The standard poker hands are ranked based on the probability of their being dealt pat in 5 cards from a full 52-card deck.
The following table lists the hands in order of increasing frequency, and shows how many ways each hand can be dealt in 3, 5, and 7 cards.

Hand 3_cards 5_cards 7_cards
cnt % cdf% cnt % cdf% cnt % cdf%
Straight_Flush 48 0.22% 0.22% 40 0.00% 0.00% 41,584 0.03% 0.03%
Four_of_a_Kind 0 0.00% 0.22% 624 0.02% 0.03% 224,848 0.17% 0.20%
Full_House 0 0.00% 0.22% 3,744 0.14% 0.17% 3,473,184 2.60% 2.80%
Flush 1,096 4.96% 5.18% 5,108 0.20% 0.37% 4,047,644 3.03% 5.82%
Straight 720 3.26% 8.43% 10,200 0.39% 0.76% 6,180,020 4.62% 10.44%
Three_of_a_Kind 52 0.24% 8.67% 54,912 2.11% 2.87% 6,461,620 4.83% 15.27%
Two_Pair 0 0.00% 8.67% 123,552 4.75% 7.63% 31,433,400 23.50% 38.77%
One_Pair 3,744 16.94% 25.61% 1,098,240 42.26% 49.88% 58,627,800 43.82% 82.59%
High_Card 16,440 74.39% 100.00% 1,302,540 50.12% 100.00% 23,294,460 17.41% 100.00%
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TOTALS 22,100 2,598,960 133,784,560