show anything regardless of his hand. For Lindgren, it means ignoring any cards he is shown.)
Next question: do we have conclusive evidence that anyone was playing a non-equilibrium strategy? I don’t think so, it’s possible that Booth was playing “always show a non-4, whichever card Lindgren selects” and Lindgren was playing “ignore the card and do what you planned.” Keep in mind, Booth had no commitment to show the card that was selected. But, if he didn’t, you ask, wouldn’t it give him away? Nope, it could be a double-bluff where the card he refused to show was insignificant!
August 23, 2010 at 10:20 am
Creative Poker Strategy « An Ode to Capitalism
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August 26, 2010 at 6:06 pm
thomas
another great article that i very much enjoyed reading, i think i will bookmark this site for the future thank you for this
February 2, 2011 at 6:46 pm
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