A poker player is dealt poor hands for several hours. He decides to bet heavily on the last hand of the evening on the grounds that after many bad hands he is due for a winner.
A) He's right, because the winnings have to average out.
B) He's wrong, because successive deals are independent of each other.
C) He's right, because successive deals are independent of each other.
D) He's wrong, because his expected winnings are $0 and he's below that now.

Question

Quizplus · Accepted Answer

The outcome of each hand in poker is determined by chance and is independent of the previous hands. Therefore, the fact that the player has had poor hands for several hours does not increase the likelihood of a good hand in the next deal. Each hand is an independent event, and the odds of getting a good hand are the same regardless of what happened in the previous hands. The idea that one is "due" for a good hand is a fallacy known as the gambler's fallacy.

A Poker Player Is Dealt Poor Hands for Several Hours