PROBLEM #9
Background: For those who are unfamiliar, Omaha Holdem is a type of poker, played with a
standard 52-card deck, where each player at the table is dealt FOUR cards, face down.
Subsequently, three community cards are dealt, face up, in the middle of the table. This is
called the FLOP. A fourth community card is dealt face up, called the TURN, and then, finally, a
fifth is dealt face up, called the RIVER. A player combines TWO of his four down cards with
THREE of the community cards to make his/her best five-card poker hand.
A few months ago, I was playing Omaha online and encountered an extremely low probability
situation. In two CONSECUTIVE hands, I was dealt a hand of four cards that contained exactly
two 9s. In each of the two hands, the flop (first three community cards) also contained two 9s,
giving me a hand of four of a kind, 9s, for two hands in a row.
TASK: Assuming that the four down cards and the three cards in the flop are the only cards you
know, calculate the odds of the exact occurrence described above.