”In poker, it is often said that lucky breaks keep suckers at the table.” [A quote from Steven Lubet's book Lawyer’s Poker: 52 Lessons that Lawyers Can Learn from Card Players]

 There’s a story that Niels Bohr, the famous Physicist, had a horse shoe over his desk.  One day a student asked if he really believed that a horse shoe brought luck, and Bohr replied, “I understand that it brings you luck if you believe in it or not.”

I’m interested in the concept of luck, especially as it applies to poker.  I’ve written about this concept in previous posts (here and here), and I’m still not sure what it means.  I’ve recently read Steven Lubet’s book Lawyer’s Poker: 52 Lessons that Lawyers can Learn from Card Players (for a review of the book see here and for interview with the author see here), and he makes some points about luck with respect to Texas Hold’em. 

On the one hand, Lubet says that good poker players are never really lucky because they have calculated the odds correctly.  He gives the example of the poker player who might take a chance on a five-to-one draw, but only because he knows that the expected value of the action would be six to one or better, and that in the long run he will make a profit.  So if he hits a good card, Lubet says, his draw is not lucky.  Likewise, if he hits a worthless card, according to Lubet, his draw is not unlucky. 

On the other hand, Lubet says that luck does play a role in poker, specifically with second-best hands.  He writes, “[I]t is not really lucky to draw pocket aces in Texas Hold’em; it is just your turn, as everyone else will eventually get the same cards the same number of times.  Your result, with aces or any lesser hand, primarily depends on how well you play your cards.  But it is lucky (or luckier) if someone else at the table draws pocket kings at the same time, because that will build up the pot.  Conversely, it is relatively unlucky if everyone else at the table draws unplayable rags, because your aces will not be worth much if all of the other players fold their hands.  The stronger the second-best hand, the luckier you are.” (p. 24 Lawyer’s Poker)

What I find unclear about Lubet’s analysis of luck in poker is that if knowing the expected value of an action eliminates luck when second-best hands are not considered, why wouldn’t knowing the expected value of an action eliminate luck when they are considered?  In other words, if it is not really lucky to draw pocket aces in Hold’em, then why is it lucky to draw pocket aces when someone else draws pocket kings?  After all, eventually everyone else will find themselves in the same sort of situation. 

On July 23 and 24, the poker-playing computer named Polaris, will play against two humans, Phil Laak and Phil (aka the Unabomber) Laak and Ali Eslami.  I’ve written about this match here and here. 

One of the interesting features of this heads-up poker duel between a computer and a human is that it is designed to eliminate luck as a factor.  In one room Polaris will play Laak and in another room Polaris will play Eslami, and Polaris will get Laak’s cards when playing Eslami and Eslami’s cards when playing Laak.  

Jonathan Schaeffer, the Polaris team leader, claims that the set up will eliminate most, not all, of the luck.   This raises the question, “In what way can luck still play a factor in this match?”  And of course this question raises the more fundamental conceptual question of what luck means, a question I’ve touched upon in previous posts (here and here).

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