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2011/11/16 16:07

참고2

출처: http://en.wikipedia.org/wiki/Poker_probability

1. Frequency of 7-card poker hands

In some popular variations of poker, a player uses the best five-card poker hand out of seven cards. The frequencies are calculated in a manner similar to that shown for 5-card hands, except additional complications arise due to the extra two cards in the 7-card poker hand. The total number of distinct 7-card hands is \begin{matrix} {52 \choose 7} = 133,784,560 \end{matrix}. It is notable that the probability of a no-pair hand is less than the probability of a one-pair or two-pair hand.

The royal flush is not included in the cumulative probability calculation because it is a type of straight flush. The Ace-high straight flush or royal flush is slightly more frequent (4324) than the lower straight flushes (4140 each) because the remaining two cards can have any value; a King-high straight flush, for example, cannot have the Ace of its suit in the hand (as that would make it ace-high instead).

Hand Frequency Probability Cumulative Odds
Royal flush 4,324 0.0032% 0.0032% 30,939 : 1
Straight flush 37,260 0.0279% 0.0311% 3,216 : 1
Four of a kind 224,848 0.168% 0.199% 594 : 1
Full house 3,473,184 2.60% 2.80% 37.5 : 1
Flush 4,047,644 3.03% 5.82% 32.1 : 1
Straight 6,180,020 4.62% 10.4% 20.6 : 1
Three of a kind 6,461,620 4.83% 15.3% 19.7 : 1
Two pair 31,433,400 23.5% 38.8% 3.26 : 1
One pair 58,627,800 43.8% 82.6% 1.28 : 1
No pair 23,294,460 17.4% 100% 4.74 : 1
Total 133,784,560 100% 100% 0 : 1

(The frequencies given are exact; the probabilities and odds are approximate.)

Since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. Eliminating identical hands that ignore relative suit values leaves 6,009,159 distinct 7-card hands.

The number of distinct 5-card poker hands that are possible from 7 cards is 4,824. Perhaps surprisingly, this is fewer than the number of 5-card poker hands from 5 cards because some 5-card hands are impossible with 7 cards (e.g. 7-high).

2. Frequency of 7-card lowball poker hands

In some variants of poker a player uses the best five-card low hand selected from seven cards. In most variants of lowball, the ace is counted as the lowest card and straights and flushes don't count against a low hand, so the lowest hand is the five-high hand A-2-3-4-5, also called a wheel. The probability is calculated based on \begin{matrix} {52 \choose 7} = 133,784,560 \end{matrix}, the total number of 7-card combinations.

The table does not extend to include five-card hands with at least one pair. Its "Total" represents 95.4% of the time that a player can select a 5-card low hand without any pair.

Hand Frequency Probability Cumulative Odds
5-high 781,824 0.584% 0.584% 170.12 : 1
6-high 3,151,360 2.36% 2.94% 41.45 : 1
7-high 7,426,560 5.55% 8.49% 17.01 : 1
8-high 13,171,200 9.85% 18.3% 9.16 : 1
9-high 19,174,400 14.3% 32.7% 5.98 : 1
10-high 23,675,904 17.7% 50.4% 4.65 : 1
Jack-high 24,837,120 18.6% 68.9% 4.39 : 1
Queen-high 21,457,920 16.0% 85.0% 5.23 : 1
King-high 13,939,200 10.4% 95.4% 8.60 : 1
Total 127,615,488 95.4% 95.4% 0.05 : 1

(The frequencies given are exact; the probabilities and odds are approximate.)

If aces are not low, simply rotate the hand descriptions so that 6-high replaces 5-high for the best hand and ace-high replaces king-high as the worst hand.


Hand Frequency Probability Cumulative Odds
Royal flush 4,324 0.0032% 0.0032% 30,939 : 1
Straight flush 37,260 0.0279% 0.0311% 3,216 : 1
Four of a kind 224,848 0.168% 0.199% 594 : 1
Full house 3,473,184 2.60% 2.80% 37.5 : 1
Flush 4,047,644 3.03% 5.82% 32.1 : 1
Straight 6,180,020 4.62% 10.4% 20.6 : 1
Three of a kind 6,461,620 4.83% 15.3% 19.7 : 1
Two pair 31,433,400 23.5% 38.8% 3.26 : 1
One pair 58,627,800 43.8% 82.6% 1.28 : 1
No pair 23,294,460 17.4% 100% 4.74 : 1
Total 133,784,560 100% 100% 0 : 1

Hand Frequency Probability Cumulative Odds
5-high 781,824 0.584% 0.584% 170.12 : 1
6-high 3,151,360 2.36% 2.94% 41.45 : 1
7-high 7,426,560 5.55% 8.49% 17.01 : 1
8-high 13,171,200 9.85% 18.3% 9.16 : 1
9-high 19,174,400 14.3% 32.7% 5.98 : 1
10-high 23,675,904 17.7% 50.4% 4.65 : 1
Jack-high 24,837,120 18.6% 68.9% 4.39 : 1
Queen-high 21,457,920 16.0% 85.0% 5.23 : 1
King-high 13,939,200 10.4% 95.4% 8.60 : 1
Total 127,615,488 95.4% 95.4% 0.05 : 1

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