How Much Luck as a Factor Does the Polaris Experiment Really Eliminate?


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).

I still don’t know what it means to say that someone is lucky in Hold’em.  If there were no betting in the game, then luck would simply be a question of what cards were dealt.  And the Polaris experiment would rule this sort of luck out, for if Laak would get lucky, then Eslami would be unlucky.  However, Hold’em has betting, and this means that there is a certain amount of skill involved in the game.

Suppose your opponent in a heads-up match gets dealt pocket aces five times in a row.  And suppose during this streak your hole cards are 2 and 7 off-suit.  Does this mean that within these five hands your opponent was lucky and you weren’t?

I think the answer is “It depends”.  It depends on whether your opponent wins with his starting cards and how much he wins if he does win.  Of course, it is more likely that he will have the winning hand in the end than you.  But getting to the “end” of a hand is not one’s primary goal when playing hold’em.  One’s primary goal as a rational gambler is to maximize winnings, and how one does this is what makes the difference between great players and not-so great players.

Now let’s turn to the Polaris match.  Suppose in the first five hands between Polaris and Laak, Polaris gets pocket rockets for its hole cards and Laak gets dealt 2 and 7 offsuit as his hole cards.  This means that between Polaris and Eslami, Polaris will have been dealt 2 and 7 as its first five hole cards and Eslami will have been dealt pocket rockets.  Isn’t it still possible that beteween Eslami and Polaris in this first hand luck can still play a big role in who makes the most profit?  Consider the following.

Suppose in the first hand before the flop Polaris bets X amount of money and Laak folds.  Suppose that before the flop Eslami bets X amount of money but Polaris doesn’t fold.  Polaris may, of course, still win the pot against Eslami with his horrible hole cards.  He/It may eventually outdraw Eslami, which indicates that he/it got lucky or he/it may win by bluffing, which again may be a result of luck.

So intuitively it seems to me that the Polaris experiment doesn’t eliminate as much luck as the designers of the experiment would like us to believe.   Perhaps I’m incorrect.  But I think that in order to show me why I’m incorrect, one needs to explain what “luck” means in Hold’em.  I’m waiting.

5 thoughts on “How Much Luck as a Factor Does the Polaris Experiment Really Eliminate?

  1. Nice blog you got here, I personally think luck plays a lot especially at the end of tournaments and during head to head play.

  2. Thanks for the compliment, Benson. I’m curious to know why you think “luck plays a lot especially at the end of tournaments and during head to head play.” I’m also curious as to what you mean by “luck”.

  3. I think the term is used in many different ways, and it really depends who’s saying it and why. Very often you will hear it used in “bad beat” stories to identify single hand ‘lucky’ events, but then you will also hear it used to describe ‘streaks’ of luck, either good or bad.

    I think that variance is what the real idea is, and people are simply looking at short-term variance as a measure of luck. Of course, short-term can actually be quite long by human standards, but I’m meaning in the sense of ‘statistically significant.’ For example, someone posted recently on Ed Miller’s blog that he had run a simulation of two hold’em players with identical average win rates, showing that after a year of playing, it was entirely possible for one player to have made twice as much as the other. Another example is “Stox” Grudzien talking about two consecutive samples of 100,000 hands from the same player showing a difference of 3BB/100 in win rate. So one could say that one of those 100,000 streaks was luckier than the other, even though the player wasn’t doing anything differently between the two.

    For someone to be a lucky player over a lifetime, though, you would have to be claiming that the mathematics of their decision-making strategy was somehow not coming out as it should. Like claiming that a coin is a genuinely fair coin, but after 10 trillion coin flips, the heads-to-tails ratio is 55:45. After enough data, the luck factor should have evened out and only the true mathematical ratio survived.

  4. Interesting topic, but I’m not sure I agree with your reasoning. When you describe how “Laak folds while Polaris doesn’t”, that is, in a sense, precisely the kind of decision making or “skill” they are trying to measure. However, I agree that any strategy is always subject to “luck” (perhaps “chance” is a better word) in any given hand. These guys are no doubt well familiar with the statistical side of things, and I suspect they view this setup as a simple way to reduce the statistical uncertainty of the experiment without having to play a forbidding number of hands.

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