Can a player be lucky in Hold’em if he is playing with skill? I started thinking about this question after reading a couple of interesting posts by F-Train and ScurvyDog. I’m not entirely clear what this question means, in part, because it’s not entirely clear to me what it means to be lucky in Hold’em. In what follows, I make a stab at an analysis of what this means.
Consider the following case:
You’re dealt 62o. The flop is two Aces and a 4. Your 2 is the same suit as the 4 in the flop, no other suited cards. You’re in a late position. Two other players are betting big. You call all the bets. The turn is a 3 of the same suit as your 6. You have no chance at a flush. But you’re one away from an inside straight. The two other players are still betting big. You call whatever is bet. The river is a 5. You hit your straight, and you finally bet. The two other players also bet, because each player has AK, which means that each of these players has three Aces. You win a lot of money.
Were you lucky? Suppose you say “yes”. You need to answer the following question: Why were you lucky? Here are two things you might say.
1. You won 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.
It does seem that these two conditions are necessary for being lucky at Hold’em. But are they sufficient? I don’t think so. Here’s why.
Suppose you knew that the other two players would fold after you started betting after the river. Then it doesn’t seem that you were lucky in pulling the straight, because your winning of the hand would not depend on this fact.
So let’s add another condition.
3. Your winning of the hand depends solely on the cards that are dealt, not on how others react to your betting.
For any of you who have thought about the meaning of “luck” as it applies to Hold’em, let me know what you think of my analysis. I have this feeling that something is wrong with it.