1659:
1029:
1654:{\displaystyle P'(a,b,n_{e},n_{w})={\frac {S}{T}}={\frac {(a+b)!}{a!b!}}\times {\frac {n_{e}!n_{w}!(n_{e}+n_{w}-a-b)!}{(n_{e}+n_{w})!(n_{e}-a)!(n_{w}-b)!}}={\binom {a+b}{a}}{\frac {n_{e}!n_{w}!(n_{e}+n_{w}-a-b)!}{(n_{e}+n_{w})!(n_{e}-a)!(n_{w}-b)!}}={\frac {{\binom {a+b}{a}}{\binom {n_{e}+n_{w}-a-b}{n_{e}-a}}}{\binom {n_{e}+n_{w}}{n_{e}}}}}
3543:
3 would be unlikely to give a different result. To make the irrelevance of small cards explicit (which is not always the case though), in bridge such small cards are generally denoted by an 'x'. Thus, the "number of possible deals" in this sense depends on how many non-honour cards (2, 3, .. 9) are
2335:
that a given hand contains no more than a specified number of HCP is given in the table below. To find the likelihood of a certain point range, one simply subtracts the two relevant cumulative probabilities. So, the likelihood of being dealt a 12-19 HCP hand (ranges inclusive) is the probability of
2182:
The more general formula can be used to calculate the probability of a suit breaking if a player is known to have cards in another suit from e.g. the bidding. Suppose East is known to have 7 spades from the bidding and after seeing dummy you deduce West to hold 2 spades; then if your two lines of
23:
mathematical probabilities play a significant role. Different declarer play strategies lead to success depending on the distribution of opponent's cards. To decide which strategy has highest likelihood of success, the declarer needs to have at least an elementary knowledge of probabilities.
2649:
Note that the hand pattern leaves unspecified which particular suits contain the indicated lengths. For a 4-4-3-2 pattern, one needs to specify which suit contains the three-card and which suit contains the doubleton in order to identify the length in each of the four suits. There are four
2180:
1912:
3206:
6-3-2-2, 6-3-3-1, 6-4-2-1, 6-4-3-0, 7-2-2-2, 7-3-2-1, 7-3-3-0, 7-4-1-1, 7-4-2-0, 7-5-1-0, 8-2-2-1, 8-3-1-1, 8-3-2-0, 8-4-1-0, 8-5-0-0, 9-2-1-1, 9-2-2-0, 9-3-1-0, 9-4-0-0, 10-1-1-1, 10-2-1-0, 10-3-0-0, 11-1-1-0, 11-2-0-0, 12-1-0-0,
1024:
2657:
Below table lists all 39 possible hand patterns, their probability of occurrence, as well as the number of suit permutations for each pattern. The list is ordered according to likelihood of occurrence of the hand patterns.
3473:) different hands that one player can hold. Furthermore, when the remaining 39 cards are included with all their combinations there are 53,644,737,765,488,792,839,237,440,000 (53.6 x 10) different deals possible (
804:
3544:
considered 'indistinguishable'. For example, if 'x' notation is applied to all cards smaller than ten, then the suit distributions A987-K106-Q54-J32 and A432-K105-Q76-J98 would be considered identical.
31:, i.e. the probabilities in the absence of any further information. During bidding and play, more information about the hands becomes available, allowing players to improve their probability estimates.
1970:
3977:
Second French edition by the authors in 1954. Translated and edited into
English by Alec Traub as The Mathematical Theory of Bridge; printed in 1974 in Taiwan through the assistance of C.C. Wei.
3420:
5-4-4-0, 5-5-3-0, 6-4-3-0, 6-5-2-0, 6-6-1-0, 7-3-3-0, 7-4-2-0, 7-5-1-0, 7-6-0-0, 8-3-2-0, 8-4-1-0, 8-5-0-0, 9-2-2-0, 9-3-1-0, 9-4-0-0, 10-2-1-0, 10-3-0-0, 11-1-1-0, 11-2-0-0, 12-1-0-0, 13-0-0-0
5110:
4050:
2321:
2253:
3666:
Note that the last entry in the table (37,478,624) corresponds to the number of different distributions of the deck (the number of deals when cards are only distinguished by their suit).
507:
1724:
3471:
1965:
3518:
854:
679:
856:
objects of which cards in the suit are indistinguishable and cards not in the suit are indistinguishable. The number of arrangements of which correspond to East having
4043:
633:
581:
534:
1719:
1699:
1679:
894:
874:
601:
554:
5236:
5635:
5231:
5131:
899:
5671:
5535:
5530:
5271:
5246:
5241:
5201:
5186:
5151:
5141:
4036:
5890:
5666:
5276:
5176:
5156:
5136:
5880:
5450:
5261:
5256:
5226:
5221:
5216:
5181:
5161:
5146:
5297:
5251:
5206:
5196:
5191:
5166:
2636:
denotes the distribution of the thirteen cards in a hand over the four suits. In total 39 hand patterns are possible, but only 13 of them have an
6161:
5509:
5266:
5211:
5171:
62:
The table also shows the number of combinations of particular cards that match any numerical split and the probabilities for each combination.
2654:
of the 4-4-3-2 pattern is twelve. Or, stated differently, in total there are twelve ways a 4-4-3-2 pattern can be mapped onto the four suits.
5999:
5445:
684:
6034:
5830:
3873:
2331:
High card points (HCP) are usually counted using the Milton Work scale of 4/3/2/1 points for each Ace/King/Queen/Jack respectively. The
6041:
5870:
5745:
6072:
4377:
4173:
4019:
3993:
3886:
52:
48:
5302:
4653:
2650:
possibilities to first identify the three-card suit and three possibilities to next identify the doubleton. Hence, the number of
5905:
5625:
5620:
5595:
5590:
5465:
5460:
5395:
4931:
3878:
5900:
5765:
5755:
5695:
5640:
5610:
5605:
5292:
5105:
4713:
5760:
3238:
Alternative grouping of the 39 hand patterns can be made either by longest suit or by shortest suit. Below tables gives the
6020:
5959:
5615:
3522:
How large an area would you need to spread all possible bridge deals if each deal would occupy only one square millimeter?
5790:
5690:
5585:
2642:
exceeding 1%. The most likely pattern is the 4-4-3-2 pattern consisting of two four-card suits, a three-card suit and a
2258:
2190:
5885:
5820:
5800:
5705:
5455:
5440:
5405:
5390:
4956:
4614:
5986:
5915:
5580:
5420:
5410:
5400:
4183:
4158:
4133:
3527:
2175:{\displaystyle P(a,b)=P(a,b,13,13)={\binom {a+b}{a}}{\frac {13!13!(26-a-b)!}{26!(13-a)!(13-b)!}}(2-\delta _{a,b})}
5976:
5825:
5100:
4407:
4397:
3547:
The table below gives the number of deals when various numbers of small cards are considered indistinguishable.
6006:
5710:
4188:
1918:
ensures that the situation where East and West have the same number of cards in the suit is not counted twice.
5920:
5700:
5740:
5600:
5470:
5425:
5359:
4488:
4148:
3409:
4-4-4-1, 5-4-3-1, 5-5-2-1, 6-3-3-1, 6-4-2-1, 6-5-1-1, 7-3-2-1, 7-4-1-1, 8-2-2-1, 8-3-1-1, 9-2-1-1, 10-1-1-1
6048:
5780:
5565:
5540:
5435:
5369:
4971:
4916:
4457:
446:
5860:
5855:
5415:
4966:
4673:
4548:
4523:
5354:
4852:
4553:
39:
This table represents the different ways that two to eight particular cards may be distributed, or may
6055:
5850:
5835:
5805:
5735:
5730:
5560:
5430:
5364:
4392:
3437:
2638:
2332:
2336:
having at most 19 HCP minus the probability of having at most 11 HCP, or: 0.9855 â 0.6518 = 0.3337.
1924:
6116:
5815:
5810:
5630:
5115:
4961:
4936:
4901:
4357:
4228:
3476:
813:
638:
6027:
5964:
5910:
5865:
5344:
5328:
5318:
4598:
4417:
4362:
4282:
4233:
4218:
4128:
4108:
3675:
6085:
4528:
6132:
5895:
5795:
5775:
5676:
5545:
4946:
4832:
4753:
4733:
4593:
4518:
4422:
4347:
4302:
4178:
4015:
3989:
3892:
3882:
28:
6099:
5840:
5750:
5031:
5010:
4926:
4896:
4886:
4881:
4698:
4693:
4493:
4412:
4322:
4168:
4163:
4153:
4123:
1907:{\displaystyle P(a,b,n_{e},n_{w})=P'(a,b,n_{e},n_{w})+(1-\delta _{a,b})P'(b,a,n_{e},n_{w})}
606:
559:
512:
6092:
5720:
5715:
5575:
5056:
5026:
4822:
4812:
4748:
4703:
4352:
4342:
4312:
4213:
4203:
4143:
4138:
4059:
3955:
1915:
20:
4837:
4588:
4007:
6013:
5661:
5349:
4996:
4981:
4951:
4941:
4906:
4842:
4827:
4743:
4668:
4658:
4573:
4503:
4442:
4297:
4292:
4113:
4088:
4014:. Master Bridge Series. London: Victor Gollancz Ltd in association with Peter Crawley.
3988:. Master Bridge Series. London: Victor Gollancz Ltd in association with Peter Crawley.
1704:
1684:
1664:
879:
859:
586:
539:
6155:
5785:
5555:
5550:
5051:
5041:
4986:
4976:
4921:
4911:
4891:
4857:
4847:
4817:
4802:
4758:
4688:
4678:
4427:
4307:
4277:
4208:
4103:
4098:
4093:
4003:
3868:
3158:
3154:
1019:{\displaystyle S={\frac {n_{e}!}{a!(n_{e}-a)!}}\times {\frac {n_{w}!}{b!(n_{w}-b)!}}}
66:
1661:
If the direction of the split is unimportant (it is only required that the split be
5725:
5525:
5061:
5036:
4991:
4738:
4728:
4708:
4583:
4558:
4467:
4462:
4447:
4332:
4223:
4193:
4118:
3166:
5981:
5656:
5323:
4867:
4788:
4568:
4533:
4513:
4437:
4402:
4327:
4287:
3981:
3242:
chance of being dealt a hand with a longest or a shortest suit of given length.
807:
35:
Probability of suit distributions (for missing trumps, etc.) in two hidden hands
3933:
3520:) The immenseness of this number can be understood by answering the question "
5770:
5570:
5374:
5046:
4862:
4578:
4472:
4452:
4432:
4372:
4367:
4198:
3162:
5845:
4807:
4663:
4508:
2643:
5875:
4543:
4382:
4337:
3944:
4783:
4683:
4563:
4387:
4317:
4238:
1967:
and that the direction of the split is unimportant, and so are given by
3218:
5-4-2-2, 5-4-3-1, 5-5-2-1, 5-5-3-0, 6-5-1-1, 6-5-2-0, 6-6-1-0, 7-6-0-0
4723:
3535:
Obviously, the deals that are identical except for swappingâsayâthe
2323:
so now the club line is significantly better than the diamond line.
799:{\displaystyle T={\frac {(n_{e}+n_{w})!}{(n_{e}+n_{w}-a-b)!(a+b)!}}}
3922:
3910:
3678:
is an alternative to the HCP count as a method of hand evaluation.
4028:
4538:
4498:
3896:
5941:
5491:
5082:
4635:
4259:
4070:
4032:
5293:
List of bridge people with
Knowledge (XXG) (English) articles
3295:
7-2-2-2, 7-3-2-1, 7-3-3-0, 7-4-1-1, 7-4-2-0, 7-5-1-0, 7-6-0-0
3284:
6-3-2-2, 6-3-3-1, 6-4-2-1, 6-4-3-0, 6-5-1-1, 6-5-2-0, 6-6-1-0
603:
cards in the given suit. The total number of arrangements of
2183:
play are to hope either for diamonds 5-3 or clubs 4-2, the
3945:
3934:
75:
Number of cards (trumps, etc.) missing from partnership
3479:
3440:
2261:
2193:
1973:
1927:
1727:
1707:
1687:
1667:
1032:
902:
882:
862:
816:
687:
641:
609:
589:
562:
542:
515:
449:
3273:
5-3-3-2, 5-4-2-2, 5-4-3-1, 5-5-2-1, 5-4-4-0, 5-5-3-0
65:
These probabilities follow directly from the law of
6125:
6109:
6065:
5952:
5649:
5518:
5502:
5383:
5337:
5311:
5285:
5124:
5093:
5019:
4767:
4646:
4607:
4481:
4270:
4081:
3512:
3465:
2315:
2247:
2174:
1959:
1906:
1713:
1693:
1673:
1653:
1018:
888:
868:
848:
798:
673:
627:
595:
575:
548:
528:
501:
3457:
3444:
3149:The 39 hand patterns can by classified into four
2316:{\displaystyle P(4,2,13-7,13-2)\thickapprox 47\%}
2248:{\displaystyle P(5,3,13-7,13-2)\thickapprox 42\%}
2052:
2031:
1701:, not that East is specifically required to hold
1326:
1305:
3173:likelihoods of being dealt a certain hand-type.
1721:cards), then the overall probability is given by
47:, between two unknown 13-card hands (before the
16:Mathematical probabilities in the game of bridge
2187:probabilities are 47% and 48% respectively but
3526:an area more than a hundred million times the
4044:
1644:
1602:
1593:
1531:
1522:
1501:
556:cards in a given suit and a West player with
8:
5636:World Transnational Open Teams Championship
3398:4-4-3-2, 5-3-3-2, 5-4-2-2, 6-3-2-2, 7-2-2-2
3306:8-2-2-1, 8-3-1-1, 8-3-2-0, 8-4-1-0, 8-5-0-0
5949:
5938:
5672:European Universities Bridge Championships
5536:Bridge at the 2012 World Mind Sports Games
5531:Bridge at the 2008 World Mind Sports Games
5499:
5488:
5090:
5079:
4643:
4632:
4267:
4256:
4078:
4067:
4051:
4037:
4029:
3909:Richard Pavlicek. "High Card Expectancy."
509:be the probability of an East player with
5891:United States Bridge Championships - Open
5667:Commonwealth Nations Bridge Championships
3504:
3486:
3478:
3456:
3443:
3441:
3439:
2260:
2192:
2157:
2058:
2051:
2030:
2028:
1972:
1945:
1932:
1926:
1895:
1882:
1840:
1815:
1802:
1763:
1750:
1726:
1706:
1686:
1666:
1643:
1636:
1625:
1612:
1601:
1592:
1578:
1554:
1541:
1530:
1528:
1521:
1500:
1498:
1495:
1471:
1446:
1427:
1414:
1381:
1368:
1352:
1339:
1332:
1325:
1304:
1302:
1278:
1253:
1234:
1221:
1188:
1175:
1159:
1146:
1139:
1098:
1085:
1073:
1060:
1031:
995:
971:
964:
940:
916:
909:
901:
881:
861:
837:
824:
815:
751:
738:
717:
704:
694:
686:
662:
649:
640:
608:
588:
567:
561:
541:
520:
514:
490:
477:
448:
5451:List of contract bridge governing bodies
3680:
3549:
3369:
3244:
3175:
2984:
2824:
2664:
2338:
71:
3855:
3564:53,644,737,765,488,792,839,237,440,000
2304:
2236:
5510:List of bridge competitions and awards
5111:List of nationality transfers in sport
3921:Richard Pavlicek. "Against All Odds."
3572:7,811,544,503,918,790,990,995,915,520
6000:25 Bridge Conventions You Should Know
5881:Sternberg Women's Board-a-Match Teams
5446:International Mind Sports Association
3861:
3859:
27:The tables below specify the various
7:
5684:North American bridge Championships:
3971:Ămile, Borel; AndrĂ©, ChĂ©ron (1940).
3580:445,905,120,201,773,774,566,940,160
6035:The Official Encyclopedia of Bridge
5831:North American Bridge Championships
3874:The Official Encyclopedia of Bridge
3871:; Francis, Dorthy A., eds. (1994).
3588:14,369,217,850,047,151,709,620,800
502:{\displaystyle P'(a,b,n_{e},n_{w})}
6042:Planning the Play of a Bridge Hand
5746:Keohane North American Swiss Teams
3670:Probability of Losing-Trick Counts
3448:
3430:Number of possible hands and deals
3317:9-2-1-1, 9-2-2-0, 9-3-1-0, 9-4-0-0
2310:
2242:
2035:
1606:
1535:
1505:
1309:
14:
6073:List of contract bridge magazines
4378:Optimum contract and par contract
4174:Glossary of contract bridge terms
3986:Bridge Odds for Practical Players
3865:"Mathematical Tables" (Table 4).
3596:314,174,475,847,313,213,527,680
5871:Smith Life Master Women's Pairs
5626:World Senior Teams Championship
5621:World Senior Pairs Championship
5596:World Junior Teams Championship
5591:World Junior Pairs Championship
5466:United States Bridge Federation
5461:South African Bridge Federation
5396:American Contract Bridge League
4932:Non-simultaneous double squeeze
3879:American Contract Bridge League
3466:{\displaystyle {52 \choose 13}}
2327:Probability of HCP distribution
1921:The above probabilities assume
5901:Von Zedtwitz Life Master Pairs
5766:Manfield Non-Life Master Pairs
5756:Leventritt Silver Ribbon Pairs
5696:Edgar Kaplan Blue Ribbon Pairs
5641:World Women Pairs Championship
5611:World Mixed Teams Championship
5606:World Mixed Pairs Championship
5106:List of contract bridge people
4714:Principle of restricted choice
3973:Théorie Mathématique du Bridge
3604:5,197,480,921,767,366,548,160
3540:
3536:
3501:
3491:
2301:
2265:
2233:
2197:
2169:
2144:
2135:
2123:
2117:
2105:
2091:
2073:
2022:
1998:
1989:
1977:
1960:{\displaystyle n_{e}=n_{w}=13}
1901:
1863:
1852:
1827:
1821:
1783:
1769:
1731:
1483:
1464:
1458:
1439:
1433:
1407:
1399:
1361:
1290:
1271:
1265:
1246:
1240:
1214:
1206:
1168:
1113:
1101:
1079:
1041:
1007:
988:
952:
933:
896:cards in the suit is given by
843:
817:
787:
775:
769:
731:
723:
697:
668:
642:
622:
610:
496:
458:
1:
6162:Contract bridge probabilities
6021:Contract Bridge for Beginners
5960:List of contract bridge books
5616:World Open Pairs Championship
5298:List of bridge administrators
3877:(5th ed.). Memphis, TN:
3513:{\displaystyle 52!/(13!)^{4}}
849:{\displaystyle (n_{e}+n_{w})}
674:{\displaystyle (n_{e}+n_{w})}
5906:Wagar Women's Knockout Teams
5791:Mitchell Board-a-Match Teams
5691:ACBL King or Queen of Bridge
5586:World IMP Pairs Championship
3553:Highest undistinguished card
3328:10-1-1-1, 10-2-1-0, 10-3-0-0
439:Calculation of probabilities
5886:Truscott Senior Swiss Teams
5821:Non-Life Master Swiss Teams
5801:Nail Life Master Open Pairs
5761:Machlin Women's Swiss Teams
5706:Chicago Mixed Board-a-Match
5456:Norwegian Bridge Federation
5441:Hungarian Bridge Federation
5406:Brazilian Bridge Federation
5391:American Bridge Association
4957:Simultaneous double squeeze
4615:List of bidding conventions
3984:; Glauert, Michael (1980).
3659:
3651:
3643:
3635:
3627:
3619:
3612:69,848,690,581,204,198,656
3611:
3603:
3595:
3587:
3579:
3571:
3563:
3434:There are 635,013,559,600 (
3136:
3081:
2877:
2783:
2728:
876:cards in the suit and West
6178:
5987:Terence Reese bibliography
5943:Publications and resources
5581:World Bridge Championships
5421:Canadian Bridge Federation
5411:Bridge Federation of India
5401:Austrian Bridge Federation
4184:History of contract bridge
4159:Duplicate bridge movements
2628:Hand pattern probabilities
5977:Edwin Kantar bibliography
5948:
5937:
5826:Norman Kay Platinum Pairs
5498:
5487:
5101:ACBL Youngest Life Master
5089:
5078:
4642:
4631:
4408:Quantitative notrump bids
4398:Principle of fast arrival
4266:
4255:
4077:
4066:
4012:Master the Odds in Bridge
3262:4-3-3-3, 4-4-3-2, 4-4-4-1
3193:4-3-3-3, 4-4-3-2, 5-3-3-2
2371:
2363:
2355:
2347:
363:
304:
245:
200:
155:
124:
93:
74:
6007:Bridge Squeezes Complete
5982:Hugh Kelsey bibliography
5711:Fall National Open Pairs
5084:People and organizations
4189:Laws of Duplicate Bridge
3620:800,827,437,699,287,808
3169:. Below table gives the
5916:Whitehead Women's Pairs
5741:Jacoby Open Swiss Teams
5601:World Mind Sports Games
5471:World Bridge Federation
5426:Dutch Bridge Federation
5360:Galatasaray Bridge Team
4654:List of play techniques
4489:List of bidding systems
4149:Contract bridge diagram
6049:Right Through the Pack
5781:Mini-Blue Ribbon Pairs
5566:Triple crown of bridge
5541:Cavendish Invitational
5436:European Bridge League
5370:Portland Club (London)
5303:List of bridge writers
4972:Stepping-stone squeeze
4917:Entry-shifting squeeze
4554:Kaplan–Sheinwold
4458:Useful space principle
3628:8,110,864,720,503,360
3514:
3467:
2333:a priori probabilities
2317:
2249:
2176:
1961:
1908:
1715:
1695:
1675:
1655:
1020:
890:
870:
850:
800:
675:
629:
597:
583:unknown cards holding
577:
550:
536:unknown cards holding
530:
503:
5861:Senior Knockout Teams
5856:Roth Open Swiss Teams
5416:British Bridge League
4549:Highly unusual method
4524:Bridge World Standard
3956:Counting Bridge Deals
3515:
3468:
2318:
2250:
2177:
1962:
1909:
1716:
1696:
1676:
1656:
1021:
891:
871:
851:
801:
676:
635:cards in the suit in
630:
628:{\displaystyle (a+b)}
598:
578:
576:{\displaystyle n_{w}}
551:
531:
529:{\displaystyle n_{e}}
504:
6056:Tickets to the Devil
5851:Rockwell Mixed Pairs
5836:North American Pairs
5806:National 199er Pairs
5736:Hilliard Mixed Pairs
5731:Grand National Teams
5561:Senior Bowl (bridge)
5431:English Bridge Union
5365:Melville Bridge Club
4393:Prepared opening bid
3477:
3438:
2639:a priori probability
2259:
2191:
1971:
1925:
1725:
1705:
1685:
1665:
1030:
900:
880:
860:
814:
685:
639:
607:
587:
560:
540:
513:
447:
6117:Grand Slam (BBC TV)
5921:Young LMâ1500 Pairs
5816:National 99er Pairs
5811:National 49er Pairs
5701:Bruce LMâ5000 Pairs
5631:World Team Olympiad
5116:Bridge Headquarters
4962:Single-suit squeeze
4937:Progressive squeeze
4902:Criss-cross squeeze
4358:Law of total tricks
4229:Traveling scoreslip
3975:. Gauthier-Villars.
3867:Francis, Henry G.;
3636:74,424,657,938,928
806:i.e. the number of
29:prior probabilities
6028:Design for Bidding
5965:Master Point Press
5911:Wernher Open Pairs
5866:Silodor Open Pairs
5650:National and Zonal
5345:Bridge Base Online
5125:Players by country
5004:Suit combinations:
4853:Morton's fork coup
4599:Strong club system
4418:Sacrifice (bridge)
4363:Losing-Trick Count
4283:Balancing (bridge)
4219:Singaporean bridge
4129:Cheating in bridge
4109:Bridge Murder case
3958:, Jeroen Warmerdam
3676:Losing-Trick Count
3524:". The answer is:
3510:
3463:
3339:11-1-1-0, 11-2-0-0
2313:
2245:
2172:
1957:
1904:
1711:
1691:
1671:
1651:
1016:
886:
866:
846:
796:
671:
625:
593:
573:
546:
526:
499:
6149:
6148:
6145:
6144:
6141:
6140:
6133:Bridge Base Basic
5933:
5932:
5929:
5928:
5896:Vanderbilt Trophy
5796:Mott-Smith Trophy
5776:Master Individual
5677:Gold Cup (bridge)
5546:Computer Olympiad
5483:
5482:
5479:
5478:
5074:
5073:
5070:
5069:
4947:Saturated squeeze
4833:Deschapelles coup
4627:
4626:
4623:
4622:
4594:Standard American
4519:Bridge Base Basic
4423:Shooting (bridge)
4348:Honor point count
4303:Bridge convention
4251:
4250:
4247:
4246:
4179:High card by suit
3869:Truscott, Alan F.
3848:
3847:
3841:12 is the maximum
3664:
3663:
3455:
3427:
3426:
3368:
3367:
3236:
3235:
3147:
3146:
3141:
3140:
2981:
2980:
2821:
2820:
2652:suit permutations
2625:
2624:
2142:
2050:
1714:{\displaystyle a}
1694:{\displaystyle b}
1674:{\displaystyle a}
1649:
1642:
1591:
1520:
1490:
1324:
1297:
1134:
1093:
1014:
959:
889:{\displaystyle b}
869:{\displaystyle a}
794:
596:{\displaystyle b}
549:{\displaystyle a}
436:
435:
6169:
6100:The Bridge World
6082:
6081:
5996:
5995:
5974:
5973:
5950:
5939:
5841:Red Ribbon Pairs
5751:Lebhar IMP Pairs
5686:
5685:
5500:
5489:
5384:Governing bodies
5091:
5080:
5032:Journalist leads
5011:Suit combination
5006:
5005:
4927:Knockout squeeze
4897:Compound squeeze
4887:Cannibal squeeze
4882:Backwash squeeze
4877:
4876:
4798:
4797:
4779:
4778:
4694:Grosvenor gambit
4644:
4633:
4494:2/1 game forcing
4413:Reverse (bridge)
4323:Five-card majors
4268:
4257:
4164:Five-suit bridge
4154:Duplicate bridge
4079:
4068:
4053:
4046:
4039:
4030:
4025:
3999:
3976:
3959:
3953:
3947:
3942:
3936:
3931:
3925:
3919:
3913:
3907:
3901:
3900:
3863:
3681:
3644:630,343,600,320
3556:Number of deals
3550:
3542:
3538:
3519:
3517:
3516:
3511:
3509:
3508:
3490:
3472:
3470:
3469:
3464:
3462:
3461:
3460:
3447:
3370:
3245:
3229:4-4-4-1, 5-4-4-0
3176:
2985:
2825:
2665:
2661:
2660:
2339:
2322:
2320:
2319:
2314:
2254:
2252:
2251:
2246:
2181:
2179:
2178:
2173:
2168:
2167:
2143:
2141:
2097:
2059:
2057:
2056:
2055:
2046:
2034:
1966:
1964:
1963:
1958:
1950:
1949:
1937:
1936:
1913:
1911:
1910:
1905:
1900:
1899:
1887:
1886:
1862:
1851:
1850:
1820:
1819:
1807:
1806:
1782:
1768:
1767:
1755:
1754:
1720:
1718:
1717:
1712:
1700:
1698:
1697:
1692:
1680:
1678:
1677:
1672:
1660:
1658:
1657:
1652:
1650:
1648:
1647:
1641:
1640:
1631:
1630:
1629:
1617:
1616:
1605:
1599:
1598:
1597:
1596:
1590:
1583:
1582:
1572:
1559:
1558:
1546:
1545:
1534:
1527:
1526:
1525:
1516:
1504:
1496:
1491:
1489:
1476:
1475:
1451:
1450:
1432:
1431:
1419:
1418:
1405:
1386:
1385:
1373:
1372:
1357:
1356:
1344:
1343:
1333:
1331:
1330:
1329:
1320:
1308:
1298:
1296:
1283:
1282:
1258:
1257:
1239:
1238:
1226:
1225:
1212:
1193:
1192:
1180:
1179:
1164:
1163:
1151:
1150:
1140:
1135:
1133:
1119:
1099:
1094:
1086:
1078:
1077:
1065:
1064:
1040:
1025:
1023:
1022:
1017:
1015:
1013:
1000:
999:
980:
976:
975:
965:
960:
958:
945:
944:
925:
921:
920:
910:
895:
893:
892:
887:
875:
873:
872:
867:
855:
853:
852:
847:
842:
841:
829:
828:
805:
803:
802:
797:
795:
793:
756:
755:
743:
742:
729:
722:
721:
709:
708:
695:
680:
678:
677:
672:
667:
666:
654:
653:
634:
632:
631:
626:
602:
600:
599:
594:
582:
580:
579:
574:
572:
571:
555:
553:
552:
547:
535:
533:
532:
527:
525:
524:
508:
506:
505:
500:
495:
494:
482:
481:
457:
72:
6177:
6176:
6172:
6171:
6170:
6168:
6167:
6166:
6152:
6151:
6150:
6137:
6121:
6105:
6093:Bridge Magazine
6086:Bridge d'Italia
6079:
6078:
6061:
5993:
5992:
5972:Bibliographies:
5971:
5970:
5944:
5925:
5721:Fishbein Trophy
5716:Fast Open Pairs
5683:
5682:
5645:
5576:WBF Youth Award
5514:
5494:
5475:
5379:
5333:
5307:
5281:
5120:
5085:
5066:
5027:Forcing defense
5015:
5003:
5002:
4874:
4873:
4823:Coup en passant
4813:Belladonna coup
4795:
4794:
4776:
4775:
4763:
4749:Trump promotion
4704:Percentage play
4638:
4619:
4603:
4529:Canapé (bridge)
4477:
4353:Inverted minors
4343:Hand evaluation
4313:Convention card
4262:
4243:
4204:Neuberg formula
4144:Contract bridge
4139:Computer bridge
4073:
4062:
4060:Contract bridge
4057:
4022:
4002:
3996:
3980:
3970:
3967:
3965:Further reading
3962:
3954:
3950:
3943:
3939:
3932:
3928:
3920:
3916:
3908:
3904:
3889:
3881:. p. 278.
3866:
3864:
3857:
3853:
3797:100,454,895,360
3786:145,394,132,760
3775:145,971,648,360
3764:104,416,332,340
3687:Number of Hands
3672:
3528:surface area of
3500:
3475:
3474:
3442:
3436:
3435:
3432:
3364:0.000000000006
3202:
3134:0.0000000000063
2630:
2329:
2257:
2256:
2189:
2188:
2153:
2098:
2060:
2036:
2029:
1969:
1968:
1941:
1928:
1923:
1922:
1916:Kronecker delta
1891:
1878:
1855:
1836:
1811:
1798:
1775:
1759:
1746:
1723:
1722:
1703:
1702:
1683:
1682:
1663:
1662:
1632:
1621:
1608:
1607:
1600:
1574:
1573:
1550:
1537:
1536:
1529:
1506:
1499:
1497:
1467:
1442:
1423:
1410:
1406:
1377:
1364:
1348:
1335:
1334:
1310:
1303:
1274:
1249:
1230:
1217:
1213:
1184:
1171:
1155:
1142:
1141:
1120:
1100:
1069:
1056:
1033:
1028:
1027:
991:
981:
967:
966:
936:
926:
912:
911:
898:
897:
878:
877:
858:
857:
833:
820:
812:
811:
747:
734:
730:
713:
700:
696:
683:
682:
658:
645:
637:
636:
605:
604:
585:
584:
563:
558:
557:
538:
537:
516:
511:
510:
486:
473:
450:
445:
444:
441:
88:
37:
19:In the game of
17:
12:
11:
5:
6175:
6173:
6165:
6164:
6154:
6153:
6147:
6146:
6143:
6142:
6139:
6138:
6136:
6135:
6129:
6127:
6126:External links
6123:
6122:
6120:
6119:
6113:
6111:
6107:
6106:
6104:
6103:
6096:
6089:
6075:
6069:
6067:
6063:
6062:
6060:
6059:
6052:
6045:
6038:
6031:
6024:
6017:
6014:The Cardturner
6010:
6003:
5989:
5984:
5979:
5967:
5962:
5956:
5954:
5946:
5945:
5942:
5935:
5934:
5931:
5930:
5927:
5926:
5924:
5923:
5918:
5913:
5908:
5903:
5898:
5893:
5888:
5883:
5878:
5873:
5868:
5863:
5858:
5853:
5848:
5843:
5838:
5833:
5828:
5823:
5818:
5813:
5808:
5803:
5798:
5793:
5788:
5783:
5778:
5773:
5768:
5763:
5758:
5753:
5748:
5743:
5738:
5733:
5728:
5723:
5718:
5713:
5708:
5703:
5698:
5693:
5688:
5679:
5674:
5669:
5664:
5662:Camrose Trophy
5659:
5653:
5651:
5647:
5646:
5644:
5643:
5638:
5633:
5628:
5623:
5618:
5613:
5608:
5603:
5598:
5593:
5588:
5583:
5578:
5573:
5568:
5563:
5558:
5553:
5548:
5543:
5538:
5533:
5528:
5522:
5520:
5516:
5515:
5513:
5512:
5506:
5504:
5496:
5495:
5492:
5485:
5484:
5481:
5480:
5477:
5476:
5474:
5473:
5468:
5463:
5458:
5453:
5448:
5443:
5438:
5433:
5428:
5423:
5418:
5413:
5408:
5403:
5398:
5393:
5387:
5385:
5381:
5380:
5378:
5377:
5372:
5367:
5362:
5357:
5352:
5350:Cavendish Club
5347:
5341:
5339:
5335:
5334:
5332:
5331:
5326:
5321:
5315:
5313:
5309:
5308:
5306:
5305:
5300:
5295:
5289:
5287:
5283:
5282:
5280:
5279:
5274:
5269:
5264:
5259:
5254:
5249:
5244:
5239:
5234:
5229:
5224:
5219:
5214:
5209:
5204:
5199:
5194:
5189:
5184:
5179:
5174:
5169:
5164:
5159:
5154:
5149:
5144:
5139:
5134:
5128:
5126:
5122:
5121:
5119:
5118:
5113:
5108:
5103:
5097:
5095:
5087:
5086:
5083:
5076:
5075:
5072:
5071:
5068:
5067:
5065:
5064:
5059:
5054:
5049:
5044:
5039:
5034:
5029:
5023:
5021:
5017:
5016:
5014:
5013:
5008:
4999:
4997:Winkle squeeze
4994:
4989:
4984:
4982:Triple squeeze
4979:
4974:
4969:
4964:
4959:
4954:
4952:Simple squeeze
4949:
4944:
4942:Pseudo-squeeze
4939:
4934:
4929:
4924:
4919:
4914:
4909:
4907:Double squeeze
4904:
4899:
4894:
4889:
4884:
4879:
4870:
4865:
4860:
4855:
4850:
4845:
4843:Loser on loser
4840:
4835:
4830:
4828:Crocodile coup
4825:
4820:
4815:
4810:
4805:
4800:
4791:
4786:
4781:
4771:
4769:
4765:
4764:
4762:
4761:
4756:
4751:
4746:
4741:
4736:
4731:
4726:
4721:
4716:
4711:
4706:
4701:
4696:
4691:
4686:
4681:
4676:
4671:
4666:
4661:
4659:Avoidance play
4656:
4650:
4648:
4640:
4639:
4636:
4629:
4628:
4625:
4624:
4621:
4620:
4618:
4617:
4611:
4609:
4605:
4604:
4602:
4601:
4596:
4591:
4586:
4581:
4576:
4574:Precision Club
4571:
4566:
4561:
4556:
4551:
4546:
4541:
4536:
4531:
4526:
4521:
4516:
4511:
4506:
4504:Bidding system
4501:
4496:
4491:
4485:
4483:
4479:
4478:
4476:
4475:
4470:
4465:
4460:
4455:
4450:
4445:
4443:Takeout double
4440:
4435:
4430:
4425:
4420:
4415:
4410:
4405:
4400:
4395:
4390:
4385:
4380:
4375:
4370:
4365:
4360:
4355:
4350:
4345:
4340:
4335:
4330:
4325:
4320:
4315:
4310:
4305:
4300:
4298:Board (bridge)
4295:
4293:Bidding system
4290:
4285:
4280:
4274:
4272:
4264:
4263:
4260:
4253:
4252:
4249:
4248:
4245:
4244:
4242:
4241:
4236:
4231:
4226:
4221:
4216:
4211:
4206:
4201:
4196:
4191:
4186:
4181:
4176:
4171:
4166:
4161:
4156:
4151:
4146:
4141:
4136:
4131:
4126:
4121:
4116:
4114:Bridge scoring
4111:
4106:
4101:
4096:
4091:
4089:Auction bridge
4085:
4083:
4075:
4074:
4071:
4064:
4063:
4058:
4056:
4055:
4048:
4041:
4033:
4027:
4026:
4020:
4004:Reese, Terence
4000:
3994:
3978:
3966:
3963:
3961:
3960:
3948:
3937:
3926:
3914:
3902:
3887:
3854:
3852:
3849:
3846:
3845:
3842:
3839:
3835:
3834:
3831:
3828:
3824:
3823:
3820:
3819:12,204,432,000
3817:
3813:
3812:
3809:
3808:45,618,822,000
3806:
3802:
3801:
3798:
3795:
3791:
3790:
3787:
3784:
3780:
3779:
3776:
3773:
3769:
3768:
3765:
3762:
3758:
3757:
3754:
3753:53,704,810,560
3751:
3747:
3746:
3743:
3742:19,749,204,780
3740:
3736:
3735:
3732:
3729:
3725:
3724:
3721:
3718:
3714:
3713:
3710:
3707:
3703:
3702:
3699:
3696:
3692:
3691:
3688:
3685:
3671:
3668:
3662:
3661:
3658:
3654:
3653:
3652:4,997,094,488
3650:
3646:
3645:
3642:
3638:
3637:
3634:
3630:
3629:
3626:
3622:
3621:
3618:
3614:
3613:
3610:
3606:
3605:
3602:
3598:
3597:
3594:
3590:
3589:
3586:
3582:
3581:
3578:
3574:
3573:
3570:
3566:
3565:
3562:
3558:
3557:
3554:
3507:
3503:
3499:
3496:
3493:
3489:
3485:
3482:
3459:
3454:
3451:
3446:
3431:
3428:
3425:
3424:
3421:
3418:
3414:
3413:
3410:
3407:
3403:
3402:
3399:
3396:
3392:
3391:
3388:
3385:
3381:
3380:
3377:
3374:
3366:
3365:
3362:
3359:
3355:
3354:
3351:
3348:
3344:
3343:
3340:
3337:
3333:
3332:
3329:
3326:
3322:
3321:
3318:
3315:
3311:
3310:
3307:
3304:
3300:
3299:
3296:
3293:
3289:
3288:
3285:
3282:
3278:
3277:
3274:
3271:
3267:
3266:
3263:
3260:
3256:
3255:
3252:
3249:
3234:
3233:
3230:
3227:
3226:2 Three-suited
3223:
3222:
3219:
3216:
3212:
3211:
3208:
3204:
3198:
3197:
3194:
3191:
3187:
3186:
3183:
3180:
3159:single suiters
3155:balanced hands
3145:
3144:
3142:
3139:
3138:
3135:
3132:
3128:
3127:
3124:
3121:
3117:
3116:
3113:
3110:
3106:
3105:
3102:
3099:
3095:
3094:
3091:
3088:
3084:
3083:
3080:
3077:
3073:
3072:
3069:
3066:
3062:
3061:
3058:
3055:
3051:
3050:
3047:
3044:
3040:
3039:
3036:
3033:
3029:
3028:
3025:
3022:
3018:
3017:
3014:
3011:
3007:
3006:
3003:
3000:
2996:
2995:
2992:
2989:
2982:
2979:
2978:
2975:
2972:
2968:
2967:
2964:
2961:
2957:
2956:
2953:
2950:
2946:
2945:
2942:
2939:
2935:
2934:
2931:
2928:
2924:
2923:
2920:
2917:
2913:
2912:
2909:
2906:
2902:
2901:
2898:
2895:
2891:
2890:
2887:
2884:
2880:
2879:
2876:
2873:
2869:
2868:
2865:
2862:
2858:
2857:
2854:
2851:
2847:
2846:
2843:
2840:
2836:
2835:
2832:
2829:
2822:
2819:
2818:
2815:
2812:
2808:
2807:
2804:
2801:
2797:
2796:
2793:
2790:
2786:
2785:
2782:
2779:
2775:
2774:
2771:
2768:
2764:
2763:
2760:
2757:
2753:
2752:
2749:
2746:
2742:
2741:
2738:
2735:
2731:
2730:
2727:
2724:
2720:
2719:
2716:
2713:
2709:
2708:
2705:
2702:
2698:
2697:
2694:
2691:
2687:
2686:
2683:
2680:
2676:
2675:
2672:
2669:
2629:
2626:
2623:
2622:
2619:
2616:
2613:
2610:
2607:
2604:
2601:
2597:
2596:
2593:
2590:
2587:
2584:
2581:
2578:
2575:
2571:
2570:
2567:
2564:
2561:
2558:
2555:
2552:
2549:
2546:
2543:
2539:
2538:
2535:
2532:
2529:
2526:
2523:
2520:
2517:
2514:
2511:
2507:
2506:
2503:
2500:
2497:
2494:
2491:
2488:
2485:
2482:
2479:
2475:
2474:
2471:
2468:
2465:
2462:
2459:
2456:
2453:
2450:
2447:
2443:
2442:
2439:
2436:
2433:
2430:
2427:
2424:
2421:
2418:
2415:
2411:
2410:
2407:
2404:
2401:
2398:
2395:
2392:
2389:
2386:
2383:
2379:
2378:
2375:
2372:
2370:
2367:
2364:
2362:
2359:
2356:
2354:
2351:
2348:
2346:
2343:
2328:
2325:
2312:
2309:
2306:
2303:
2300:
2297:
2294:
2291:
2288:
2285:
2282:
2279:
2276:
2273:
2270:
2267:
2264:
2244:
2241:
2238:
2235:
2232:
2229:
2226:
2223:
2220:
2217:
2214:
2211:
2208:
2205:
2202:
2199:
2196:
2171:
2166:
2163:
2160:
2156:
2152:
2149:
2146:
2140:
2137:
2134:
2131:
2128:
2125:
2122:
2119:
2116:
2113:
2110:
2107:
2104:
2101:
2096:
2093:
2090:
2087:
2084:
2081:
2078:
2075:
2072:
2069:
2066:
2063:
2054:
2049:
2045:
2042:
2039:
2033:
2027:
2024:
2021:
2018:
2015:
2012:
2009:
2006:
2003:
2000:
1997:
1994:
1991:
1988:
1985:
1982:
1979:
1976:
1956:
1953:
1948:
1944:
1940:
1935:
1931:
1903:
1898:
1894:
1890:
1885:
1881:
1877:
1874:
1871:
1868:
1865:
1861:
1858:
1854:
1849:
1846:
1843:
1839:
1835:
1832:
1829:
1826:
1823:
1818:
1814:
1810:
1805:
1801:
1797:
1794:
1791:
1788:
1785:
1781:
1778:
1774:
1771:
1766:
1762:
1758:
1753:
1749:
1745:
1742:
1739:
1736:
1733:
1730:
1710:
1690:
1670:
1646:
1639:
1635:
1628:
1624:
1620:
1615:
1611:
1604:
1595:
1589:
1586:
1581:
1577:
1571:
1568:
1565:
1562:
1557:
1553:
1549:
1544:
1540:
1533:
1524:
1519:
1515:
1512:
1509:
1503:
1494:
1488:
1485:
1482:
1479:
1474:
1470:
1466:
1463:
1460:
1457:
1454:
1449:
1445:
1441:
1438:
1435:
1430:
1426:
1422:
1417:
1413:
1409:
1404:
1401:
1398:
1395:
1392:
1389:
1384:
1380:
1376:
1371:
1367:
1363:
1360:
1355:
1351:
1347:
1342:
1338:
1328:
1323:
1319:
1316:
1313:
1307:
1301:
1295:
1292:
1289:
1286:
1281:
1277:
1273:
1270:
1267:
1264:
1261:
1256:
1252:
1248:
1245:
1242:
1237:
1233:
1229:
1224:
1220:
1216:
1211:
1208:
1205:
1202:
1199:
1196:
1191:
1187:
1183:
1178:
1174:
1170:
1167:
1162:
1158:
1154:
1149:
1145:
1138:
1132:
1129:
1126:
1123:
1118:
1115:
1112:
1109:
1106:
1103:
1097:
1092:
1089:
1084:
1081:
1076:
1072:
1068:
1063:
1059:
1055:
1052:
1049:
1046:
1043:
1039:
1036:
1012:
1009:
1006:
1003:
998:
994:
990:
987:
984:
979:
974:
970:
963:
957:
954:
951:
948:
943:
939:
935:
932:
929:
924:
919:
915:
908:
905:
885:
865:
845:
840:
836:
832:
827:
823:
819:
792:
789:
786:
783:
780:
777:
774:
771:
768:
765:
762:
759:
754:
750:
746:
741:
737:
733:
728:
725:
720:
716:
712:
707:
703:
699:
693:
690:
670:
665:
661:
657:
652:
648:
644:
624:
621:
618:
615:
612:
592:
570:
566:
545:
523:
519:
498:
493:
489:
485:
480:
476:
472:
469:
466:
463:
460:
456:
453:
440:
437:
434:
433:
430:
427:
424:
420:
419:
416:
413:
410:
406:
405:
402:
399:
396:
392:
391:
388:
385:
382:
378:
377:
374:
371:
368:
365:
361:
360:
357:
354:
351:
347:
346:
343:
340:
337:
333:
332:
329:
326:
323:
319:
318:
315:
312:
309:
306:
302:
301:
298:
295:
292:
288:
287:
284:
281:
278:
274:
273:
270:
267:
264:
260:
259:
256:
253:
250:
247:
243:
242:
239:
236:
233:
229:
228:
225:
222:
219:
215:
214:
211:
208:
205:
202:
198:
197:
194:
191:
188:
184:
183:
180:
177:
174:
170:
169:
166:
163:
160:
157:
153:
152:
149:
146:
143:
139:
138:
135:
132:
129:
126:
122:
121:
118:
115:
112:
108:
107:
104:
101:
98:
95:
91:
90:
85:
82:
79:
76:
36:
33:
15:
13:
10:
9:
6:
4:
3:
2:
6174:
6163:
6160:
6159:
6157:
6134:
6131:
6130:
6128:
6124:
6118:
6115:
6114:
6112:
6108:
6102:
6101:
6097:
6095:
6094:
6090:
6088:
6087:
6083:
6076:
6074:
6071:
6070:
6068:
6064:
6058:
6057:
6053:
6051:
6050:
6046:
6044:
6043:
6039:
6037:
6036:
6032:
6030:
6029:
6025:
6023:
6022:
6018:
6016:
6015:
6011:
6009:
6008:
6004:
6002:
6001:
5997:
5990:
5988:
5985:
5983:
5980:
5978:
5975:
5968:
5966:
5963:
5961:
5958:
5957:
5955:
5951:
5947:
5940:
5936:
5922:
5919:
5917:
5914:
5912:
5909:
5907:
5904:
5902:
5899:
5897:
5894:
5892:
5889:
5887:
5884:
5882:
5879:
5877:
5874:
5872:
5869:
5867:
5864:
5862:
5859:
5857:
5854:
5852:
5849:
5847:
5844:
5842:
5839:
5837:
5834:
5832:
5829:
5827:
5824:
5822:
5819:
5817:
5814:
5812:
5809:
5807:
5804:
5802:
5799:
5797:
5794:
5792:
5789:
5787:
5786:Mini-Spingold
5784:
5782:
5779:
5777:
5774:
5772:
5769:
5767:
5764:
5762:
5759:
5757:
5754:
5752:
5749:
5747:
5744:
5742:
5739:
5737:
5734:
5732:
5729:
5727:
5724:
5722:
5719:
5717:
5714:
5712:
5709:
5707:
5704:
5702:
5699:
5697:
5694:
5692:
5689:
5687:
5680:
5678:
5675:
5673:
5670:
5668:
5665:
5663:
5660:
5658:
5655:
5654:
5652:
5648:
5642:
5639:
5637:
5634:
5632:
5629:
5627:
5624:
5622:
5619:
5617:
5614:
5612:
5609:
5607:
5604:
5602:
5599:
5597:
5594:
5592:
5589:
5587:
5584:
5582:
5579:
5577:
5574:
5572:
5569:
5567:
5564:
5562:
5559:
5557:
5556:Rosenblum Cup
5554:
5552:
5551:McConnell Cup
5549:
5547:
5544:
5542:
5539:
5537:
5534:
5532:
5529:
5527:
5524:
5523:
5521:
5517:
5511:
5508:
5507:
5505:
5501:
5497:
5493:Championships
5490:
5486:
5472:
5469:
5467:
5464:
5462:
5459:
5457:
5454:
5452:
5449:
5447:
5444:
5442:
5439:
5437:
5434:
5432:
5429:
5427:
5424:
5422:
5419:
5417:
5414:
5412:
5409:
5407:
5404:
5402:
5399:
5397:
5394:
5392:
5389:
5388:
5386:
5382:
5376:
5373:
5371:
5368:
5366:
5363:
5361:
5358:
5356:
5353:
5351:
5348:
5346:
5343:
5342:
5340:
5336:
5330:
5327:
5325:
5322:
5320:
5317:
5316:
5314:
5310:
5304:
5301:
5299:
5296:
5294:
5291:
5290:
5288:
5284:
5278:
5277:United States
5275:
5273:
5270:
5268:
5265:
5263:
5260:
5258:
5255:
5253:
5250:
5248:
5245:
5243:
5240:
5238:
5235:
5233:
5230:
5228:
5225:
5223:
5220:
5218:
5215:
5213:
5210:
5208:
5205:
5203:
5200:
5198:
5195:
5193:
5190:
5188:
5185:
5183:
5180:
5178:
5175:
5173:
5170:
5168:
5165:
5163:
5160:
5158:
5155:
5153:
5150:
5148:
5145:
5143:
5140:
5138:
5135:
5133:
5130:
5129:
5127:
5123:
5117:
5114:
5112:
5109:
5107:
5104:
5102:
5099:
5098:
5096:
5092:
5088:
5081:
5077:
5063:
5060:
5058:
5055:
5053:
5052:Rusinow leads
5050:
5048:
5045:
5043:
5042:Rule of 10-12
5040:
5038:
5035:
5033:
5030:
5028:
5025:
5024:
5022:
5020:Defender play
5018:
5012:
5009:
5007:
5000:
4998:
4995:
4993:
4990:
4988:
4987:Trump squeeze
4985:
4983:
4980:
4978:
4977:Strip squeeze
4975:
4973:
4970:
4968:
4965:
4963:
4960:
4958:
4955:
4953:
4950:
4948:
4945:
4943:
4940:
4938:
4935:
4933:
4930:
4928:
4925:
4923:
4922:Guard squeeze
4920:
4918:
4915:
4913:
4912:Entry squeeze
4910:
4908:
4905:
4903:
4900:
4898:
4895:
4893:
4892:Clash squeeze
4890:
4888:
4885:
4883:
4880:
4878:
4871:
4869:
4866:
4864:
4861:
4859:
4858:Scissors coup
4856:
4854:
4851:
4849:
4848:Merrimac coup
4846:
4844:
4841:
4839:
4836:
4834:
4831:
4829:
4826:
4824:
4821:
4819:
4816:
4814:
4811:
4809:
4806:
4804:
4803:Alcatraz coup
4801:
4799:
4792:
4790:
4787:
4785:
4782:
4780:
4773:
4772:
4770:
4768:Declarer play
4766:
4760:
4759:Vacant Places
4757:
4755:
4752:
4750:
4747:
4745:
4742:
4740:
4737:
4735:
4732:
4730:
4727:
4725:
4722:
4720:
4719:Probabilities
4717:
4715:
4712:
4710:
4707:
4705:
4702:
4700:
4697:
4695:
4692:
4690:
4687:
4685:
4682:
4680:
4677:
4675:
4672:
4670:
4667:
4665:
4662:
4660:
4657:
4655:
4652:
4651:
4649:
4645:
4641:
4634:
4630:
4616:
4613:
4612:
4610:
4606:
4600:
4597:
4595:
4592:
4590:
4587:
4585:
4582:
4580:
4577:
4575:
4572:
4570:
4567:
4565:
4562:
4560:
4557:
4555:
4552:
4550:
4547:
4545:
4542:
4540:
4537:
4535:
4532:
4530:
4527:
4525:
4522:
4520:
4517:
4515:
4512:
4510:
4507:
4505:
4502:
4500:
4497:
4495:
4492:
4490:
4487:
4486:
4484:
4480:
4474:
4471:
4469:
4466:
4464:
4461:
4459:
4456:
4454:
4451:
4449:
4446:
4444:
4441:
4439:
4436:
4434:
4431:
4429:
4428:Single suiter
4426:
4424:
4421:
4419:
4416:
4414:
4411:
4409:
4406:
4404:
4401:
4399:
4396:
4394:
4391:
4389:
4386:
4384:
4381:
4379:
4376:
4374:
4371:
4369:
4366:
4364:
4361:
4359:
4356:
4354:
4351:
4349:
4346:
4344:
4341:
4339:
4336:
4334:
4331:
4329:
4326:
4324:
4321:
4319:
4316:
4314:
4311:
4309:
4308:Brown sticker
4306:
4304:
4301:
4299:
4296:
4294:
4291:
4289:
4286:
4284:
4281:
4279:
4278:Balanced hand
4276:
4275:
4273:
4269:
4265:
4258:
4254:
4240:
4237:
4235:
4232:
4230:
4227:
4225:
4222:
4220:
4217:
4215:
4212:
4210:
4209:Rubber bridge
4207:
4205:
4202:
4200:
4197:
4195:
4192:
4190:
4187:
4185:
4182:
4180:
4177:
4175:
4172:
4170:
4167:
4165:
4162:
4160:
4157:
4155:
4152:
4150:
4147:
4145:
4142:
4140:
4137:
4135:
4132:
4130:
4127:
4125:
4122:
4120:
4117:
4115:
4112:
4110:
4107:
4105:
4104:Bridge maxims
4102:
4100:
4099:Bridge-O-Rama
4097:
4095:
4094:Bridge ethics
4092:
4090:
4087:
4086:
4084:
4080:
4076:
4069:
4065:
4061:
4054:
4049:
4047:
4042:
4040:
4035:
4034:
4031:
4023:
4021:0-575-02597-2
4017:
4013:
4009:
4008:Trézel, Roger
4005:
4001:
3997:
3995:0-575-02799-1
3991:
3987:
3983:
3979:
3974:
3969:
3968:
3964:
3957:
3952:
3949:
3946:
3941:
3938:
3935:
3930:
3927:
3924:
3918:
3915:
3912:
3906:
3903:
3898:
3894:
3890:
3888:0-943855-48-9
3884:
3880:
3876:
3875:
3870:
3862:
3860:
3856:
3850:
3843:
3840:
3837:
3836:
3832:
3830:1,451,520,000
3829:
3826:
3825:
3821:
3818:
3815:
3814:
3810:
3807:
3804:
3803:
3799:
3796:
3793:
3792:
3788:
3785:
3782:
3781:
3777:
3774:
3771:
3770:
3766:
3763:
3760:
3759:
3755:
3752:
3749:
3748:
3744:
3741:
3738:
3737:
3733:
3731:5,080,948,428
3730:
3727:
3726:
3722:
3719:
3716:
3715:
3711:
3708:
3705:
3704:
3700:
3697:
3694:
3693:
3689:
3686:
3683:
3682:
3679:
3677:
3669:
3667:
3656:
3655:
3648:
3647:
3640:
3639:
3632:
3631:
3624:
3623:
3616:
3615:
3608:
3607:
3600:
3599:
3592:
3591:
3584:
3583:
3576:
3575:
3568:
3567:
3560:
3559:
3555:
3552:
3551:
3548:
3545:
3533:
3531:
3529:
3523:
3505:
3497:
3494:
3487:
3483:
3480:
3452:
3449:
3429:
3422:
3419:
3416:
3415:
3411:
3408:
3405:
3404:
3400:
3397:
3394:
3393:
3389:
3386:
3383:
3382:
3378:
3375:
3373:Shortest suit
3372:
3371:
3363:
3360:
3357:
3356:
3352:
3349:
3346:
3345:
3341:
3338:
3335:
3334:
3330:
3327:
3324:
3323:
3319:
3316:
3313:
3312:
3308:
3305:
3302:
3301:
3297:
3294:
3291:
3290:
3286:
3283:
3280:
3279:
3275:
3272:
3269:
3268:
3264:
3261:
3258:
3257:
3253:
3250:
3247:
3246:
3243:
3241:
3231:
3228:
3225:
3224:
3220:
3217:
3214:
3213:
3209:
3205:
3203:Single-suited
3200:
3199:
3195:
3192:
3189:
3188:
3184:
3181:
3178:
3177:
3174:
3172:
3168:
3167:three-suiters
3164:
3160:
3156:
3152:
3143:
3133:
3130:
3129:
3125:
3122:
3119:
3118:
3114:
3111:
3108:
3107:
3103:
3100:
3097:
3096:
3092:
3089:
3086:
3085:
3078:
3075:
3074:
3070:
3067:
3064:
3063:
3059:
3056:
3053:
3052:
3048:
3045:
3042:
3041:
3037:
3034:
3031:
3030:
3026:
3023:
3020:
3019:
3015:
3012:
3009:
3008:
3004:
3001:
2998:
2997:
2993:
2990:
2987:
2986:
2983:
2976:
2973:
2970:
2969:
2965:
2962:
2959:
2958:
2954:
2951:
2948:
2947:
2943:
2940:
2937:
2936:
2932:
2929:
2926:
2925:
2921:
2918:
2915:
2914:
2910:
2907:
2904:
2903:
2899:
2896:
2893:
2892:
2888:
2885:
2882:
2881:
2874:
2871:
2870:
2866:
2863:
2860:
2859:
2855:
2852:
2849:
2848:
2844:
2841:
2838:
2837:
2833:
2830:
2827:
2826:
2823:
2816:
2813:
2810:
2809:
2805:
2802:
2799:
2798:
2794:
2791:
2788:
2787:
2780:
2777:
2776:
2772:
2769:
2766:
2765:
2761:
2758:
2755:
2754:
2750:
2747:
2744:
2743:
2739:
2736:
2733:
2732:
2725:
2722:
2721:
2717:
2714:
2711:
2710:
2706:
2703:
2700:
2699:
2695:
2692:
2689:
2688:
2684:
2681:
2678:
2677:
2673:
2670:
2667:
2666:
2663:
2662:
2659:
2655:
2653:
2647:
2645:
2641:
2640:
2635:
2627:
2620:
2617:
2614:
2611:
2608:
2605:
2602:
2599:
2598:
2594:
2591:
2588:
2585:
2582:
2579:
2576:
2573:
2572:
2568:
2565:
2562:
2559:
2556:
2553:
2550:
2547:
2544:
2541:
2540:
2536:
2533:
2530:
2527:
2524:
2521:
2518:
2515:
2512:
2509:
2508:
2504:
2501:
2498:
2495:
2492:
2489:
2486:
2483:
2480:
2477:
2476:
2472:
2469:
2466:
2463:
2460:
2457:
2454:
2451:
2448:
2445:
2444:
2440:
2437:
2434:
2431:
2428:
2425:
2422:
2419:
2416:
2413:
2412:
2408:
2405:
2402:
2399:
2396:
2393:
2390:
2387:
2384:
2381:
2380:
2376:
2373:
2368:
2365:
2360:
2357:
2352:
2349:
2344:
2341:
2340:
2337:
2334:
2326:
2324:
2307:
2298:
2295:
2292:
2289:
2286:
2283:
2280:
2277:
2274:
2271:
2268:
2262:
2239:
2230:
2227:
2224:
2221:
2218:
2215:
2212:
2209:
2206:
2203:
2200:
2194:
2186:
2164:
2161:
2158:
2154:
2150:
2147:
2138:
2132:
2129:
2126:
2120:
2114:
2111:
2108:
2102:
2099:
2094:
2088:
2085:
2082:
2079:
2076:
2070:
2067:
2064:
2061:
2047:
2043:
2040:
2037:
2025:
2019:
2016:
2013:
2010:
2007:
2004:
2001:
1995:
1992:
1986:
1983:
1980:
1974:
1954:
1951:
1946:
1942:
1938:
1933:
1929:
1919:
1917:
1896:
1892:
1888:
1883:
1879:
1875:
1872:
1869:
1866:
1859:
1856:
1847:
1844:
1841:
1837:
1833:
1830:
1824:
1816:
1812:
1808:
1803:
1799:
1795:
1792:
1789:
1786:
1779:
1776:
1772:
1764:
1760:
1756:
1751:
1747:
1743:
1740:
1737:
1734:
1728:
1708:
1688:
1668:
1637:
1633:
1626:
1622:
1618:
1613:
1609:
1587:
1584:
1579:
1575:
1569:
1566:
1563:
1560:
1555:
1551:
1547:
1542:
1538:
1517:
1513:
1510:
1507:
1492:
1486:
1480:
1477:
1472:
1468:
1461:
1455:
1452:
1447:
1443:
1436:
1428:
1424:
1420:
1415:
1411:
1402:
1396:
1393:
1390:
1387:
1382:
1378:
1374:
1369:
1365:
1358:
1353:
1349:
1345:
1340:
1336:
1321:
1317:
1314:
1311:
1299:
1293:
1287:
1284:
1279:
1275:
1268:
1262:
1259:
1254:
1250:
1243:
1235:
1231:
1227:
1222:
1218:
1209:
1203:
1200:
1197:
1194:
1189:
1185:
1181:
1176:
1172:
1165:
1160:
1156:
1152:
1147:
1143:
1136:
1130:
1127:
1124:
1121:
1116:
1110:
1107:
1104:
1095:
1090:
1087:
1082:
1074:
1070:
1066:
1061:
1057:
1053:
1050:
1047:
1044:
1037:
1034:
1026:. Therefore,
1010:
1004:
1001:
996:
992:
985:
982:
977:
972:
968:
961:
955:
949:
946:
941:
937:
930:
927:
922:
917:
913:
906:
903:
883:
863:
838:
834:
830:
825:
821:
809:
790:
784:
781:
778:
772:
766:
763:
760:
757:
752:
748:
744:
739:
735:
726:
718:
714:
710:
705:
701:
691:
688:
663:
659:
655:
650:
646:
619:
616:
613:
590:
568:
564:
543:
521:
517:
491:
487:
483:
478:
474:
470:
467:
464:
461:
454:
451:
438:
431:
428:
425:
422:
421:
417:
414:
411:
408:
407:
403:
400:
397:
394:
393:
389:
386:
383:
380:
379:
375:
372:
369:
366:
362:
358:
355:
352:
349:
348:
344:
341:
338:
335:
334:
330:
327:
324:
321:
320:
316:
313:
310:
307:
303:
299:
296:
293:
290:
289:
285:
282:
279:
276:
275:
271:
268:
265:
262:
261:
257:
254:
251:
248:
244:
240:
237:
234:
231:
230:
226:
223:
220:
217:
216:
212:
209:
206:
203:
199:
195:
192:
189:
186:
185:
181:
178:
175:
172:
171:
167:
164:
161:
158:
154:
150:
147:
144:
141:
140:
136:
133:
130:
127:
123:
119:
116:
113:
110:
109:
105:
102:
99:
96:
92:
86:
83:
80:
77:
73:
70:
68:
67:Vacant Places
63:
60:
58:
54:
50:
46:
42:
34:
32:
30:
25:
22:
6110:TV and Radio
6098:
6091:
6084:
6077:
6054:
6047:
6040:
6033:
6026:
6019:
6012:
6005:
5998:
5991:
5969:
5726:Goren Trophy
5681:
5526:Bermuda Bowl
5062:Smith signal
5037:Opening lead
5001:
4992:Vice squeeze
4967:Squeeze play
4872:
4838:Devil's coup
4793:
4774:
4739:Smother play
4718:
4709:Pin (bridge)
4674:Card reading
4589:SĂ€ffle Spade
4584:Romex system
4559:Little Major
4468:Weak two bid
4463:Void (cards)
4448:Three suiter
4333:Forcing pass
4194:Masterpoints
4119:Bridge whist
4011:
3985:
3982:Kelsey, Hugh
3972:
3951:
3940:
3929:
3917:
3905:
3872:
3690:Probability
3673:
3665:
3546:
3534:
3525:
3521:
3433:
3379:Probability
3353:0.000000003
3254:Probability
3248:Longest suit
3239:
3237:
3215:8 Two-suited
3185:Probability
3170:
3150:
3148:
3123:0.0000000032
2656:
2651:
2648:
2637:
2634:hand pattern
2633:
2631:
2377:Probability
2330:
2184:
1920:
808:permutations
442:
89:Probability
84:Combinations
78:Distribution
64:
61:
56:
44:
40:
38:
26:
18:
5657:Buffett Cup
5355:Crockford's
5324:Dallas Aces
5286:Other lists
5267:Switzerland
5237:New Zealand
5172:Netherlands
4868:Vienna coup
4789:Safety play
4608:Conventions
4569:Polish Club
4534:Carrot Club
4514:Boring Club
4438:Strong pass
4403:Psychic bid
4328:Forcing bid
4288:Bidding box
3720:872,361,936
3660:37,478,624
3163:two suiters
2991:Probability
2831:Probability
2671:Probability
2369:Probability
2361:Probability
2353:Probability
2345:Probability
81:Probability
6080:Magazines:
5771:Marcus Cup
5571:Venice Cup
5375:Savoy Club
5047:Rule of 11
4863:Trump coup
4579:Roman Club
4473:Zar Points
4453:Two suiter
4433:Stolen bid
4373:Minor suit
4368:Major suit
4199:Minibridge
3851:References
3709:90,206,044
3701:0.000668%
3539:2 and the
3384:Three card
3342:0.0000003
3190:3 Balanced
3151:hand types
3112:0.00000011
3101:0.00000025
1914:where the
681:spaces is
87:Individual
6066:Magazines
5846:Reisinger
5329:Four Aces
5319:Blue Team
5132:Australia
4875:Squeezes:
4808:Bath coup
4664:Beer card
4637:Card play
4509:Blue Club
4124:Bridgette
3698:4,245,032
3406:Singleton
3395:Doubleton
3331:0.000017
3179:Hand type
3090:0.0000015
3079:0.0000040
3068:0.0000097
2644:doubleton
2621:1.000000
2595:0.999999
2569:1.000000
2537:1.000000
2505:1.000000
2473:1.000000
2441:1.000000
2409:1.000000
2311:%
2305:≈
2296:−
2284:−
2243:%
2237:≈
2228:−
2216:−
2155:δ
2151:−
2130:−
2112:−
2086:−
2080:−
1838:δ
1834:−
1585:−
1567:−
1561:−
1478:−
1453:−
1394:−
1388:−
1285:−
1260:−
1201:−
1195:−
1137:×
1002:−
962:×
947:−
764:−
758:−
432:0.00082~
418:0.00178~
404:0.00306~
390:0.00421~
376:0.00467~
359:0.00261~
345:0.00484~
331:0.00727~
317:0.00888~
300:0.00745~
286:0.01211~
272:0.01615~
258:0.01776~
241:0.01956~
227:0.02826~
6156:Category
5876:Spingold
5247:Pakistan
5152:Bulgaria
4754:Uppercut
4734:Shooting
4544:Fantunes
4383:Overcall
4338:Game try
4072:Overview
4010:(1986).
3897:96188639
3712:0.0142%
3376:Patterns
3361:13-0-0-0
3350:12-1-0-0
3320:0.00037
3251:Patterns
3240:a priori
3207:13-0-0-0
3182:Patterns
3171:a priori
3131:13-0-0-0
3120:12-1-0-0
3109:11-2-0-0
3098:11-1-1-0
3087:10-3-0-0
3076:10-1-1-1
3057:0.000011
3054:10-2-1-0
3046:0.000031
3035:0.000056
3024:0.000082
2615:0.998983
2609:0.902410
2603:0.285846
2589:0.997864
2583:0.858174
2577:0.205565
2563:0.999997
2557:0.995763
2551:0.801240
2545:0.140025
2531:0.999990
2525:0.991985
2519:0.732097
2513:0.088163
2499:0.999972
2493:0.985549
2487:0.651828
2481:0.049708
2467:0.999923
2461:0.975187
2455:0.562382
2449:0.025085
2435:0.999806
2429:0.959137
2423:0.468331
2417:0.011523
2403:0.999542
2397:0.935520
2391:0.374768
2385:0.003639
2185:a priori
1860:′
1780:′
1038:′
455:′
213:0.0339~
196:0.0478~
182:0.0622~
168:0.0678~
57:a priori
5503:General
5212:Ireland
5202:Hungary
5197:Germany
5187:Fiction
5182:England
5167:Denmark
5147:Britain
5137:Austria
5094:General
4784:Finesse
4699:Hold up
4684:Endplay
4647:General
4564:Moscito
4482:Systems
4388:Preempt
4318:Cue bid
4271:General
4261:Bidding
4239:Vugraph
4169:Goulash
4134:Chicago
4082:General
3833:0.229%
3723:0.137%
3423:0.0511
3412:0.3055
3401:0.5380
3390:0.1054
3387:4-3-3-3
3358:13 card
3347:12 card
3336:11 card
3325:10 card
3309:0.0047
3298:0.0353
3287:0.1655
3276:0.4434
3265:0.3508
3232:0.0423
3221:0.2902
3210:0.1915
3196:0.4761
3065:9-4-0-0
3043:8-5-0-0
3032:7-6-0-0
3021:9-2-2-0
3013:0.00010
3010:9-3-1-0
3002:0.00018
2999:9-2-1-1
2988:Pattern
2974:0.00045
2971:8-4-1-0
2963:0.00072
2960:6-6-1-0
2952:0.00109
2949:8-3-2-0
2941:0.00109
2938:7-5-1-0
2930:0.00118
2927:8-3-1-1
2919:0.00192
2916:8-2-2-1
2908:0.00265
2905:7-3-3-0
2897:0.00362
2894:7-4-2-0
2886:0.00392
2883:7-4-1-1
2875:0.00513
2872:7-2-2-2
2864:0.00651
2861:6-5-2-0
2853:0.00705
2850:6-5-1-1
2842:0.00895
2839:5-5-3-0
2828:Pattern
2814:0.01243
2811:5-4-4-0
2803:0.01326
2800:6-4-3-0
2792:0.01881
2789:7-3-2-1
2781:0.02993
2778:4-4-4-1
2770:0.03174
2767:5-5-2-1
2759:0.03448
2756:6-3-3-1
2748:0.04702
2745:6-4-2-1
2737:0.05642
2734:6-3-2-2
2726:0.10536
2723:4-3-3-3
2715:0.10580
2712:5-4-2-2
2704:0.12931
2701:5-4-3-1
2693:0.15517
2690:5-3-3-2
2682:0.21551
2679:4-4-3-2
2668:Pattern
49:bidding
5994:Books:
5272:Taiwan
5262:Sweden
5257:Russia
5252:Poland
5242:Norway
5232:Monaco
5227:Mexico
5217:Israel
5192:France
5157:Canada
5142:Brazil
5057:Signal
4796:Coups:
4777:Basic:
4724:Revoke
4214:Screen
4018:
3992:
3895:
3885:
3822:1.92%
3811:7.18%
3800:15.8%
3789:22.9%
3778:23.0%
3767:16.4%
3756:8.46%
3745:3.11%
3314:9 card
3303:8 card
3292:7 card
3281:6 card
3270:5 card
3259:4 card
21:bridge
5953:Books
5519:World
5338:Clubs
5312:Teams
5222:Italy
5207:India
5177:Egypt
5162:China
4744:Tempo
4689:Entry
4669:Caddy
4234:Trump
3734:0.8%
3530:Earth
423:8 - 0
409:7 - 1
395:6 - 2
381:5 - 3
367:4 - 4
350:7 - 0
336:6 - 1
322:5 - 2
308:4 - 3
291:6 - 0
277:5 - 1
263:4 - 2
249:3 - 3
232:5 - 0
218:4 - 1
204:3 - 2
187:4 - 0
173:3 - 1
159:2 - 2
151:0.11
142:3 - 0
137:0.13
128:2 - 1
120:0.24
111:2 - 0
106:0.26
97:1 - 1
55:, or
45:split
4818:Coup
4729:Ruff
4679:Duck
4539:EHAA
4499:Acol
4224:Suit
4016:ISBN
3990:ISBN
3923:link
3911:link
3893:LCCN
3883:ISBN
3844:N/A
3674:The
3417:Void
3165:and
2255:and
443:Let
426:0.00
412:0.03
398:0.17
384:0.47
370:0.33
353:0.01
339:0.07
325:0.30
311:0.62
294:0.01
280:0.15
266:0.48
252:0.36
235:0.04
221:0.28
207:0.68
190:0.10
176:0.50
162:0.40
145:0.22
131:0.78
114:0.48
100:0.52
53:play
51:and
3684:LTC
3126:12
3115:12
3104:12
3093:12
3071:12
3060:24
3049:12
3038:12
3027:12
3016:24
3005:12
2977:24
2966:12
2955:24
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2933:12
2922:12
2911:12
2900:24
2889:12
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2806:24
2795:24
2773:12
2762:12
2751:24
2740:12
2718:12
2707:24
2696:12
2685:12
2374:HCP
2366:HCP
2358:HCP
2350:HCP
2342:HCP
810:of
387:112
59:).
43:or
41:lie
6158::
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3891:.
3858:^
3838:13
3827:12
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2240:42
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2020:13
2014:13
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2023:)
2017:,
2011:,
2008:b
2005:,
2002:a
1999:(
1996:P
1993:=
1990:)
1987:b
1984:,
1981:a
1978:(
1975:P
1952:=
1947:w
1943:n
1939:=
1934:e
1930:n
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1897:w
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