Poker, Cognitive Bias and the Metaphysics of Luck

Amidst a poker game last night, I posited the following:

Every poker player has worse than average luck.

Call it the anti-Lake Wobegon Effect (aLWE).

This claim, at first glance, is entirely absurd.  Treating poker as a zero-sum game, one player’s good luck must be offset by another player’s bad luck, such that not all players can possibly have below average luck.  We learn this in kindergarten, and then again in advanced college mathematics.  So why am I trying to argue something that is patently absurd?  Below I will argue both why it is wise to believe aLWE, and also reasons why it may be true.

1. The utility of framing

Even if aLWE is false, believing it to be true probably makes you a better poker player.  I’ve written about this effect before, when  talking about basketball.  Many poker players, directly after an unlucky event occurs, play worse than they normally would.  Their unlucky outcome causes them to doubt themselves–why is this happening to me?  When you believe an event has a 12% chance of occurring, and then it occurs, and has negative consequences for you, you may feel like something is wrong with you.  If you instead believe that nothing is wrong with you, but instead that everyone has bad luck, it would presumably be easier for you to keep playing well, since your bad luck now proves you normal rather than proving you abnormal.  Thus even if you think aLWE is wrong and absurd, you may have reason to want to convince yourself it is true when you play poker.  I will now try to help you do this.

2. Almost everyone has worse than average luck

Accepting poker as a zero-sum game, mathematics allows that almost everyone could have worse than average luck.  It could even be that exactly one poker player has above average luck, and that every other poker player has below average luck, so long as you ignore groups of poker players that are completely isolated from the rest of the poker world.  For instance, maybe there are nine poker players in Brisbane, Australia who only play poker against each other and never have played against anyone else.  Then at least one of them has to have above average luck.  But if any one were to play poker online or at a casino, or to play against someone who had played online or at a casino, they would all become connected to the greater poker universe, and it would become possible for them all to have below average luck.

This dumbed-down version of aLWE has the advantages of 1) still allowing unlucky players to feel normal, and 2) avoid the apparent utter absurdity of the full-on aLWE.  Of course it is still highly improbably that, say, 99% of poker players would have worse than average luck and only 1% better than average.  It’s more likely that 70% of poker players would have worse than average luck, meaning that a considerable majority of players are in the majority with regard to luck.

3. Everyone perceives themselves to have below average luck

Many people are more likely to remember bad luck than good luck, due to a specific cognitive bias.  For instance, consider the following bad-beat story:

Player 1: So I’m all in on the flop with with a full house against a runner-runner straight flush draw.  Do you know what the odds are that I lose that hand?

Player 2: I’d say pretty close to 100%

Player 1: What?  No, it’s like 0.1%.  How do you figure?

Player 2: Well, I know this is a bad beat story, so the odds of you losing are not actually 0.1% like you think they are; they’re more like 100%.

Player 2 is able to infer based on the fact Player 1 is telling this story, that something unusual will happen.  When the above poker situation occurs, 999 times out of 1000, player 1 wins the hand, but then doesn’t choose to tell a story about it.  However, the one time out of 1000 that he loses the hand, he remembers it forever and tells everybody.

Recognizing that most players perceive themselves to be below average luck, and that they do so honestly (even if by flawed thinking), also allows poker players to feel normal when they feel unlucky.

4. The rake

When playing poker in a casino, there is a rake, a percentage of winnings taken by the casino.  This turns poker into a non-zero sum game, allowing the possibility that even if some players are above average luck, they’re not far enough above average to offset the rake.  Even ignoring the rake, playing poker takes time which has a cost, which also makes poker non-zero sum.

5. The game of life

While poker is thought to be a zero-sum game, there are many non-zero sum games in life, such as investing, dating, or conversing with friends.  It could be that some people are above-average luck in poker, but below-average elsewhere in life.  This allows for the possibility that everyone is, across all spheres of life, below average luck.

6. A cruel, cruel world

Even ignoring arguments 2-5, I would argue that it is entirely plausible that everyone in the world is below average luck at poker.  To understand why requires recognizing that there are situations in poker in which multiple players, each playing poker optimally, can reasonably expect that their play will lead to positive outcomes, when in fact this is not possible.  The combined value of each player’s expected winnings (given the information each of them has) exceeds the value that can possibly be won.  Similarly, there are situations in poker in which the combined value of each player’s expected winnings is less than the value that is ultimately won.  The total impact of these situations depends on their relative likelihood, which we generally assume is even, since dealing of cards is assumed to be random.

But what if dealing of cards is not actually random?  Or, more broadly, what if random events, such as sub-atomic randomness, don’t actually behave in neutral ways?  Randomness is posited as an explanation in cases where it is difficult to predict behaviors, but asserting that a behavior is random is to create a map, not to define the territory.  An alternative theory for unpredictable behaviors is that they operate mostly randomly, but that sometimes, due to the inherent cruelty of the universe, they deliberately behave in evil ways, so as to cause human suffering.

Note that under this alternative theory, rational analysis of history would likely lead observers to believe that poker luck-outcomes indeed are random, since they mostly behave randomly and only behave non-randomly in very specific instances where they’re able to do great evil.  In this scenario, most scientists would reject the (true) theory that the universe is evil, possibly invoking statistical significance.  Only some individuals, to whom acts of great cruelty had been committed by the universe at the poker table, would correctly recognize the cruelty of the world, and further the fact that all poker players have worse than average luck.

7. Conclusions

How people think about luck can affect outcomes, both in poker and in life.  There are a certain instances, such as when playing poker, when it may be beneficial to believe that everyone is unlucky.  There are a number of reasons why it is entirely reasonable to believe that everyone is unlucky.  Further, our current understanding of randomness, metaphysically, is not on as solid grounding as many people believe.  Poker players thus can, and probably should convince themselves that they, and everyone else they know, are unlucky.