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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Poker probability (Omaha) ： ウィキペディア英語版 Poker probability (Omaha) Omaha Hold'em, (love) like many similar poker variants, is probabilistic. Thus, the probability of many events can be determined by direct calculation. The probabilities are shown here for many commonly occurring events in the game of Omaha hold 'em as well as probabilities and odds for specific situations. In most cases, the probabilities and odds are approximations due to rounding. When calculating probabilities for a card game such as Omaha, there are two basic approaches. # Determine the number of outcomes that satisfy the condition being evaluated and divide this by the total number of possible outcomes. # Use conditional probabilities, or in more complex situations, a decision graph. Often, the key to determining probability is selecting the best approach for a given problem. This article uses both of these approaches, but relies primarily on enumeration. == Starting hands == The probability of being dealt various starting hands can be explicitly calculated. In Omaha, a player is dealt four down (or ''hole'') cards. The first card can be any one of 52 playing cards in the deck; the second card can be any one of the 51 remaining cards; the third and fourth any of the 50 and 49 remaining cards, respectively. There are 4! = 24 ways (4! is read "four factorial") to order the four cards (ABCD, ABDC, ACBD, ACDB, ...) which gives 52 × 51 × 50 × 49 ÷ 24 = 270,725 possible starting hand combinations. Alternatively, the number of possible starting hands is represented as the binomial coefficient :$=\; 270,725$ which is the number of possible combinations of choosing 4 cards from a deck of 52 playing cards. The 270,725 starting hands can be reduced for purposes of determining the probability of starting hands for Omaha—since suits have no relative value in poker, many of these hands are identical in value before the flop. The only factors determining the strength of a starting hand are the ranks of the cards and whether cards in the hand share the same suit. Of the 270,725 combinations, there are 16,432 distinct starting hands grouped into 16 ''shapes''. Throughout this article, hand shape is indicated with the ranks denoted using uppercase letters and suits denoted using lower case letters. For example, the hand shape XaXbYaYc is any hand containing two pair (XX and YY) that share one suit (a), but not the other suits (b and c). The 16 hand shapes can be organized into the following five hand types based on the ranks of the cards. : There are also five types of hands based on the suits of the cards that mirror the five rank types: aaaa, aaab, aabb, aabc, and abcd. The following are the probabilities and odds of being dealt each suit type. : Unlike the rank types, the suit types can be absolutely ranked in terms of starting hand value because suits in poker hands only factor in flushes and straight flushes. From best to worst starting hand value the suit types are: aabb, aabc, aaab, aaaa, and abcd. The relative probability of being dealt a hand of each given shape is different. The following shows the probabilities and odds of being dealt each shape of starting hand. : \end | align=right| 13 | $\backslash begin\; \backslash end$ | align=right| 1 | align=right| 13 | 0.00000369 || align=right| 270,724 : 1 | 0.0000480 || align=right| 20,824 : 1 |- ! rowspan=2 | Three of a kind ! XaXbXcYa | $\backslash begin\; \backslash end$ | align=right| 156 | $\backslash begin\; \backslash end$ | align=right| 12 | align=right| 1,872 | 0.0000443 || align=right| 22,559 : 1 | 0.00691 || align=right| 144 : 1 |- ! XaXbXcYd | $\backslash begin\; \backslash end$ | align=right| 156 | $\backslash begin\; \backslash end$ | align=right| 4 | align=right| 624 | 0.0000148 || align=right| 67,680 : 1 | 0.00230 || align=right| 433 : 1 |- ! rowspan=3 | Two pair ! XaXbYaYb | $\backslash begin\; \backslash end$ | align=right| 78 | $\backslash begin\; \backslash end$ | align=right| 6 | align=right| 468 | 0.0000222 || align=right| 45,120 : 1 | 0.00173 || align=right| 577 : 1 |- ! XaXbYaYc | $\backslash begin\; \backslash end$ | align=right| 78 | $\backslash begin\; ^2\; \backslash end$ | align=right| 24 | align=right| 1,872 | 0.0000887 || align=right| 11,279 : 1 | 0.00691 || align=right| 144 : 1 |- ! XaXbYcYd | $\backslash begin\; \backslash end$ | align=right| 78 | $\backslash begin\; \backslash end$ | align=right| 6 | align=right| 468 | 0.0000222 || align=right| 45,120 : 1 | 0.00173 || align=right| 577 : 1 |- ! rowspan=5 | One pair ! XaXbYaZa | $\backslash begin\; \backslash end$ | align=right| 858 | $\backslash begin\; \backslash end$ | align=right| 12 | align=right| 10,296 | 0.0000443 || align=right| 22,559 : 1 | 0.0380 || align=right| 25.3 : 1 |- ! XaXbYaZb | $\backslash begin\; \backslash end$ | align=right| 858 | $\backslash begin\; \backslash end$ | align=right| 12 | align=right| 10,296 | 0.0000443 || align=right| 22,559 : 1 | 0.0380 || align=right| 25.3 : 1 |- ! XaXbYaZc | $\backslash begin\; \backslash end$ | align=right| 1,716 | $\backslash begin\; ^2\; \backslash end$ | align=right| 24 | align=right| 41,184 | 0.0000887 || align=right| 11,279 : 1 | 0.152 || align=right| 5.57 : 1 |- ! XaXbYcZc | $\backslash begin\; \backslash end$ | align=right| 858 | $\backslash begin\; \backslash end$ | align=right| 12 | align=right| 10,296 | 0.0000443 || align=right| 22,559 : 1 | 0.0380 || align=right| 25.3 : 1 |- ! XaXbYcZd | $\backslash begin\; \backslash end$ | align=right| 858 | $\backslash begin\; \backslash times\; 2!\; \backslash end$ | align=right| 12 | align=right| 10,296 | 0.0000443 || align=right| 22,559 : 1 | 0.0380 || align=right| 25.3 : 1 |- ! rowspan=5 | No pair ! XaYaZaRa | $\backslash begin\; \backslash end$ | align=right| 715 | $\backslash begin\; \backslash end$ | align=right| 4 | align=right| 2,860 | 0.0000148 || align=right| 67,680 : 1 | 0.0106 || align=right| 93.7 : 1 |- ! XaYaZaRb | $\backslash begin\; \backslash end$ | align=right| 2,860 | $\backslash begin\; \backslash end$ | align=right| 12 | align=right| 34,320 | 0.0000443 || align=right| 22,559 : 1 | 0.127 || align=right| 6.89 : 1 |- ! XaYaZbRb | $\backslash begin\; \backslash div\; 2!\; \backslash end$ | align=right| 2,145 | $\backslash begin\; \backslash end$ | align=right| 12 | align=right| 25,740 | 0.0000443 || align=right| 22,559 : 1 | 0.0951 || align=right| 9.52 : 1 |- ! XaYaZbRc | $\backslash begin\; \backslash end$ | align=right| 4,290 | $\backslash begin\; \backslash times\; 2!\; \backslash end$ | align=right| 24 | align=right| 102,960 | 0.0000887 || align=right| 11,279 : 1 | 0.380 || align=right| 1.63 : 1 |- ! XaYbZcRd | $\backslash begin\; \backslash end$ | align=right| 715 | $\backslash begin\; 4!\; \backslash end$ | align=right| 24 | align=right| 17,160 | 0.0000148 || align=right| 67,680 : 1 | 0.0634 || align=right| 14.8 : 1 |} 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Poker probability (Omaha)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.