Poker probability The "nCr" function on most scientific calculators can be used to calculate hand frequencies; entering with and , for example, yields formula_2 as above. The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1. When ace-low straights and ace-low straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes each become 9/10 as common as they otherwise would be. The 4 missed straight flushes become flushes and the 1,020 missed straights become no
Fundamental theorem of poker The flop comes A♣ K♦ 10♦, and Carol bets. Bob now has a decision to make based upon incomplete information. In this particular circumstance, the correct decision is almost certainly to fold. There are too many turn and river cards that could kill his hand. Even if Carol does not have an A or a K, there are 3 cards to a straight and 2 cards to a flush on the flop, and she could easily be on a straight or flush draw. Bob is essentially drawing to 2 outs (another 9), and even if he catches one of these