3550:
1290:
3983:
3560:
3540:
2406:
2170:
1626:
1300:
1280:
646:
423:
4100:
3752:
3545:
3303:
2950:
2530:
2525:
2175:
2165:
1785:
1463:
1285:
1134:
964:
817:
812:
428:
418:
4085:
3978:
3737:
3293:
2515:
2421:
2416:
2401:
2180:
1770:
1621:
1448:
1124:
802:
661:
656:
641:
433:
4105:
3298:
2411:
2160:
1790:
1129:
651:
413:
4095:
4090:
3968:
3963:
3747:
3732:
3555:
3288:
2940:
2510:
2290:
2285:
2280:
2275:
2270:
1780:
1775:
1611:
1606:
1458:
1443:
1295:
1119:
954:
797:
524:
519:
514:
509:
504:
3973:
3742:
3283:
2960:
2955:
2945:
2520:
1616:
1453:
1114:
974:
969:
959:
807:
4895:
79:
61:(1623-1662) also contributed to probability theory. His friend, Chevalier de Méré, was an avid gambler with the goal to become wealthy from it. De Méré tried a new mathematical approach to a gambling game but did not get the desired results. Determined to know why his strategy was unsuccessful, he consulted with Pascal. Pascal's work on this problem began an important correspondence between him and fellow mathematician
6049:
5500:
6069:
5524:
6079:
6059:
5512:
65:(1601-1665). Communicating through letters, the two continued to exchange their ideas and thoughts. These interactions led to the conception of basic probability theory. To this day, many gamblers still rely on the basic concepts of probability theory in order to make informed decisions while gambling.
2048:
are not identical hands when just ignoring suit assignments because one hand has three suits, while the other hand has only two—that difference could affect the relative value of each hand when there are more cards to come. However, even though the hands are not identical from that perspective, they
2016:
When ace-low straights and ace-low straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes each become 9/10 as common as they otherwise would be. The 4 missed straight flushes become flushes and the 1,020 missed straights become no pair.
3269:
3527:
267:. For instance, with a royal flush, there are 4 ways to draw one, and 2,598,956 ways to draw something else, so the odds against drawing a royal flush are 2,598,956 : 4, or 649,739 : 1. The formula for establishing the odds can also be stated as
4250:
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.
4254:
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, as some 5-card hands are impossible with 7 cards (e.g. 7-high and 8-high).
4882:
with at least two suits. Probabilities are adjusted in the above table such that "5-high" is not listed, "6-high" has 781,824 distinct hands, and "King-high" has 21,457,920 distinct hands, respectively. The Total line also needs adjusting.
4585:
with at least two suits. Probabilities are adjusted in the above table such that "5-high" is not listed", "6-high" has one distinct hand, and "King-high" having 330 distinct hands, respectively. The Total line also needs adjusting.
2030:
because replacing all of the clubs in the first hand with diamonds and all of the spades with hearts produces the second hand. So eliminating identical hands that ignore relative suit values, there are only 134,459 distinct hands.
2926:
2068:
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
3950:
1267:
1756:
1593:
1430:
1100:
940:
784:
2980:
3323:
628:
2388:
4277:
to determine the winning hand. 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
57:, discussed the concepts of probability and how they were directly related to gambling. However, his work did not receive any immediate recognition since it was not published until after his death.
3719:
4604:
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
3777:
3328:
2985:
2555:
4071:
2497:
2256:
2112:
4672:
The table does not extend to include five-card hands with at least one pair. Its "Total" represents the 95.4% of the time that a player can select a 5-card low hand without any pair.
4667:
2020:
Note that 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. For example, the hand
4340:
375:
218:
4181:
4238:
2006:
136:
is the number of different ways to draw the hand, not counting different suits. In particular, a set of hands that all tie each other is counted exactly once, not multiply.
490:
1946:
250:
as good as three of a kind is about 2.87%. The cumulative probability is determined by adding one hand's probability with the probabilities of all hands above it.
2013:
The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1.
4875:
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.
4578:
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.
39:
Probability and gambling have been ideas since long before the invention of poker. The development of probability theory in the late 1400s was attributed to
2550:
2125:
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).
3772:
2121:
The Ace-high straight flush or royal flush is slightly more frequent (4324) than the lower straight flushes (4140 each) because the remaining two
1157:
43:; when playing a game with high stakes, players wanted to know what the chance of winning would be. In 1494, Fra Luca Paccioli released his work
1649:
1486:
1323:
5921:
997:
840:
684:
5926:
5183:
246:
the specified one. For example, the probability of drawing three of a kind is approximately 2.11%, while the probability of drawing a hand
5931:
5562:
3264:{\displaystyle {\begin{aligned}&\left\right]\\+&\left\times 39\right]\\+&\left\times {39 \choose 2}\right]\end{aligned}}}
4923:
3522:{\displaystyle {\begin{aligned}&\left\right]\\+&{}\left\\+&\left+10\times {5 \choose 2}\times 2268\right]\end{aligned}}}
6082:
4575:
As can be seen from the table, just over half the time a player gets a hand that has no pairs, threes- or fours-of-a-kind. (50.7%)
5008:
3549:
1289:
236:, or one in 649,740. One would then expect to draw this hand about once in every 649,740 draws, or nearly 0.000154% of the time.
5120:
547:
2310:
5887:
4342:, the total number of 5-card combinations. (The frequencies given are exact; the probabilities and odds are approximate.)
3982:
3559:
3539:
2405:
2169:
1625:
1299:
1279:
645:
422:
5908:
5580:
4878:
Some players do not ignore straights and flushes when computing the low hand in lowball. In this case, the lowest hand is
4581:
Some players do not ignore straights and flushes when computing the low hand in lowball. In this case, the lowest hand is
3580:
4099:
3751:
3544:
3302:
2949:
2529:
2524:
2174:
2164:
1784:
1462:
1284:
1133:
963:
816:
811:
427:
417:
5936:
5444:
5799:
5704:
4084:
3977:
3736:
3292:
2514:
2420:
2415:
2400:
2179:
1769:
1620:
1447:
1123:
801:
660:
655:
640:
432:
4003:
4104:
3297:
2410:
2159:
1789:
1128:
650:
412:
6105:
5046:
4928:
4094:
4089:
3967:
3962:
3746:
3731:
3554:
3287:
2939:
2509:
2441:
2289:
2284:
2279:
2274:
2269:
1779:
1774:
1610:
1605:
1457:
1442:
1294:
1118:
953:
796:
523:
518:
513:
508:
503:
5649:
4918:
2200:
2072:
5804:
5741:
3972:
3741:
3282:
2959:
2954:
2944:
2519:
1615:
1452:
1113:
973:
968:
958:
806:
5064:
2065:, the most widespread poker variant overall, a player uses the best five-card poker hand out of seven cards.
5985:
5959:
5424:
5395:
5236:
5166:
5140:
4615:
220:). For example, there are 4 different ways to draw a royal flush (one for each suit), so the probability is
5757:
5555:
5303:
4288:
323:
166:
126:
5954:
5816:
5772:
5475:
6068:
4125:
6062:
6034:
5826:
5794:
5762:
5699:
5644:
5390:
5376:
5355:
4908:
304:
4204:
1972:
5882:
5852:
5836:
5736:
5449:
5231:
5113:
456:
5973:
5916:
5903:
5877:
5872:
5867:
5857:
5831:
5821:
5811:
5731:
5694:
5672:
5284:
5259:
4938:
5033:
4983:
1813:
5516:
6052:
5862:
5789:
5784:
5777:
5767:
5548:
5371:
5366:
5361:
5279:
5161:
2062:
31:
can be computed by calculating the proportion of hands of that type among all possible hands.
6029:
5664:
5621:
5528:
5405:
5400:
5311:
5216:
5188:
5171:
5156:
308:
function on most scientific calculators can be used to calculate hand frequencies; entering
62:
50:
5599:
5410:
5342:
5068:
4933:
4595:
4270:
4264:
155:
of drawing a given hand is calculated by dividing the number of ways of drawing the hand (
4894:
53:(1501-1576) made further developments in probability theory. His work from 1550, titled
5998:
5689:
5504:
5436:
5337:
5323:
5106:
99:
95:
6099:
6003:
5677:
5606:
5418:
5289:
5264:
4077:
3956:
3725:
3533:
3275:
2932:
2503:
2394:
2262:
2153:
1762:
1599:
1436:
1273:
1106:
946:
790:
634:
496:
406:
83:
58:
78:
6008:
5684:
5480:
5347:
5274:
5243:
5226:
5211:
4958:
4900:
2122:
160:
2921:{\displaystyle {\begin{aligned}&\left\\+&\left\\+&\left\end{aligned}}}
263:
to draw the hand, to the number of ways to draw it. In statistics, this is called
5093:
5993:
5485:
5384:
5269:
5221:
5047:
https://www.pokerstrategy.com/strategy/various-poker/texas-holdem-probabilities/
4953:
4948:
4913:
151:
118:
110:
87:
24:
4872:(The frequencies given are exact; the probabilities and odds are approximate.)
4247:(The frequencies given are exact; the probabilities and odds are approximate.)
49:
which was the first written text on probability. Motivated by
Paccioli's work,
6024:
5331:
5317:
5176:
4963:
4890:
28:
6072:
5459:
3945:{\displaystyle {\begin{aligned}&\left\right]\\+&\left\end{aligned}}}
114:
103:
5078:
1262:{\displaystyle {10 \choose 1}{4 \choose 1}^{5}-{10 \choose 1}{4 \choose 1}}
5083:
5073:
1751:{\displaystyle {13 \choose 1}{4 \choose 2}{12 \choose 3}{4 \choose 1}^{3}}
1588:{\displaystyle {13 \choose 2}{4 \choose 2}^{2}{11 \choose 1}{4 \choose 1}}
1425:{\displaystyle {13 \choose 1}{4 \choose 3}{12 \choose 2}{4 \choose 1}^{2}}
5611:
5571:
5454:
4601:
4274:
40:
5088:
1095:{\displaystyle {13 \choose 5}{4 \choose 1}-{10 \choose 1}{4 \choose 1}}
935:{\displaystyle {13 \choose 1}{4 \choose 3}{12 \choose 1}{4 \choose 2}}
779:{\displaystyle {13 \choose 1}{4 \choose 4}{12 \choose 1}{4 \choose 1}}
5616:
5594:
122:
5061:
5129:
2034:
The number of distinct poker hands is even smaller. For example,
77:
20:
86:
depicting poker hands and their odds from a typical
American 9/6
4943:
255:
5544:
5102:
46:
Summa de arithmetica, geometria, proportioni e proportionalita
5540:
4600:
In some variants of poker a player uses the best five-card
2114:. It is notable that the probability of a no-pair hand is
2049:
still form equivalent poker hands because each hand is an
623:{\displaystyle {10 \choose 1}{4 \choose 1}-{4 \choose 1}}
106:, players are simply dealt five cards from a deck of 52.
5098:
2383:{\displaystyle {9 \choose 1}{4 \choose 1}{46 \choose 2}}
2053:
high card hand. There are 7,462 distinct poker hands.
242:
refers to the probability of drawing a hand as good as
5079:
Poker probabilities including conditional calculations
4618:
4291:
2075:
326:
169:
4207:
4128:
4006:
3775:
3583:
3326:
2983:
2553:
2444:
2313:
2203:
2118:
than the probability of a one-pair or two-pair hand.
1975:
1816:
1652:
1489:
1326:
1160:
1000:
843:
687:
550:
459:
3714:{\displaystyle \left{5 \choose 1}{4 \choose 1}\left}
6017:
5984:
5968:
5947:
5896:
5845:
5750:
5724:
5717:
5663:
5637:
5630:
5587:
5468:
5435:
5302:
5252:
5204:
5197:
5149:
317:
313:
309:
4661:
4334:
4232:
4175:
4065:
3944:
3713:
3521:
3263:
2920:
2491:
2382:
2250:
2106:
2000:
1940:
1750:
1587:
1424:
1261:
1094:
934:
778:
622:
484:
369:
212:
125:drawn from a full deck of 52 without replacement.
4224:
4211:
4028:
4015:
3927:
3914:
3899:
3886:
3876:
3863:
3688:
3675:
3660:
3647:
3638:
3625:
3605:
3592:
3498:
3485:
3246:
3233:
3210:
3197:
3180:
3167:
3122:
3109:
3092:
3079:
3040:
3027:
3010:
2997:
2897:
2884:
2874:
2861:
2852:
2839:
2830:
2817:
2808:
2795:
2786:
2773:
2739:
2726:
2716:
2703:
2694:
2681:
2672:
2659:
2631:
2618:
2603:
2590:
2580:
2567:
2483:
2470:
2461:
2448:
2374:
2361:
2352:
2339:
2330:
2317:
2242:
2229:
2220:
2207:
1992:
1979:
1927:
1914:
1896:
1883:
1863:
1850:
1838:
1825:
1736:
1723:
1713:
1700:
1691:
1678:
1669:
1656:
1579:
1566:
1557:
1544:
1529:
1516:
1506:
1493:
1410:
1397:
1387:
1374:
1365:
1352:
1343:
1330:
1253:
1240:
1231:
1218:
1200:
1187:
1177:
1164:
1086:
1073:
1064:
1051:
1039:
1026:
1017:
1004:
926:
913:
904:
891:
882:
869:
860:
847:
770:
757:
748:
735:
726:
713:
704:
691:
614:
601:
589:
576:
567:
554:
476:
463:
4066:{\displaystyle \left\times 6\times 6\times 990}
259:are defined as the ratio of the number of ways
2148:Mathematical expression of absolute frequency
401:Mathematical expression of absolute frequency
5556:
5114:
5034:"How to Play the Most Popular Types of Poker"
4635:
4622:
4308:
4295:
2092:
2079:
343:
330:
186:
173:
8:
2492:{\displaystyle {13 \choose 1}{48 \choose 3}}
2061:In some popular variations of poker such as
4669:, the total number of 7-card combinations.
2251:{\displaystyle {4 \choose 1}{47 \choose 2}}
2107:{\textstyle {52 \choose 7}=133{,}784{,}560}
159:) by the total number of 5-card hands (the
44:
5721:
5634:
5563:
5549:
5541:
5201:
5121:
5107:
5099:
5062:Brian Alspach's mathematics and poker page
4612:. The probability is calculated based on
4285:. The probability is calculated based on
3278:(excluding royal flush and straight flush)
2935:(excluding royal flush and straight flush)
1109:(excluding royal flush and straight flush)
949:(excluding royal flush and straight flush)
4634:
4621:
4619:
4617:
4307:
4294:
4292:
4290:
4223:
4210:
4208:
4206:
4144:
4127:
4027:
4014:
4012:
4005:
3926:
3913:
3911:
3905:
3898:
3885:
3883:
3875:
3862:
3860:
3776:
3774:
3694:
3687:
3674:
3672:
3659:
3646:
3644:
3637:
3624:
3622:
3604:
3591:
3589:
3582:
3497:
3484:
3482:
3395:
3352:
3327:
3325:
3245:
3232:
3230:
3209:
3196:
3194:
3179:
3166:
3164:
3121:
3108:
3106:
3091:
3078:
3076:
3039:
3026:
3024:
3009:
2996:
2994:
2984:
2982:
2903:
2896:
2883:
2881:
2873:
2860:
2858:
2851:
2838:
2836:
2829:
2816:
2814:
2807:
2794:
2792:
2785:
2772:
2770:
2745:
2738:
2725:
2723:
2715:
2702:
2700:
2693:
2680:
2678:
2671:
2658:
2656:
2630:
2617:
2615:
2609:
2602:
2589:
2587:
2579:
2566:
2564:
2554:
2552:
2482:
2469:
2467:
2460:
2447:
2445:
2443:
2373:
2360:
2358:
2351:
2338:
2336:
2329:
2316:
2314:
2312:
2241:
2228:
2226:
2219:
2206:
2204:
2202:
2091:
2078:
2076:
2074:
1991:
1978:
1976:
1974:
1926:
1913:
1911:
1902:
1895:
1882:
1880:
1862:
1849:
1847:
1837:
1824:
1822:
1815:
1742:
1735:
1722:
1720:
1712:
1699:
1697:
1690:
1677:
1675:
1668:
1655:
1653:
1651:
1578:
1565:
1563:
1556:
1543:
1541:
1535:
1528:
1515:
1513:
1505:
1492:
1490:
1488:
1416:
1409:
1396:
1394:
1386:
1373:
1371:
1364:
1351:
1349:
1342:
1329:
1327:
1325:
1252:
1239:
1237:
1230:
1217:
1215:
1206:
1199:
1186:
1184:
1176:
1163:
1161:
1159:
1085:
1072:
1070:
1063:
1050:
1048:
1038:
1025:
1023:
1016:
1003:
1001:
999:
925:
912:
910:
903:
890:
888:
881:
868:
866:
859:
846:
844:
842:
769:
756:
754:
747:
734:
732:
725:
712:
710:
703:
690:
688:
686:
613:
600:
598:
588:
575:
573:
566:
553:
551:
549:
475:
462:
460:
458:
342:
329:
327:
325:
185:
172:
170:
168:
4676:
4346:
2129:
379:
146:the same card values in different suits.
142:is the number of ways to draw the hand,
4975:
4662:{\textstyle {52 \choose 7}=133,784,560}
4335:{\textstyle {52 \choose 5}=2,598,960}
370:{\textstyle {52 \choose 5}=2,598,960}
213:{\textstyle {52 \choose 5}=2,598,960}
16:Chances of card combinations in poker
7:
6058:
5511:
5184:List of poker playing card nicknames
5089:5, 6, and 7 card poker probabilities
290:are rounded off for simplicity; the
6078:
129:are not considered. In this chart:
4626:
4299:
4215:
4019:
3918:
3890:
3867:
3679:
3651:
3629:
3596:
3489:
3237:
3201:
3171:
3113:
3083:
3031:
3001:
2888:
2865:
2843:
2821:
2799:
2777:
2730:
2707:
2685:
2663:
2622:
2594:
2571:
2474:
2452:
2365:
2343:
2321:
2233:
2211:
2083:
1983:
1918:
1887:
1854:
1829:
1727:
1704:
1682:
1660:
1570:
1548:
1520:
1497:
1401:
1378:
1356:
1334:
1244:
1222:
1191:
1168:
1077:
1055:
1030:
1008:
917:
895:
873:
851:
761:
739:
717:
695:
605:
580:
558:
467:
334:
275:is the aforementioned probability.
177:
14:
5084:Numerous poker probability tables
4924:Effective hand strength algorithm
6077:
6067:
6057:
6048:
6047:
5522:
5510:
5499:
5498:
4893:
4176:{\displaystyle 1499\times \left}
4103:
4098:
4093:
4088:
4083:
3981:
3976:
3971:
3966:
3961:
3750:
3745:
3740:
3735:
3730:
3558:
3553:
3548:
3543:
3538:
3301:
3296:
3291:
3286:
3281:
2958:
2953:
2948:
2943:
2938:
2528:
2523:
2518:
2513:
2508:
2419:
2414:
2409:
2404:
2399:
2288:
2283:
2278:
2273:
2268:
2178:
2173:
2168:
2163:
2158:
1788:
1783:
1778:
1773:
1768:
1624:
1619:
1614:
1609:
1604:
1461:
1456:
1451:
1446:
1441:
1298:
1293:
1288:
1283:
1278:
1132:
1127:
1122:
1117:
1112:
972:
967:
962:
957:
952:
815:
810:
805:
800:
795:
659:
654:
649:
644:
639:
522:
517:
512:
507:
502:
431:
426:
421:
416:
411:
5523:
4269:Some variants of poker, called
5009:"Brief History of Probability"
4233:{\displaystyle {52 \choose 7}}
2001:{\displaystyle {52 \choose 5}}
1:
485:{\displaystyle {4 \choose 1}}
5445:Fundamental theorem of poker
4198:
4189:
4119:
4110:
3997:
3988:
3766:
3757:
3574:
3565:
3317:
3308:
2974:
2965:
2544:
2535:
2435:
2426:
2304:
2295:
2194:
2185:
5094:Hold'em poker probabilities
4863:
4854:
4844:
4835:
4827:
4818:
4810:
4801:
4793:
4784:
4776:
4767:
4759:
4750:
4742:
4733:
4725:
4716:
4708:
4699:
4566:
4557:
4554:
4544:
4535:
4532:
4524:
4515:
4512:
4504:
4495:
4492:
4484:
4475:
4472:
4464:
4455:
4452:
4444:
4435:
4432:
4424:
4415:
4412:
4404:
4395:
4392:
4384:
4375:
4372:
6122:
4929:Event (probability theory)
4593:
4590:7-card lowball poker hands
4262:
4259:5-card lowball poker hands
1941:{\displaystyle \left\left}
6043:
5650:Mathematics of bookmaking
5578:
5494:
5136:
4919:Combinatorial game theory
117:of each hand, given all
5425:Open-face Chinese poker
5141:Index of poker articles
2265:(excluding royal flush)
499:(excluding royal flush)
27:of each type of 5-card
4663:
4336:
4234:
4177:
4067:
3946:
3715:
3523:
3265:
2922:
2493:
2384:
2252:
2108:
2002:
1942:
1752:
1589:
1426:
1263:
1096:
936:
780:
624:
486:
395:Cumulative probability
371:
320:, for example, yields
284:Cumulative probability
240:Cumulative probability
214:
91:
45:
5476:Computer poker player
4664:
4337:
4235:
4178:
4068:
3947:
3716:
3524:
3266:
2923:
2494:
2385:
2253:
2109:
2003:
1943:
1753:
1590:
1427:
1264:
1097:
937:
781:
625:
487:
372:
278:The values given for
215:
102:, where there are no
81:
6035:Video game addiction
5645:Gambling mathematics
5581:Gambling terminology
5356:Community card poker
5067:9 April 2015 at the
4984:"Probability Theory"
4909:Binomial coefficient
4616:
4289:
4205:
4126:
4004:
3773:
3581:
3324:
2981:
2551:
2442:
2311:
2201:
2073:
1973:
1814:
1650:
1487:
1324:
1158:
998:
841:
685:
548:
457:
324:
167:
109:The following chart
1808:0.9953015 : 1
542:72,192.33 : 1
55:Liber de Ludo Aleae
5695:Due Column betting
5673:Advantage gambling
4939:Gaming mathematics
4659:
4385:2,537.05 : 1
4332:
4230:
4173:
4063:
3942:
3940:
3711:
3519:
3517:
3261:
3259:
2918:
2916:
2489:
2380:
2248:
2104:
2057:7-card poker hands
1998:
1938:
1748:
1644:1.366477 : 1
1585:
1481:20.03535 : 1
1422:
1318:46.32955 : 1
1259:
1092:
992:507.8019 : 1
932:
835:693.1667 : 1
776:
620:
482:
367:
269:(1/p) - 1 : 1
210:
92:
74:5-card poker hands
6106:Poker probability
6091:
6090:
5980:
5979:
5713:
5712:
5700:Labouchère system
5655:Poker probability
5538:
5537:
5385:Casino games
5377:Six-plus hold 'em
5298:
5297:
5036:. 14 August 2019.
4988:Science Clarified
4868:
4867:
4633:
4571:
4570:
4306:
4243:
4242:
4222:
4026:
3925:
3897:
3874:
3686:
3658:
3636:
3603:
3496:
3244:
3208:
3178:
3120:
3090:
3038:
3008:
2895:
2872:
2850:
2828:
2806:
2784:
2737:
2714:
2692:
2670:
2629:
2601:
2578:
2481:
2459:
2372:
2350:
2328:
2305:3,589.6 : 1
2240:
2218:
2090:
2011:
2010:
1990:
1925:
1894:
1861:
1836:
1734:
1711:
1689:
1667:
1577:
1555:
1527:
1504:
1408:
1385:
1363:
1341:
1251:
1229:
1198:
1175:
1084:
1062:
1037:
1015:
924:
902:
880:
858:
768:
746:
724:
702:
612:
587:
565:
474:
451:649,739 : 1
341:
298:values are exact.
184:
6113:
6081:
6080:
6071:
6061:
6060:
6051:
6050:
6030:Problem gambling
5722:
5635:
5622:Riverboat casino
5565:
5558:
5551:
5542:
5526:
5525:
5514:
5513:
5502:
5501:
5450:Morton's theorem
5406:Three Card Poker
5401:Mississippi Stud
5202:
5123:
5116:
5109:
5100:
5074:MathWorld: Poker
5049:
5044:
5038:
5037:
5030:
5024:
5023:
5021:
5019:
5005:
4999:
4998:
4996:
4994:
4980:
4903:
4898:
4897:
4709:170.12 : 1
4677:
4668:
4666:
4665:
4660:
4640:
4639:
4638:
4625:
4608:, also called a
4425:168.20 : 1
4405:506.61 : 1
4347:
4341:
4339:
4338:
4333:
4313:
4312:
4311:
4298:
4281:, also called a
4239:
4237:
4236:
4231:
4229:
4228:
4227:
4214:
4182:
4180:
4179:
4174:
4172:
4168:
4149:
4148:
4107:
4102:
4097:
4092:
4087:
4072:
4070:
4069:
4064:
4044:
4040:
4033:
4032:
4031:
4018:
3985:
3980:
3975:
3970:
3965:
3951:
3949:
3948:
3943:
3941:
3937:
3933:
3932:
3931:
3930:
3917:
3910:
3909:
3904:
3903:
3902:
3889:
3881:
3880:
3879:
3866:
3845:
3841:
3840:
3836:
3779:
3754:
3749:
3744:
3739:
3734:
3720:
3718:
3717:
3712:
3710:
3706:
3699:
3698:
3693:
3692:
3691:
3678:
3665:
3664:
3663:
3650:
3643:
3642:
3641:
3628:
3621:
3617:
3610:
3609:
3608:
3595:
3562:
3557:
3552:
3547:
3542:
3528:
3526:
3525:
3520:
3518:
3514:
3510:
3503:
3502:
3501:
3488:
3472:
3468:
3421:
3417:
3396:
3385:
3381:
3380:
3376:
3357:
3356:
3330:
3305:
3300:
3295:
3290:
3285:
3270:
3268:
3267:
3262:
3260:
3256:
3252:
3251:
3250:
3249:
3236:
3226:
3222:
3215:
3214:
3213:
3200:
3185:
3184:
3183:
3170:
3149:
3145:
3138:
3134:
3127:
3126:
3125:
3112:
3097:
3096:
3095:
3082:
3061:
3057:
3056:
3052:
3045:
3044:
3043:
3030:
3015:
3014:
3013:
3000:
2987:
2962:
2957:
2952:
2947:
2942:
2927:
2925:
2924:
2919:
2917:
2913:
2909:
2908:
2907:
2902:
2901:
2900:
2887:
2879:
2878:
2877:
2864:
2857:
2856:
2855:
2842:
2835:
2834:
2833:
2820:
2813:
2812:
2811:
2798:
2791:
2790:
2789:
2776:
2755:
2751:
2750:
2749:
2744:
2743:
2742:
2729:
2721:
2720:
2719:
2706:
2699:
2698:
2697:
2684:
2677:
2676:
2675:
2662:
2641:
2637:
2636:
2635:
2634:
2621:
2614:
2613:
2608:
2607:
2606:
2593:
2585:
2584:
2583:
2570:
2557:
2532:
2527:
2522:
2517:
2512:
2498:
2496:
2495:
2490:
2488:
2487:
2486:
2473:
2466:
2465:
2464:
2451:
2423:
2418:
2413:
2408:
2403:
2389:
2387:
2386:
2381:
2379:
2378:
2377:
2364:
2357:
2356:
2355:
2342:
2335:
2334:
2333:
2320:
2292:
2287:
2282:
2277:
2272:
2257:
2255:
2254:
2249:
2247:
2246:
2245:
2232:
2225:
2224:
2223:
2210:
2195:30,939 : 1
2182:
2177:
2172:
2167:
2162:
2130:
2113:
2111:
2110:
2105:
2097:
2096:
2095:
2082:
2046:
2042:
2028:
2024:is identical to
2007:
2005:
2004:
1999:
1997:
1996:
1995:
1982:
1947:
1945:
1944:
1939:
1937:
1933:
1932:
1931:
1930:
1917:
1907:
1906:
1901:
1900:
1899:
1886:
1873:
1869:
1868:
1867:
1866:
1853:
1843:
1842:
1841:
1828:
1792:
1787:
1782:
1777:
1772:
1757:
1755:
1754:
1749:
1747:
1746:
1741:
1740:
1739:
1726:
1718:
1717:
1716:
1703:
1696:
1695:
1694:
1681:
1674:
1673:
1672:
1659:
1628:
1623:
1618:
1613:
1608:
1594:
1592:
1591:
1586:
1584:
1583:
1582:
1569:
1562:
1561:
1560:
1547:
1540:
1539:
1534:
1533:
1532:
1519:
1511:
1510:
1509:
1496:
1465:
1460:
1455:
1450:
1445:
1431:
1429:
1428:
1423:
1421:
1420:
1415:
1414:
1413:
1400:
1392:
1391:
1390:
1377:
1370:
1369:
1368:
1355:
1348:
1347:
1346:
1333:
1302:
1297:
1292:
1287:
1282:
1268:
1266:
1265:
1260:
1258:
1257:
1256:
1243:
1236:
1235:
1234:
1221:
1211:
1210:
1205:
1204:
1203:
1190:
1182:
1181:
1180:
1167:
1136:
1131:
1126:
1121:
1116:
1101:
1099:
1098:
1093:
1091:
1090:
1089:
1076:
1069:
1068:
1067:
1054:
1044:
1043:
1042:
1029:
1022:
1021:
1020:
1007:
976:
971:
966:
961:
956:
941:
939:
938:
933:
931:
930:
929:
916:
909:
908:
907:
894:
887:
886:
885:
872:
865:
864:
863:
850:
819:
814:
809:
804:
799:
785:
783:
782:
777:
775:
774:
773:
760:
753:
752:
751:
738:
731:
730:
729:
716:
709:
708:
707:
694:
663:
658:
653:
648:
643:
629:
627:
626:
621:
619:
618:
617:
604:
594:
593:
592:
579:
572:
571:
570:
557:
526:
521:
516:
511:
506:
491:
489:
488:
483:
481:
480:
479:
466:
435:
430:
425:
420:
415:
380:
376:
374:
373:
368:
348:
347:
346:
333:
319:
315:
311:
235:
233:
232:
229:
226:
219:
217:
216:
211:
191:
190:
189:
176:
63:Pierre de Fermat
51:Girolamo Cardano
48:
6121:
6120:
6116:
6115:
6114:
6112:
6111:
6110:
6096:
6095:
6092:
6087:
6039:
6013:
5976:
5964:
5943:
5937:Atlantic Canada
5892:
5841:
5746:
5709:
5659:
5626:
5583:
5574:
5569:
5539:
5534:
5490:
5464:
5431:
5411:Four Card Poker
5343:Seven-card stud
5294:
5248:
5193:
5145:
5132:
5127:
5069:Wayback Machine
5058:
5053:
5052:
5045:
5041:
5032:
5031:
5027:
5017:
5015:
5007:
5006:
5002:
4992:
4990:
4982:
4981:
4977:
4972:
4934:Game complexity
4899:
4892:
4889:
4743:17.01 : 1
4726:41.45 : 1
4620:
4614:
4613:
4598:
4596:Lowball (poker)
4592:
4505:11.09 : 1
4485:19.14 : 1
4465:35.26 : 1
4445:71.52 : 1
4293:
4287:
4286:
4267:
4265:Lowball (poker)
4261:
4209:
4203:
4202:
4140:
4139:
4135:
4124:
4123:
4081:
4013:
4011:
4007:
4002:
4001:
3959:
3939:
3938:
3912:
3884:
3882:
3861:
3859:
3855:
3853:
3847:
3846:
3802:
3798:
3785:
3781:
3771:
3770:
3728:
3673:
3671:
3670:
3666:
3645:
3623:
3590:
3588:
3584:
3579:
3578:
3536:
3534:Three of a kind
3516:
3515:
3483:
3458:
3454:
3435:
3431:
3429:
3423:
3422:
3401:
3397:
3393:
3387:
3386:
3348:
3347:
3343:
3336:
3332:
3322:
3321:
3279:
3258:
3257:
3231:
3195:
3193:
3189:
3165:
3163:
3159:
3157:
3151:
3150:
3107:
3105:
3101:
3077:
3075:
3071:
3069:
3063:
3062:
3025:
3023:
3019:
2995:
2993:
2989:
2979:
2978:
2936:
2915:
2914:
2882:
2880:
2859:
2837:
2815:
2793:
2771:
2769:
2765:
2763:
2757:
2756:
2724:
2722:
2701:
2679:
2657:
2655:
2651:
2649:
2643:
2642:
2616:
2588:
2586:
2565:
2563:
2559:
2549:
2548:
2506:
2468:
2446:
2440:
2439:
2397:
2359:
2337:
2315:
2309:
2308:
2266:
2227:
2205:
2199:
2198:
2156:
2077:
2071:
2070:
2059:
2044:
2040:
2026:
1977:
1971:
1970:
1912:
1881:
1879:
1878:
1874:
1848:
1823:
1821:
1817:
1812:
1811:
1766:
1721:
1719:
1698:
1676:
1654:
1648:
1647:
1602:
1564:
1542:
1514:
1512:
1491:
1485:
1484:
1439:
1395:
1393:
1372:
1350:
1328:
1322:
1321:
1276:
1274:Three of a kind
1238:
1216:
1185:
1183:
1162:
1156:
1155:
1152:253.8 : 1
1110:
1071:
1049:
1024:
1002:
996:
995:
950:
911:
889:
867:
845:
839:
838:
793:
755:
733:
711:
689:
683:
682:
679:4,164 : 1
637:
599:
574:
552:
546:
545:
500:
461:
455:
454:
409:
328:
322:
321:
230:
227:
224:
223:
221:
171:
165:
164:
113:the (absolute)
88:Jacks or Better
76:
71:
37:
17:
12:
11:
5:
6119:
6117:
6109:
6108:
6098:
6097:
6089:
6088:
6086:
6085:
6075:
6065:
6055:
6044:
6041:
6040:
6038:
6037:
6032:
6027:
6021:
6019:
6015:
6014:
6012:
6011:
6006:
6001:
5999:Game of chance
5996:
5990:
5988:
5982:
5981:
5978:
5977:
5972:
5970:
5966:
5965:
5963:
5962:
5957:
5951:
5949:
5945:
5944:
5942:
5941:
5940:
5939:
5934:
5932:Western Canada
5929:
5924:
5919:
5911:
5906:
5900:
5898:
5894:
5893:
5891:
5890:
5888:United Kingdom
5885:
5880:
5875:
5870:
5865:
5860:
5855:
5849:
5847:
5843:
5842:
5840:
5839:
5834:
5829:
5824:
5819:
5814:
5809:
5808:
5807:
5797:
5792:
5787:
5782:
5781:
5780:
5775:
5765:
5760:
5754:
5752:
5748:
5747:
5745:
5744:
5739:
5734:
5728:
5726:
5719:
5715:
5714:
5711:
5710:
5708:
5707:
5702:
5697:
5692:
5690:Asian handicap
5687:
5682:
5681:
5680:
5669:
5667:
5661:
5660:
5658:
5657:
5652:
5647:
5641:
5639:
5632:
5628:
5627:
5625:
5624:
5619:
5614:
5609:
5604:
5603:
5602:
5591:
5589:
5585:
5584:
5579:
5576:
5575:
5570:
5568:
5567:
5560:
5553:
5545:
5536:
5535:
5533:
5532:
5520:
5508:
5495:
5492:
5491:
5489:
5488:
5483:
5478:
5472:
5470:
5466:
5465:
5463:
5462:
5457:
5452:
5447:
5441:
5439:
5433:
5432:
5430:
5429:
5428:
5427:
5415:
5414:
5413:
5408:
5403:
5398:
5393:
5391:Caribbean stud
5381:
5380:
5379:
5374:
5372:Omaha hold 'em
5369:
5367:Greek hold 'em
5364:
5362:Texas hold 'em
5352:
5351:
5350:
5345:
5340:
5338:Five-card stud
5328:
5327:
5326:
5324:Five-card draw
5314:
5308:
5306:
5300:
5299:
5296:
5295:
5293:
5292:
5287:
5282:
5277:
5272:
5267:
5262:
5256:
5254:
5250:
5249:
5247:
5246:
5241:
5240:
5239:
5229:
5224:
5219:
5214:
5208:
5206:
5199:
5195:
5194:
5192:
5191:
5186:
5181:
5180:
5179:
5169:
5164:
5159:
5153:
5151:
5147:
5146:
5144:
5143:
5137:
5134:
5133:
5128:
5126:
5125:
5118:
5111:
5103:
5097:
5096:
5091:
5086:
5081:
5076:
5071:
5057:
5056:External links
5054:
5051:
5050:
5039:
5025:
5000:
4974:
4973:
4971:
4968:
4967:
4966:
4961:
4956:
4951:
4946:
4941:
4936:
4931:
4926:
4921:
4916:
4911:
4905:
4904:
4888:
4885:
4870:
4869:
4866:
4865:
4864:0.05 : 1
4862:
4859:
4856:
4853:
4847:
4846:
4845:8.60 : 1
4843:
4840:
4837:
4834:
4830:
4829:
4828:5.23 : 1
4826:
4823:
4820:
4817:
4813:
4812:
4811:4.39 : 1
4809:
4806:
4803:
4800:
4796:
4795:
4794:4.65 : 1
4792:
4789:
4786:
4783:
4779:
4778:
4777:5.98 : 1
4775:
4772:
4769:
4766:
4762:
4761:
4760:9.16 : 1
4758:
4755:
4752:
4749:
4745:
4744:
4741:
4738:
4735:
4732:
4728:
4727:
4724:
4721:
4718:
4715:
4711:
4710:
4707:
4704:
4701:
4698:
4694:
4693:
4690:
4687:
4684:
4681:
4658:
4655:
4652:
4649:
4646:
4643:
4637:
4632:
4629:
4624:
4591:
4588:
4573:
4572:
4569:
4568:
4567:0.97 : 1
4565:
4562:
4559:
4556:
4553:
4547:
4546:
4545:4.13 : 1
4543:
4540:
4537:
4534:
4531:
4527:
4526:
4525:6.69 : 1
4523:
4520:
4517:
4514:
4511:
4507:
4506:
4503:
4500:
4497:
4494:
4491:
4487:
4486:
4483:
4480:
4477:
4474:
4471:
4467:
4466:
4463:
4460:
4457:
4454:
4451:
4447:
4446:
4443:
4440:
4437:
4434:
4431:
4427:
4426:
4423:
4420:
4417:
4414:
4411:
4407:
4406:
4403:
4400:
4397:
4394:
4391:
4387:
4386:
4383:
4380:
4377:
4374:
4371:
4367:
4366:
4363:
4360:
4357:
4354:
4353:Distinct hands
4351:
4331:
4328:
4325:
4322:
4319:
4316:
4310:
4305:
4302:
4297:
4260:
4257:
4245:
4244:
4241:
4240:
4226:
4221:
4218:
4213:
4200:
4197:
4194:
4191:
4188:
4184:
4183:
4171:
4167:
4164:
4161:
4158:
4155:
4152:
4147:
4143:
4138:
4134:
4131:
4121:
4120:4.74 : 1
4118:
4115:
4112:
4109:
4074:
4073:
4062:
4059:
4056:
4053:
4050:
4047:
4043:
4039:
4036:
4030:
4025:
4022:
4017:
4010:
3999:
3998:1.28 : 1
3996:
3993:
3990:
3987:
3953:
3952:
3936:
3929:
3924:
3921:
3916:
3908:
3901:
3896:
3893:
3888:
3878:
3873:
3870:
3865:
3858:
3854:
3852:
3849:
3848:
3844:
3839:
3835:
3832:
3829:
3826:
3823:
3820:
3817:
3814:
3811:
3808:
3805:
3801:
3797:
3794:
3791:
3788:
3784:
3780:
3778:
3768:
3767:3.26 : 1
3765:
3762:
3759:
3756:
3722:
3721:
3709:
3705:
3702:
3697:
3690:
3685:
3682:
3677:
3669:
3662:
3657:
3654:
3649:
3640:
3635:
3632:
3627:
3620:
3616:
3613:
3607:
3602:
3599:
3594:
3587:
3576:
3575:19.7 : 1
3573:
3570:
3567:
3564:
3530:
3529:
3513:
3509:
3506:
3500:
3495:
3492:
3487:
3481:
3478:
3475:
3471:
3467:
3464:
3461:
3457:
3453:
3450:
3447:
3444:
3441:
3438:
3434:
3430:
3428:
3425:
3424:
3420:
3416:
3413:
3410:
3407:
3404:
3400:
3394:
3392:
3389:
3388:
3384:
3379:
3375:
3372:
3369:
3366:
3363:
3360:
3355:
3351:
3346:
3342:
3339:
3335:
3331:
3329:
3319:
3318:20.6 : 1
3316:
3313:
3310:
3307:
3272:
3271:
3255:
3248:
3243:
3240:
3235:
3229:
3225:
3221:
3218:
3212:
3207:
3204:
3199:
3192:
3188:
3182:
3177:
3174:
3169:
3162:
3158:
3156:
3153:
3152:
3148:
3144:
3141:
3137:
3133:
3130:
3124:
3119:
3116:
3111:
3104:
3100:
3094:
3089:
3086:
3081:
3074:
3070:
3068:
3065:
3064:
3060:
3055:
3051:
3048:
3042:
3037:
3034:
3029:
3022:
3018:
3012:
3007:
3004:
2999:
2992:
2988:
2986:
2976:
2975:32.1 : 1
2973:
2970:
2967:
2964:
2929:
2928:
2912:
2906:
2899:
2894:
2891:
2886:
2876:
2871:
2868:
2863:
2854:
2849:
2846:
2841:
2832:
2827:
2824:
2819:
2810:
2805:
2802:
2797:
2788:
2783:
2780:
2775:
2768:
2764:
2762:
2759:
2758:
2754:
2748:
2741:
2736:
2733:
2728:
2718:
2713:
2710:
2705:
2696:
2691:
2688:
2683:
2674:
2669:
2666:
2661:
2654:
2650:
2648:
2645:
2644:
2640:
2633:
2628:
2625:
2620:
2612:
2605:
2600:
2597:
2592:
2582:
2577:
2574:
2569:
2562:
2558:
2556:
2546:
2545:37.5 : 1
2543:
2540:
2537:
2534:
2500:
2499:
2485:
2480:
2477:
2472:
2463:
2458:
2455:
2450:
2437:
2434:
2431:
2428:
2425:
2395:Four of a kind
2391:
2390:
2376:
2371:
2368:
2363:
2354:
2349:
2346:
2341:
2332:
2327:
2324:
2319:
2306:
2303:
2300:
2297:
2294:
2263:Straight flush
2259:
2258:
2244:
2239:
2236:
2231:
2222:
2217:
2214:
2209:
2196:
2193:
2190:
2187:
2184:
2150:
2149:
2146:
2143:
2140:
2137:
2134:
2103:
2100:
2094:
2089:
2086:
2081:
2063:Texas hold 'em
2058:
2055:
2036:3♣ 7♣ 8♣ Q♠ A♠
2027:3♦ 7♦ 8♦ Q♥ A♥
2022:3♣ 7♣ 8♣ Q♠ A♠
2009:
2008:
1994:
1989:
1986:
1981:
1968:
1965:
1962:
1959:
1956:
1953:
1949:
1948:
1936:
1929:
1924:
1921:
1916:
1910:
1905:
1898:
1893:
1890:
1885:
1877:
1872:
1865:
1860:
1857:
1852:
1846:
1840:
1835:
1832:
1827:
1820:
1809:
1806:
1803:
1800:
1797:
1794:
1759:
1758:
1745:
1738:
1733:
1730:
1725:
1715:
1710:
1707:
1702:
1693:
1688:
1685:
1680:
1671:
1666:
1663:
1658:
1645:
1642:
1639:
1636:
1633:
1630:
1596:
1595:
1581:
1576:
1573:
1568:
1559:
1554:
1551:
1546:
1538:
1531:
1526:
1523:
1518:
1508:
1503:
1500:
1495:
1482:
1479:
1476:
1473:
1470:
1467:
1433:
1432:
1419:
1412:
1407:
1404:
1399:
1389:
1384:
1381:
1376:
1367:
1362:
1359:
1354:
1345:
1340:
1337:
1332:
1319:
1316:
1313:
1310:
1307:
1304:
1270:
1269:
1255:
1250:
1247:
1242:
1233:
1228:
1225:
1220:
1214:
1209:
1202:
1197:
1194:
1189:
1179:
1174:
1171:
1166:
1153:
1150:
1147:
1144:
1141:
1138:
1103:
1102:
1088:
1083:
1080:
1075:
1066:
1061:
1058:
1053:
1047:
1041:
1036:
1033:
1028:
1019:
1014:
1011:
1006:
993:
990:
987:
984:
981:
978:
943:
942:
928:
923:
920:
915:
906:
901:
898:
893:
884:
879:
876:
871:
862:
857:
854:
849:
836:
833:
830:
827:
824:
821:
787:
786:
772:
767:
764:
759:
750:
745:
742:
737:
728:
723:
720:
715:
706:
701:
698:
693:
680:
677:
674:
671:
668:
665:
635:Four of a kind
631:
630:
616:
611:
608:
603:
597:
591:
586:
583:
578:
569:
564:
561:
556:
543:
540:
537:
534:
531:
528:
497:Straight flush
493:
492:
478:
473:
470:
465:
452:
449:
446:
443:
440:
437:
403:
402:
399:
396:
393:
390:
387:
386:Distinct hands
384:
366:
363:
360:
357:
354:
351:
345:
340:
337:
332:
300:
299:
292:Distinct hands
276:
251:
244:or better than
237:
209:
206:
203:
200:
197:
194:
188:
183:
180:
175:
147:
137:
134:Distinct hands
121:of five cards
100:five-card draw
96:straight poker
75:
72:
70:
67:
36:
33:
15:
13:
10:
9:
6:
4:
3:
2:
6118:
6107:
6104:
6103:
6101:
6094:
6084:
6076:
6074:
6070:
6066:
6064:
6056:
6054:
6046:
6045:
6042:
6036:
6033:
6031:
6028:
6026:
6023:
6022:
6020:
6016:
6010:
6007:
6005:
6004:Game of skill
6002:
6000:
5997:
5995:
5992:
5991:
5989:
5987:
5983:
5975:
5971:
5969:South America
5967:
5961:
5958:
5956:
5953:
5952:
5950:
5946:
5938:
5935:
5933:
5930:
5928:
5925:
5923:
5920:
5918:
5915:
5914:
5912:
5910:
5909:United States
5907:
5905:
5902:
5901:
5899:
5897:North America
5895:
5889:
5886:
5884:
5881:
5879:
5876:
5874:
5871:
5869:
5866:
5864:
5861:
5859:
5856:
5854:
5851:
5850:
5848:
5844:
5838:
5835:
5833:
5830:
5828:
5825:
5823:
5820:
5818:
5815:
5813:
5810:
5806:
5803:
5802:
5801:
5798:
5796:
5793:
5791:
5788:
5786:
5783:
5779:
5776:
5774:
5771:
5770:
5769:
5766:
5764:
5761:
5759:
5756:
5755:
5753:
5749:
5743:
5740:
5738:
5735:
5733:
5730:
5729:
5727:
5723:
5720:
5716:
5706:
5703:
5701:
5698:
5696:
5693:
5691:
5688:
5686:
5683:
5679:
5678:Card counting
5676:
5675:
5674:
5671:
5670:
5668:
5666:
5662:
5656:
5653:
5651:
5648:
5646:
5643:
5642:
5640:
5636:
5633:
5629:
5623:
5620:
5618:
5615:
5613:
5610:
5608:
5607:Online casino
5605:
5601:
5598:
5597:
5596:
5593:
5592:
5590:
5586:
5582:
5577:
5573:
5566:
5561:
5559:
5554:
5552:
5547:
5546:
5543:
5531:
5530:
5521:
5519:
5518:
5509:
5507:
5506:
5497:
5496:
5493:
5487:
5484:
5482:
5479:
5477:
5474:
5473:
5471:
5467:
5461:
5458:
5456:
5453:
5451:
5448:
5446:
5443:
5442:
5440:
5438:
5434:
5426:
5423:
5422:
5421:
5420:
5419:Chinese poker
5416:
5412:
5409:
5407:
5404:
5402:
5399:
5397:
5394:
5392:
5389:
5388:
5387:
5386:
5382:
5378:
5375:
5373:
5370:
5368:
5365:
5363:
5360:
5359:
5358:
5357:
5353:
5349:
5346:
5344:
5341:
5339:
5336:
5335:
5334:
5333:
5329:
5325:
5322:
5321:
5320:
5319:
5315:
5313:
5310:
5309:
5307:
5305:
5301:
5291:
5288:
5286:
5283:
5281:
5278:
5276:
5273:
5271:
5268:
5266:
5263:
5261:
5258:
5257:
5255:
5251:
5245:
5242:
5238:
5235:
5234:
5233:
5230:
5228:
5225:
5223:
5220:
5218:
5215:
5213:
5210:
5209:
5207:
5203:
5200:
5196:
5190:
5187:
5185:
5182:
5178:
5175:
5174:
5173:
5170:
5168:
5165:
5163:
5160:
5158:
5155:
5154:
5152:
5148:
5142:
5139:
5138:
5135:
5131:
5124:
5119:
5117:
5112:
5110:
5105:
5104:
5101:
5095:
5092:
5090:
5087:
5085:
5082:
5080:
5077:
5075:
5072:
5070:
5066:
5063:
5060:
5059:
5055:
5048:
5043:
5040:
5035:
5029:
5026:
5014:
5010:
5004:
5001:
4989:
4985:
4979:
4976:
4969:
4965:
4962:
4960:
4957:
4955:
4952:
4950:
4947:
4945:
4942:
4940:
4937:
4935:
4932:
4930:
4927:
4925:
4922:
4920:
4917:
4915:
4912:
4910:
4907:
4906:
4902:
4896:
4891:
4886:
4884:
4881:
4876:
4873:
4860:
4857:
4852:
4849:
4848:
4841:
4838:
4832:
4831:
4824:
4821:
4815:
4814:
4807:
4804:
4798:
4797:
4790:
4787:
4781:
4780:
4773:
4770:
4764:
4763:
4756:
4753:
4747:
4746:
4739:
4736:
4730:
4729:
4722:
4719:
4713:
4712:
4705:
4702:
4696:
4695:
4692:Odds against
4691:
4688:
4685:
4682:
4679:
4678:
4675:
4674:
4673:
4670:
4656:
4653:
4650:
4647:
4644:
4641:
4630:
4627:
4611:
4607:
4603:
4597:
4589:
4587:
4584:
4579:
4576:
4563:
4560:
4552:
4549:
4548:
4541:
4538:
4529:
4528:
4521:
4518:
4509:
4508:
4501:
4498:
4489:
4488:
4481:
4478:
4469:
4468:
4461:
4458:
4449:
4448:
4441:
4438:
4429:
4428:
4421:
4418:
4409:
4408:
4401:
4398:
4389:
4388:
4381:
4378:
4369:
4368:
4365:Odds against
4364:
4361:
4358:
4355:
4352:
4349:
4348:
4345:
4344:
4343:
4329:
4326:
4323:
4320:
4317:
4314:
4303:
4300:
4284:
4280:
4276:
4272:
4266:
4258:
4256:
4252:
4248:
4219:
4216:
4201:
4195:
4192:
4186:
4185:
4169:
4165:
4162:
4159:
4156:
4153:
4150:
4145:
4141:
4136:
4132:
4129:
4122:
4116:
4113:
4108:
4106:
4101:
4096:
4091:
4086:
4079:
4076:
4075:
4060:
4057:
4054:
4051:
4048:
4045:
4041:
4037:
4034:
4023:
4020:
4008:
4000:
3994:
3991:
3986:
3984:
3979:
3974:
3969:
3964:
3958:
3955:
3954:
3934:
3922:
3919:
3906:
3894:
3891:
3871:
3868:
3856:
3850:
3842:
3837:
3833:
3830:
3827:
3824:
3821:
3818:
3815:
3812:
3809:
3806:
3803:
3799:
3795:
3792:
3789:
3786:
3782:
3769:
3763:
3760:
3755:
3753:
3748:
3743:
3738:
3733:
3727:
3724:
3723:
3707:
3703:
3700:
3695:
3683:
3680:
3667:
3655:
3652:
3633:
3630:
3618:
3614:
3611:
3600:
3597:
3585:
3577:
3571:
3568:
3563:
3561:
3556:
3551:
3546:
3541:
3535:
3532:
3531:
3511:
3507:
3504:
3493:
3490:
3479:
3476:
3473:
3469:
3465:
3462:
3459:
3455:
3451:
3448:
3445:
3442:
3439:
3436:
3432:
3426:
3418:
3414:
3411:
3408:
3405:
3402:
3398:
3390:
3382:
3377:
3373:
3370:
3367:
3364:
3361:
3358:
3353:
3349:
3344:
3340:
3337:
3333:
3320:
3314:
3311:
3306:
3304:
3299:
3294:
3289:
3284:
3277:
3274:
3273:
3253:
3241:
3238:
3227:
3223:
3219:
3216:
3205:
3202:
3190:
3186:
3175:
3172:
3160:
3154:
3146:
3142:
3139:
3135:
3131:
3128:
3117:
3114:
3102:
3098:
3087:
3084:
3072:
3066:
3058:
3053:
3049:
3046:
3035:
3032:
3020:
3016:
3005:
3002:
2990:
2977:
2971:
2968:
2963:
2961:
2956:
2951:
2946:
2941:
2934:
2931:
2930:
2910:
2904:
2892:
2889:
2869:
2866:
2847:
2844:
2825:
2822:
2803:
2800:
2781:
2778:
2766:
2760:
2752:
2746:
2734:
2731:
2711:
2708:
2689:
2686:
2667:
2664:
2652:
2646:
2638:
2626:
2623:
2610:
2598:
2595:
2575:
2572:
2560:
2547:
2541:
2538:
2533:
2531:
2526:
2521:
2516:
2511:
2505:
2502:
2501:
2478:
2475:
2456:
2453:
2438:
2436:594 : 1
2432:
2429:
2424:
2422:
2417:
2412:
2407:
2402:
2396:
2393:
2392:
2369:
2366:
2347:
2344:
2325:
2322:
2307:
2301:
2298:
2293:
2291:
2286:
2281:
2276:
2271:
2264:
2261:
2260:
2237:
2234:
2215:
2212:
2197:
2191:
2188:
2183:
2181:
2176:
2171:
2166:
2161:
2155:
2152:
2151:
2147:
2145:Odds against
2144:
2141:
2138:
2135:
2132:
2131:
2128:
2127:
2126:
2124:
2119:
2117:
2101:
2098:
2087:
2084:
2066:
2064:
2056:
2054:
2052:
2047:
2037:
2032:
2029:
2023:
2018:
2014:
1987:
1984:
1969:
1966:
1963:
1960:
1957:
1954:
1951:
1950:
1934:
1922:
1919:
1908:
1903:
1891:
1888:
1875:
1870:
1858:
1855:
1844:
1833:
1830:
1818:
1810:
1807:
1804:
1801:
1798:
1795:
1793:
1791:
1786:
1781:
1776:
1771:
1764:
1761:
1760:
1743:
1731:
1728:
1708:
1705:
1686:
1683:
1664:
1661:
1646:
1643:
1640:
1637:
1634:
1631:
1629:
1627:
1622:
1617:
1612:
1607:
1601:
1598:
1597:
1574:
1571:
1552:
1549:
1536:
1524:
1521:
1501:
1498:
1483:
1480:
1477:
1474:
1471:
1468:
1466:
1464:
1459:
1454:
1449:
1444:
1438:
1435:
1434:
1417:
1405:
1402:
1382:
1379:
1360:
1357:
1338:
1335:
1320:
1317:
1314:
1311:
1308:
1305:
1303:
1301:
1296:
1291:
1286:
1281:
1275:
1272:
1271:
1248:
1245:
1226:
1223:
1212:
1207:
1195:
1192:
1172:
1169:
1154:
1151:
1148:
1145:
1142:
1139:
1137:
1135:
1130:
1125:
1120:
1115:
1108:
1105:
1104:
1081:
1078:
1059:
1056:
1045:
1034:
1031:
1012:
1009:
994:
991:
988:
985:
982:
979:
977:
975:
970:
965:
960:
955:
948:
945:
944:
921:
918:
899:
896:
877:
874:
855:
852:
837:
834:
831:
828:
825:
822:
820:
818:
813:
808:
803:
798:
792:
789:
788:
765:
762:
743:
740:
721:
718:
699:
696:
681:
678:
675:
672:
669:
666:
664:
662:
657:
652:
647:
642:
636:
633:
632:
609:
606:
595:
584:
581:
562:
559:
544:
541:
538:
535:
532:
529:
527:
525:
520:
515:
510:
505:
498:
495:
494:
471:
468:
453:
450:
447:
444:
441:
438:
436:
434:
429:
424:
419:
414:
408:
405:
404:
400:
398:Odds against
397:
394:
391:
388:
385:
382:
381:
378:
364:
361:
358:
355:
352:
349:
338:
335:
307:
306:
297:
293:
289:
285:
281:
277:
274:
270:
266:
262:
258:
257:
252:
249:
245:
241:
238:
207:
204:
201:
198:
195:
192:
181:
178:
162:
158:
154:
153:
148:
145:
141:
138:
135:
132:
131:
130:
128:
124:
120:
116:
112:
107:
105:
101:
97:
89:
85:
84:Euler diagram
80:
73:
68:
66:
64:
60:
59:Blaise Pascal
56:
52:
47:
42:
34:
32:
30:
26:
22:
6093:
6009:List of bets
5742:South Africa
5685:Dice control
5654:
5527:
5515:
5503:
5481:Online poker
5417:
5383:
5354:
5330:
5316:
5237:Non-standard
5227:Playing card
5042:
5028:
5016:. Retrieved
5013:teacher link
5012:
5003:
4991:. Retrieved
4987:
4978:
4959:Sample space
4901:Games portal
4879:
4877:
4874:
4871:
4850:
4671:
4609:
4605:
4599:
4582:
4580:
4577:
4574:
4550:
4282:
4278:
4268:
4253:
4249:
4246:
4082:
3960:
3729:
3537:
3280:
2937:
2507:
2398:
2267:
2157:
2120:
2115:
2067:
2060:
2050:
2039:
2035:
2033:
2025:
2021:
2019:
2015:
2012:
1767:
1603:
1440:
1277:
1111:
951:
794:
638:
501:
410:
303:
301:
295:
291:
287:
283:
279:
272:
268:
265:odds against
264:
260:
254:
247:
243:
239:
161:sample space
156:
150:
143:
139:
133:
119:combinations
108:
93:
54:
38:
18:
6083:WikiProject
5994:Casino game
5960:New Zealand
5800:Philippines
5638:Mathematics
5486:Poker tools
5396:Let It Ride
5270:Check-raise
5189:Tournaments
4954:Probability
4949:Permutation
4914:Combination
4855:127,615,488
4686:Probability
4359:Probability
4199:0 : 1
4190:133,784,560
4080:/ High card
2154:Royal flush
2139:Probability
2102:133,784,560
1967:0 : 1
1765:/ High card
407:Royal flush
392:Probability
280:Probability
152:Probability
69:Frequencies
25:probability
6073:Wiktionary
6025:Gaming law
5758:Bangladesh
5705:Martingale
5665:Strategies
5332:Stud poker
5318:Draw poker
5304:Variations
5285:Protection
5260:Aggression
5177:Poker boom
5018:7 December
4993:7 December
4970:References
4964:Set theory
4836:13,939,200
4819:21,457,920
4816:Queen-high
4802:24,837,120
4785:23,675,904
4768:19,174,400
4751:13,171,200
4689:Cumulative
4594:See also:
4510:Queen-high
4362:Cumulative
4263:See also:
4111:23,294,460
3989:58,627,800
3758:31,433,400
2504:Full house
2142:Cumulative
1958:2,598,960
1799:1,302,540
1635:1,098,240
791:Full house
448:0.000154%
445:0.000154%
377:as above.
127:Wild cards
111:enumerates
104:hole cards
5955:Australia
5817:Singapore
5773:Hong Kong
5718:By region
5469:Computing
5460:Slow play
5280:Isolation
4880:A-2-3-4-6
4833:King-high
4799:Jack-high
4734:7,426,560
4717:3,151,360
4683:Frequency
4606:A-2-3-4-5
4583:A-2-3-4-6
4558:1,317,888
4530:King-high
4490:Jack-high
4356:Frequency
4279:A-2-3-4-5
4163:−
4157:−
4151:−
4133:×
4058:×
4052:×
4046:×
4035:−
3831:×
3819:×
3807:×
3796:×
3790:×
3701:−
3612:−
3566:6,461,620
3505:×
3480:×
3463:−
3452:×
3446:×
3440:×
3412:×
3406:×
3371:−
3365:−
3359:−
3341:×
3309:6,180,020
3228:×
3217:−
3187:×
3140:×
3129:−
3099:×
3047:−
3017:×
2966:4,047,644
2536:3,473,184
2136:Frequency
2051:A-Q-8-7-3
1909:−
1845:−
1802:50.1177%
1638:42.2569%
1213:−
1046:−
673:0.02401%
596:−
539:0.00154%
536:0.00139%
389:Frequency
296:Frequency
231:2,598,960
157:Frequency
144:including
140:Frequency
115:frequency
6100:Category
6053:Category
5827:Thailand
5795:Pakistan
5763:Cambodia
5612:Cardroom
5572:Gambling
5505:Category
5455:Pot odds
5437:Strategy
5217:Position
5205:Elements
5167:Glossary
5162:Cheating
5150:Overview
5065:Archived
4887:See also
4602:low hand
4275:low hand
4273:, use a
3957:One pair
3726:Two pair
3276:Straight
2045:8♦ Q♥ A♥
1600:One pair
1475:4.7539%
1472:123,552
1437:Two pair
1312:2.1128%
1146:0.3925%
1107:Straight
986:0.1965%
829:0.1441%
676:0.0255%
271:, where
248:at least
123:randomly
41:gambling
6063:Commons
5948:Oceania
5922:Ontario
5913:Canada
5883:Ukraine
5853:Estonia
5837:Vietnam
5737:Nigeria
5631:Science
5529:Outline
5517:Commons
5172:History
5157:Betting
4782:10-high
4700:781,824
4536:506,880
4516:337,920
4496:215,040
4476:129,024
4470:10-high
4382:0.0394%
4379:0.0394%
4271:lowball
4078:No pair
2427:224,848
2302:0.0311%
2299:0.0279%
2192:0.0032%
2189:0.0032%
1763:No pair
1309:54,912
1143:10,200
234:
222:
90:machine
35:History
6018:Issues
5974:Brazil
5917:Quebec
5904:Mexico
5878:Turkey
5873:Russia
5868:Norway
5858:France
5846:Europe
5832:Turkey
5822:Taiwan
5812:Russia
5805:Manila
5732:Angola
5725:Africa
5617:Racino
5595:Casino
5588:Venues
4765:9-high
4748:8-high
4731:7-high
4714:6-high
4706:0.584%
4703:0.584%
4697:5-high
4456:71,680
4450:9-high
4436:35,840
4430:8-high
4422:0.827%
4419:0.591%
4416:15,360
4410:7-high
4402:0.236%
4399:0.197%
4390:6-high
4370:5-high
4187:Total
2433:0.199%
2430:0.168%
2296:37,260
1955:7,462
1952:Total
1796:1,277
1641:49.9%
1632:2,860
1478:7.63%
1315:2.87%
1149:0.76%
989:0.37%
983:5,108
980:1,277
832:0.17%
826:3,744
286:, and
23:, the
5986:Games
5863:Italy
5790:Japan
5785:India
5778:Macau
5768:China
5290:Steal
5265:Bluff
5253:Plays
5232:Hands
5130:Poker
4861:95.4%
4858:95.4%
4851:Total
4842:95.4%
4839:10.4%
4825:85.0%
4822:16.0%
4808:68.9%
4805:18.6%
4791:50.4%
4788:17.7%
4774:32.7%
4771:14.3%
4757:18.3%
4754:9.85%
4740:8.49%
4737:5.55%
4723:2.94%
4720:2.36%
4610:wheel
4564:50.7%
4561:50.7%
4555:1,287
4551:Total
4542:50.7%
4539:19.5%
4522:31.2%
4519:13.0%
4502:18.2%
4499:8.27%
4482:9.93%
4479:4.96%
4462:4.96%
4459:2.76%
4442:2.21%
4439:1.38%
4396:5,120
4376:1,024
4283:wheel
4114:17.4%
3995:82.6%
3992:43.8%
3764:38.8%
3761:23.5%
3572:15.3%
3569:4.83%
3315:10.4%
3312:4.62%
2972:5.82%
2969:3.03%
2933:Flush
2542:2.80%
2539:2.60%
2186:4,324
2123:cards
2116:lower
1961:100%
1805:100%
947:Flush
312:with
21:poker
5751:Asia
5600:List
5348:Razz
5312:Brag
5275:Draw
5244:Tell
5212:Chip
5198:Play
5020:2015
4995:2015
4944:Odds
4680:Hand
4350:Hand
4193:100%
4130:1499
4117:100%
3787:1277
3508:2268
2133:Hand
2038:and
1964:---
1469:858
1306:858
823:156
670:624
667:156
383:Hand
316:and
302:The
294:and
288:Odds
256:Odds
253:The
149:The
98:and
29:hand
5222:Pot
4657:560
4651:784
4645:133
4533:495
4513:330
4493:210
4473:126
4330:960
4324:598
4196:---
4154:756
4061:990
3460:256
3415:990
3362:756
3338:217
3050:217
2043:7♣
1140:10
533:36
365:960
359:598
310:nCr
305:nCr
261:not
208:960
202:598
94:In
82:An
19:In
6102::
5927:BC
5011:.
4986:.
4628:52
4453:70
4433:35
4413:15
4301:52
4217:52
4166:84
4038:71
4021:13
3920:40
3869:13
3834:64
3822:63
3816:24
3810:62
3793:10
3615:10
3598:13
3477:10
3437:10
3409:36
3403:71
3374:84
3239:39
3220:10
3203:13
3143:39
3132:71
3115:13
3033:13
2823:11
2801:12
2779:13
2687:12
2665:13
2624:44
2573:13
2476:48
2454:13
2367:46
2235:47
2085:52
2041:3♦
1985:52
1856:10
1831:13
1706:12
1662:13
1550:11
1499:13
1380:12
1336:13
1224:10
1170:10
1057:10
1010:13
897:12
853:13
741:12
697:13
560:10
530:9
442:4
439:1
336:52
314:52
282:,
179:52
163:;
5564:e
5557:t
5550:v
5122:e
5115:t
5108:v
5022:.
4997:.
4654:,
4648:,
4642:=
4636:)
4631:7
4623:(
4393:5
4373:1
4327:,
4321:,
4318:2
4315:=
4309:)
4304:5
4296:(
4225:)
4220:7
4212:(
4170:]
4160:4
4146:7
4142:4
4137:[
4055:6
4049:6
4042:]
4029:)
4024:6
4016:(
4009:[
3935:]
3928:)
3923:1
3915:(
3907:3
3900:)
3895:2
3892:4
3887:(
3877:)
3872:3
3864:(
3857:[
3851:+
3843:]
3838:]
3828:6
3825:+
3813:+
3804:6
3800:[
3783:[
3708:]
3704:3
3696:4
3689:)
3684:1
3681:4
3676:(
3668:[
3661:)
3656:1
3653:4
3648:(
3639:)
3634:1
3631:5
3626:(
3619:]
3606:)
3601:5
3593:(
3586:[
3512:]
3499:)
3494:2
3491:5
3486:(
3474:+
3470:]
3466:3
3456:[
3449:4
3443:5
3433:[
3427:+
3419:]
3399:[
3391:+
3383:]
3378:]
3368:4
3354:7
3350:4
3345:[
3334:[
3254:]
3247:)
3242:2
3234:(
3224:]
3211:)
3206:5
3198:(
3191:[
3181:)
3176:1
3173:4
3168:(
3161:[
3155:+
3147:]
3136:]
3123:)
3118:6
3110:(
3103:[
3093:)
3088:1
3085:4
3080:(
3073:[
3067:+
3059:]
3054:]
3041:)
3036:7
3028:(
3021:[
3011:)
3006:1
3003:4
2998:(
2991:[
2911:]
2905:2
2898:)
2893:1
2890:4
2885:(
2875:)
2870:2
2867:4
2862:(
2853:)
2848:3
2845:4
2840:(
2831:)
2826:2
2818:(
2809:)
2804:1
2796:(
2787:)
2782:1
2774:(
2767:[
2761:+
2753:]
2747:2
2740:)
2735:2
2732:4
2727:(
2717:)
2712:3
2709:4
2704:(
2695:)
2690:2
2682:(
2673:)
2668:1
2660:(
2653:[
2647:+
2639:]
2632:)
2627:1
2619:(
2611:2
2604:)
2599:3
2596:4
2591:(
2581:)
2576:2
2568:(
2561:[
2484:)
2479:3
2471:(
2462:)
2457:1
2449:(
2375:)
2370:2
2362:(
2353:)
2348:1
2345:4
2340:(
2331:)
2326:1
2323:9
2318:(
2243:)
2238:2
2230:(
2221:)
2216:1
2213:4
2208:(
2099:=
2093:)
2088:7
2080:(
1993:)
1988:5
1980:(
1935:]
1928:)
1923:1
1920:4
1915:(
1904:5
1897:)
1892:1
1889:4
1884:(
1876:[
1871:]
1864:)
1859:1
1851:(
1839:)
1834:5
1826:(
1819:[
1744:3
1737:)
1732:1
1729:4
1724:(
1714:)
1709:3
1701:(
1692:)
1687:2
1684:4
1679:(
1670:)
1665:1
1657:(
1580:)
1575:1
1572:4
1567:(
1558:)
1553:1
1545:(
1537:2
1530:)
1525:2
1522:4
1517:(
1507:)
1502:2
1494:(
1418:2
1411:)
1406:1
1403:4
1398:(
1388:)
1383:2
1375:(
1366:)
1361:3
1358:4
1353:(
1344:)
1339:1
1331:(
1254:)
1249:1
1246:4
1241:(
1232:)
1227:1
1219:(
1208:5
1201:)
1196:1
1193:4
1188:(
1178:)
1173:1
1165:(
1087:)
1082:1
1079:4
1074:(
1065:)
1060:1
1052:(
1040:)
1035:1
1032:4
1027:(
1018:)
1013:5
1005:(
927:)
922:2
919:4
914:(
905:)
900:1
892:(
883:)
878:3
875:4
870:(
861:)
856:1
848:(
771:)
766:1
763:4
758:(
749:)
744:1
736:(
727:)
722:4
719:4
714:(
705:)
700:1
692:(
615:)
610:1
607:4
602:(
590:)
585:1
582:4
577:(
568:)
563:1
555:(
477:)
472:1
469:4
464:(
362:,
356:,
353:2
350:=
344:)
339:5
331:(
318:5
273:p
228:/
225:4
205:,
199:,
196:2
193:=
187:)
182:5
174:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
