A Problem With My Analysis of Luck in Hold’em

In one of my previous posts I tried to explain what it means to say that you’re lucky in a hand of Hold’em.  I explained this idea in terms of the following conditions, which I thought were individually necessary and jointly sufficient:

(1) You have to win the hand.

(2) Your odds of winning the hand at each round of betting prior to the river were much lower than each of the other two players’ odds of winning the hand.

(3) Your winning of the hand depends solely on the cards that are dealt, not on how others react to your betting.

After thinking more about my analysis, I’ve come to the conclusion that I was mistaken.  A person can be lucky in Hold’em without satisfying all of these conditions.  I still think the first condition is necessary.  But I think the following case shows what is problematic about conditions (2) and (3).

Suppose you have the weakest hand after the river card is dealt.  The only way you can win the hand is if everyone else folds.  Suppose you unjustifiably think you’re hand is strongest, and as a consequence you make a bet or raise.  It is reasonable to say that your bet was unwise, given that your thoughts about your hand are unjustied.  Even if your beliefs about your hand are justified, it seems that you can make an unwise bet.  However, we can also suppose that your unwise bet causes the other players to fold.  Isn’t this a case of where you’re being lucky, but your winning the hand does not depend on the cards that are dealt.  And this means that neither condition (2) nor condition (3) is necessary.

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