What are the odds of picking up aces in pot limit omaha? Or in other words, if I take four cards out of a deck, what are the odds of at least two of them being an ace?
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1 Answer
Probability of 2 out of 4 being Aces:
Odds of getting an ace is 4/52, odds of getting a second ace in another card is 3/51. Then getting a non-Ace is 48/50 on the third and 47/49 on the fourth. The total is 0.00416658971.
Now you have 4 cards and there are 6 combinations of 2 Aces out of the 4 cards (1100,1010,1001,0110,0101,0011), so the grand total is 6 * 0.00416658971 = 0.0250
Probability of 3 out of 4 being Aces:
4/52 * 3/51 * 2/50 * 48/49 = 0.00017730168
4 combinations (1110,1101,1011,0111), so 4 * 0.00017730168 = 0.0007
Probability of 4 out of 4 Aces:
4/52 * 3/51 * 2/50 * 1/49 = 0.00000369378
1 combination, so 0.0000, basically 0.
=== Grand Total === 0.0250 + 0.0007 + 0.0000 = 0.0257 (approximately 1/39).
