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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