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Practice Matters

CHANCES OF HOLDING VARIOUS POKER HANDS IN

CHANCES OF HOLDING VARIOUS POKER HANDS IN THE FIRST FIVE CARDS DEALT WHEN THE JOKER IS ADDED MAKING A 53-CARD DECK Rank of hand Number of each Chance Five of a kind 13 1 in 220,745 Royal flush 24 1 in 119,570 Straight flush 216 1 in 13,286 Four of a kind 3,120 1 in 920 Full house 6,552 1 in 438 Flush 7,768 1 in 369 Straight 20,532 1 in 140 Three of a kind 137,280 1 in 21 Two pairs 123,552 1 in 23 One pair 1,268,0881 in 2 1/4 No-pair hand 1,302,540 1 in 2 1/5 Total hands 2,869,685

I bring to the attention of the reader a very unusual mathematical

I bring to the attention of the reader a very unusual mathematical situation that arises in Joker Wild regarding the relative value of three of a kind and two pairs. Studying the above chart closely, the reader will observe that the chances of drawing three of a kind are one in 137,280 and the chances of drawing two pair are one in 123,552. Since there are more chances of drawing three of a kind than two pairs, two pairs should be of a higher rank and beat three of a kind. But they don't. This peculiar situation is caused by the fact that there are 82,368 possible five-card Online Hold'em Poker hands that contain a pair plus the joker. When a player holds one of these 82,368 hands, he values his hand at three of a kind, making the joker count the same denomination as the pair he is holding.

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