![]() (Note: the ace may be the card above a king or below a 2, but we wouldhave a royal flush if it were the card above the king.) There are 9possibilities. If we order the 5-card hand from highest number to lowest,the first card may be one of the following: king, queen, jack, 10, 9, 8, 7, 6,or 5. Thus, there are 4possible royal flushes:ĭividing by the number of possible hands gives theprobability:ī) Astraight-flush (excluding royal flush) is all cards the same suit and showingconsecutive numbers (but not the highest 5 consecutive numbers). After that, the other four cards are completely determined. There are four possible suits for the ace. If we order the 5-card hand from highest card to lowest,the first card will be an ace. Sol'n: a) Aroyal flush is ace, king, queen, jack, and ten of the same suit. (The number of possible 5-card hands is 52C 5 = 2,598,960.) Ex : Calculatethe odds (or probabilities) of the following 5-card poker hands:Īlso, verify that the probabilities sum to unity.
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