1670:
1040:
1665:{\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}}}}}
3554:
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
2346:
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
2193:
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
34:
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.
2660:
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
2191:
1923:
3217:
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,
1035:
2668:
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.
3484:) 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 (
815:
3555:
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.
42:, 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.
1981:
3988:
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.
3431:
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
2332:
2264:
3677:
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).
518:
1735:
5121:
3482:
1976:
3529:
865:
690:
4061:
867:
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
644:
592:
545:
1730:
1710:
1690:
905:
885:
612:
565:
910:
2647:
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
4054:
73:
The table also shows the number of combinations of particular cards that match any numerical split and the probabilities for each combination.
5303:
2665:
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.
5247:
695:
5646:
5242:
5142:
2342:
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
5682:
5546:
5541:
5282:
5257:
5252:
5212:
5197:
5162:
5152:
4047:
5901:
5677:
5287:
5187:
5167:
5147:
5891:
5461:
5272:
5267:
5237:
5232:
5227:
5192:
5172:
5157:
5308:
5262:
5217:
5207:
5202:
5177:
2661:
possibilities to first identify the three-card suit and three possibilities to next identify the doubleton. Hence, the number of
6172:
5520:
5277:
5222:
5182:
6010:
5456:
59:
3249:
Alternative grouping of the 39 hand patterns can be made either by longest suit or by shortest suit. Below tables gives the
17:
3533:
How large an area would you need to spread all possible bridge deals if each deal would occupy only one square millimeter?
63:
6045:
5841:
3884:
2653:
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
6052:
5881:
5756:
2269:
2201:
6083:
4388:
4184:
4030:
4004:
3897:
5313:
4664:
2186:{\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})}
5916:
5636:
5631:
5606:
5601:
5476:
5471:
5406:
4942:
3889:
3558:
The table below gives the number of deals when various numbers of small cards are considered indistinguishable.
5911:
5776:
5771:
5766:
5706:
5651:
5621:
5616:
5116:
4724:
1929:
ensures that the situation where East and West have the same number of cards in the suit is not counted twice.
6031:
5970:
5626:
5801:
5701:
5596:
3420:
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
5896:
5831:
5811:
5716:
5466:
5451:
5416:
5401:
4967:
4625:
457:
5997:
5926:
5591:
5431:
5421:
5411:
4194:
4169:
4144:
3538:
50:
This table represents the different ways that two to eight particular cards may be distributed, or may
5987:
5836:
5111:
4418:
4408:
3448:
2347:
having at most 19 HCP minus the probability of having at most 11 HCP, or: 0.9855 â 0.6518 = 0.3337.
1935:
6017:
5721:
4199:
3487:
824:
649:
45:
5931:
5751:
5711:
5611:
5481:
5436:
5370:
4499:
4159:
6059:
5791:
5576:
5551:
5446:
5380:
4982:
4927:
4468:
5871:
5866:
5426:
5365:
4977:
4863:
4684:
4559:
4534:
5556:
6066:
5861:
5846:
5816:
5746:
5741:
5571:
5441:
5375:
4564:
4403:
2649:
2343:
1918:{\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})}
617:
570:
523:
3966:
8:
6127:
5826:
5821:
5641:
5126:
4972:
4947:
4912:
4368:
4239:
6096:
6038:
5975:
5921:
5876:
5355:
5339:
5329:
4609:
4428:
4373:
4293:
4244:
4229:
4139:
4119:
4025:. Master Bridge Series. London: Victor Gollancz Ltd in association with Peter Crawley.
3999:. Master Bridge Series. London: Victor Gollancz Ltd in association with Peter Crawley.
3686:
1715:
1695:
1675:
890:
870:
597:
550:
5992:
4539:
6143:
5906:
5806:
5786:
5687:
4957:
4843:
4764:
4744:
4604:
4529:
4433:
4358:
4313:
4189:
4026:
4000:
3903:
3893:
1030:{\displaystyle S={\frac {n_{e}!}{a!(n_{e}-a)!}}\times {\frac {n_{w}!}{b!(n_{w}-b)!}}}
39:
1672:
If the direction of the split is unimportant (it is only required that the split be
6110:
5851:
5761:
5042:
5021:
4937:
4907:
4897:
4892:
4709:
4704:
4504:
4423:
4333:
4179:
4174:
4164:
4134:
6103:
5731:
5726:
5586:
5067:
5037:
4848:
4833:
4823:
4759:
4714:
4363:
4353:
4323:
4224:
4214:
4154:
4149:
4070:
1926:
31:
4599:
4018:
3253:
chance of being dealt a hand with a longest or a shortest suit of given length.
46:
Probability of suit distributions (for missing trumps, etc.) in two hidden hands
6024:
5672:
5360:
5007:
4992:
4962:
4952:
4917:
4853:
4838:
4754:
4679:
4669:
4584:
4514:
4453:
4308:
4303:
4124:
4099:
3944:
3531:) The immenseness of this number can be understood by answering the question "
6166:
5796:
5566:
5561:
5062:
5052:
4997:
4987:
4932:
4922:
4902:
4868:
4858:
4828:
4813:
4769:
4699:
4689:
4438:
4318:
4288:
4219:
4114:
4109:
4104:
4014:
3879:
3169:
3165:
77:
5736:
5536:
5072:
5047:
5002:
4749:
4739:
4719:
4594:
4569:
4478:
4473:
4458:
4343:
4234:
4204:
4129:
3177:
5667:
5334:
4878:
4799:
4579:
4544:
4524:
4448:
4413:
4338:
4298:
3992:
3955:
818:
5781:
5581:
5385:
5057:
4873:
4589:
4483:
4463:
4443:
4383:
4378:
4209:
3173:
1978:
and that the direction of the split is unimportant, and so are given by
3229:
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
5856:
4818:
4674:
4519:
2654:
3546:
Obviously, the deals that are identical except for swappingâsayâthe
2334:
so now the club line is significantly better than the diamond line.
810:{\displaystyle T={\frac {(n_{e}+n_{w})!}{(n_{e}+n_{w}-a-b)!(a+b)!}}}
5886:
4554:
4393:
4348:
3933:
3921:
3689:
is an alternative to the HCP count as a method of hand evaluation.
4039:
4794:
4694:
4574:
4398:
4328:
4249:
3907:
4734:
3306:
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
3295:
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
614:
cards in the given suit. The total number of arrangements of
4549:
4509:
2194:
play are to hope either for diamonds 5-3 or clubs 4-2, the
5304:
List of bridge people with
Knowledge (English) articles
3956:
3945:
86:
Number of cards (trumps, etc.) missing from partnership
3877:
3680:
3490:
3451:
3440:
2272:
2204:
1984:
1938:
1738:
1718:
1698:
1678:
1043:
913:
893:
873:
827:
698:
652:
620:
600:
573:
553:
526:
460:
3284:
5-3-3-2, 5-4-2-2, 5-4-3-1, 5-5-2-1, 5-4-4-0, 5-5-3-0
76:
These probabilities follow directly from the law of
3523:
3476:
2337:
2326:
2258:
2185:
1970:
1917:
1724:
1704:
1684:
1664:
1029:
899:
879:
859:
809:
684:
638:
606:
586:
559:
539:
512:
3468:
3455:
3160:The 39 hand patterns can by classified into four
2327:{\displaystyle P(4,2,13-7,13-2)\thickapprox 47\%}
2259:{\displaystyle P(5,3,13-7,13-2)\thickapprox 42\%}
2063:
2042:
1712:, not that East is specifically required to hold
1337:
1316:
6164:
3184:likelihoods of being dealt a certain hand-type.
1732:cards), then the overall probability is given by
58:, between two unknown 13-card hands (before the
27:Mathematical probabilities in the game of bridge
2198:probabilities are 47% and 48% respectively but
449:
5953:
3537:an area more than a hundred million times the
4055:
3991:
2638:
1655:
1613:
1604:
1542:
1533:
1512:
567:cards in a given suit and a West player with
5094:
5647:World Transnational Open Teams Championship
4013:
3409:4-4-3-2, 5-3-3-2, 5-4-2-2, 6-3-2-2, 7-2-2-2
3317:8-2-2-1, 8-3-1-1, 8-3-2-0, 8-4-1-0, 8-5-0-0
5683:European Universities Bridge Championships
5547:Bridge at the 2012 World Mind Sports Games
5542:Bridge at the 2008 World Mind Sports Games
4062:
4048:
3981:
3920:Richard Pavlicek. "High Card Expectancy."
520:be the probability of an East player with
5902:United States Bridge Championships - Open
5678:Commonwealth Nations Bridge Championships
5462:List of contract bridge governing bodies
3926:
3575:53,644,737,765,488,792,839,237,440,000
14:
6165:
5521:List of bridge competitions and awards
5122:List of nationality transfers in sport
4092:
3932:Richard Pavlicek. "Against All Odds."
3583:7,811,544,503,918,790,990,995,915,520
6011:25 Bridge Conventions You Should Know
5952:
5892:Sternberg Women's Board-a-Match Teams
5502:
5457:International Mind Sports Association
5093:
4646:
4270:
4081:
4043:
3872:
3870:
38:The tables below specify the various
5695:North American bridge Championships:
3982:Ămile, Borel; AndrĂ©, ChĂ©ron (1940).
3591:445,905,120,201,773,774,566,940,160
6046:The Official Encyclopedia of Bridge
5842:North American Bridge Championships
4069:
3885:The Official Encyclopedia of Bridge
3882:; Francis, Dorthy A., eds. (1994).
3599:14,369,217,850,047,151,709,620,800
513:{\displaystyle P'(a,b,n_{e},n_{w})}
24:
6053:Planning the Play of a Bridge Hand
5757:Keohane North American Swiss Teams
3975:
3867:
3681:Probability of Losing-Trick Counts
3459:
3441:Number of possible hands and deals
3328:9-2-1-1, 9-2-2-0, 9-3-1-0, 9-4-0-0
2321:
2253:
2046:
1617:
1546:
1516:
1320:
25:
6184:
6084:List of contract bridge magazines
5503:
4389:Optimum contract and par contract
4185:Glossary of contract bridge terms
3997:Bridge Odds for Practical Players
3876:"Mathematical Tables" (Table 4).
2315:
2247:
3607:314,174,475,847,313,213,527,680
5882:Smith Life Master Women's Pairs
5637:World Senior Teams Championship
5632:World Senior Pairs Championship
5607:World Junior Teams Championship
5602:World Junior Pairs Championship
5477:United States Bridge Federation
5472:South African Bridge Federation
5407:American Contract Bridge League
4943:Non-simultaneous double squeeze
3890:American Contract Bridge League
3477:{\displaystyle {52 \choose 13}}
2338:Probability of HCP distribution
1932:The above probabilities assume
5912:Von Zedtwitz Life Master Pairs
5777:Manfield Non-Life Master Pairs
5767:Leventritt Silver Ribbon Pairs
5707:Edgar Kaplan Blue Ribbon Pairs
5652:World Women Pairs Championship
5622:World Mixed Teams Championship
5617:World Mixed Pairs Championship
5117:List of contract bridge people
4725:Principle of restricted choice
3984:Théorie Mathématique du Bridge
3960:
3949:
3938:
3914:
3615:5,197,480,921,767,366,548,160
3551:
3547:
3512:
3502:
2312:
2276:
2244:
2208:
2180:
2155:
2146:
2134:
2128:
2116:
2102:
2084:
2033:
2009:
2000:
1988:
1971:{\displaystyle n_{e}=n_{w}=13}
1912:
1874:
1863:
1838:
1832:
1794:
1780:
1742:
1494:
1475:
1469:
1450:
1444:
1418:
1410:
1372:
1301:
1282:
1276:
1257:
1251:
1225:
1217:
1179:
1124:
1112:
1090:
1052:
1018:
999:
963:
944:
907:cards in the suit is given by
854:
828:
798:
786:
780:
742:
734:
708:
679:
653:
633:
621:
507:
469:
13:
1:
6173:Contract bridge probabilities
6032:Contract Bridge for Beginners
5971:List of contract bridge books
5627:World Open Pairs Championship
5309:List of bridge administrators
4647:
3888:(5th ed.). Memphis, TN:
3861:
3524:{\displaystyle 52!/(13!)^{4}}
860:{\displaystyle (n_{e}+n_{w})}
685:{\displaystyle (n_{e}+n_{w})}
5917:Wagar Women's Knockout Teams
5802:Mitchell Board-a-Match Teams
5702:ACBL King or Queen of Bridge
5597:World IMP Pairs Championship
4082:
3564:Highest undistinguished card
3339:10-1-1-1, 10-2-1-0, 10-3-0-0
450:Calculation of probabilities
7:
5897:Truscott Senior Swiss Teams
5832:Non-Life Master Swiss Teams
5812:Nail Life Master Open Pairs
5772:Machlin Women's Swiss Teams
5717:Chicago Mixed Board-a-Match
5467:Norwegian Bridge Federation
5452:Hungarian Bridge Federation
5417:Brazilian Bridge Federation
5402:American Bridge Association
4968:Simultaneous double squeeze
4626:List of bidding conventions
4271:
3995:; Glauert, Michael (1980).
3670:
3662:
3654:
3646:
3638:
3630:
3623:69,848,690,581,204,198,656
3622:
3614:
3606:
3598:
3590:
3582:
3574:
3445:There are 635,013,559,600 (
3147:
3092:
2888:
2794:
2739:
887:cards in the suit and West
10:
6189:
5998:Terence Reese bibliography
5954:Publications and resources
5592:World Bridge Championships
5432:Canadian Bridge Federation
5422:Bridge Federation of India
5412:Austrian Bridge Federation
4195:History of contract bridge
4170:Duplicate bridge movements
2639:Hand pattern probabilities
6136:
6120:
6076:
5988:Edwin Kantar bibliography
5963:
5959:
5948:
5837:Norman Kay Platinum Pairs
5660:
5529:
5513:
5509:
5498:
5394:
5348:
5322:
5296:
5135:
5112:ACBL Youngest Life Master
5104:
5100:
5089:
5030:
4778:
4657:
4653:
4642:
4618:
4492:
4419:Quantitative notrump bids
4409:Principle of fast arrival
4281:
4277:
4266:
4088:
4077:
4023:Master the Odds in Bridge
3273:4-3-3-3, 4-4-3-2, 4-4-4-1
3204:4-3-3-3, 4-4-3-2, 5-3-3-2
2382:
2374:
2366:
2358:
374:
315:
256:
211:
166:
135:
104:
85:
6018:Bridge Squeezes Complete
5993:Hugh Kelsey bibliography
5722:Fall National Open Pairs
5095:People and organizations
4200:Laws of Duplicate Bridge
3631:800,827,437,699,287,808
3180:. Below table gives the
5927:Whitehead Women's Pairs
5752:Jacoby Open Swiss Teams
5612:World Mind Sports Games
5482:World Bridge Federation
5437:Dutch Bridge Federation
5371:Galatasaray Bridge Team
4665:List of play techniques
4500:List of bidding systems
4160:Contract bridge diagram
6060:Right Through the Pack
5792:Mini-Blue Ribbon Pairs
5577:Triple crown of bridge
5552:Cavendish Invitational
5447:European Bridge League
5381:Portland Club (London)
5314:List of bridge writers
4983:Stepping-stone squeeze
4928:Entry-shifting squeeze
4565:Kaplan–Sheinwold
4469:Useful space principle
3639:8,110,864,720,503,360
3525:
3478:
2344:a priori probabilities
2328:
2260:
2187:
1972:
1919:
1726:
1706:
1686:
1666:
1031:
901:
881:
861:
811:
686:
640:
608:
594:unknown cards holding
588:
561:
547:unknown cards holding
541:
514:
5872:Senior Knockout Teams
5867:Roth Open Swiss Teams
5427:British Bridge League
4560:Highly unusual method
4535:Bridge World Standard
3967:Counting Bridge Deals
3526:
3479:
2329:
2261:
2188:
1973:
1920:
1727:
1707:
1687:
1667:
1032:
902:
882:
862:
812:
687:
646:cards in the suit in
641:
639:{\displaystyle (a+b)}
609:
589:
587:{\displaystyle n_{w}}
562:
542:
540:{\displaystyle n_{e}}
515:
6067:Tickets to the Devil
5862:Rockwell Mixed Pairs
5847:North American Pairs
5817:National 199er Pairs
5747:Hilliard Mixed Pairs
5742:Grand National Teams
5572:Senior Bowl (bridge)
5442:English Bridge Union
5376:Melville Bridge Club
4404:Prepared opening bid
3488:
3449:
2650:a priori probability
2270:
2202:
1982:
1936:
1736:
1716:
1696:
1676:
1041:
911:
891:
871:
825:
696:
650:
618:
598:
571:
551:
524:
458:
18:Bridge probabilities
6128:Grand Slam (BBC TV)
5932:Young LMâ1500 Pairs
5827:National 99er Pairs
5822:National 49er Pairs
5712:Bruce LMâ5000 Pairs
5642:World Team Olympiad
5127:Bridge Headquarters
4973:Single-suit squeeze
4948:Progressive squeeze
4913:Criss-cross squeeze
4369:Law of total tricks
4240:Traveling scoreslip
3986:. Gauthier-Villars.
3878:Francis, Henry G.;
3647:74,424,657,938,928
817:i.e. the number of
40:prior probabilities
6039:Design for Bidding
5976:Master Point Press
5922:Wernher Open Pairs
5877:Silodor Open Pairs
5661:National and Zonal
5356:Bridge Base Online
5136:Players by country
5015:Suit combinations:
4864:Morton's fork coup
4610:Strong club system
4429:Sacrifice (bridge)
4374:Losing-Trick Count
4294:Balancing (bridge)
4230:Singaporean bridge
4140:Cheating in bridge
4120:Bridge Murder case
3969:, Jeroen Warmerdam
3687:Losing-Trick Count
3535:". The answer is:
3521:
3474:
3350:11-1-1-0, 11-2-0-0
2324:
2256:
2183:
1968:
1915:
1722:
1702:
1682:
1662:
1027:
897:
877:
857:
807:
682:
636:
604:
584:
557:
537:
510:
6160:
6159:
6156:
6155:
6152:
6151:
6144:Bridge Base Basic
5944:
5943:
5940:
5939:
5907:Vanderbilt Trophy
5807:Mott-Smith Trophy
5787:Master Individual
5688:Gold Cup (bridge)
5557:Computer Olympiad
5494:
5493:
5490:
5489:
5085:
5084:
5081:
5080:
4958:Saturated squeeze
4844:Deschapelles coup
4638:
4637:
4634:
4633:
4605:Standard American
4530:Bridge Base Basic
4434:Shooting (bridge)
4359:Honor point count
4314:Bridge convention
4262:
4261:
4258:
4257:
4190:High card by suit
3880:Truscott, Alan F.
3859:
3858:
3852:12 is the maximum
3675:
3674:
3466:
3438:
3437:
3379:
3378:
3247:
3246:
3158:
3157:
3152:
3151:
2992:
2991:
2832:
2831:
2663:suit permutations
2636:
2635:
2153:
2061:
1725:{\displaystyle a}
1705:{\displaystyle b}
1685:{\displaystyle a}
1660:
1653:
1602:
1531:
1501:
1335:
1308:
1145:
1104:
1025:
970:
900:{\displaystyle b}
880:{\displaystyle a}
805:
607:{\displaystyle b}
560:{\displaystyle a}
447:
446:
16:(Redirected from
6180:
6111:The Bridge World
6093:
6092:
6007:
6006:
5985:
5984:
5961:
5960:
5950:
5949:
5852:Red Ribbon Pairs
5762:Lebhar IMP Pairs
5697:
5696:
5511:
5510:
5500:
5499:
5395:Governing bodies
5102:
5101:
5091:
5090:
5043:Journalist leads
5022:Suit combination
5017:
5016:
4938:Knockout squeeze
4908:Compound squeeze
4898:Cannibal squeeze
4893:Backwash squeeze
4888:
4887:
4809:
4808:
4790:
4789:
4705:Grosvenor gambit
4655:
4654:
4644:
4643:
4505:2/1 game forcing
4424:Reverse (bridge)
4334:Five-card majors
4279:
4278:
4268:
4267:
4175:Five-suit bridge
4165:Duplicate bridge
4090:
4089:
4079:
4078:
4064:
4057:
4050:
4041:
4040:
4036:
4010:
3987:
3970:
3964:
3958:
3953:
3947:
3942:
3936:
3930:
3924:
3918:
3912:
3911:
3874:
3692:
3691:
3655:630,343,600,320
3567:Number of deals
3561:
3560:
3553:
3549:
3530:
3528:
3527:
3522:
3520:
3519:
3501:
3483:
3481:
3480:
3475:
3473:
3472:
3471:
3458:
3381:
3380:
3256:
3255:
3240:4-4-4-1, 5-4-4-0
3187:
3186:
2996:
2995:
2836:
2835:
2676:
2675:
2672:
2671:
2350:
2349:
2333:
2331:
2330:
2325:
2265:
2263:
2262:
2257:
2192:
2190:
2189:
2184:
2179:
2178:
2154:
2152:
2108:
2070:
2068:
2067:
2066:
2057:
2045:
1977:
1975:
1974:
1969:
1961:
1960:
1948:
1947:
1924:
1922:
1921:
1916:
1911:
1910:
1898:
1897:
1873:
1862:
1861:
1831:
1830:
1818:
1817:
1793:
1779:
1778:
1766:
1765:
1731:
1729:
1728:
1723:
1711:
1709:
1708:
1703:
1691:
1689:
1688:
1683:
1671:
1669:
1668:
1663:
1661:
1659:
1658:
1652:
1651:
1642:
1641:
1640:
1628:
1627:
1616:
1610:
1609:
1608:
1607:
1601:
1594:
1593:
1583:
1570:
1569:
1557:
1556:
1545:
1538:
1537:
1536:
1527:
1515:
1507:
1502:
1500:
1487:
1486:
1462:
1461:
1443:
1442:
1430:
1429:
1416:
1397:
1396:
1384:
1383:
1368:
1367:
1355:
1354:
1344:
1342:
1341:
1340:
1331:
1319:
1309:
1307:
1294:
1293:
1269:
1268:
1250:
1249:
1237:
1236:
1223:
1204:
1203:
1191:
1190:
1175:
1174:
1162:
1161:
1151:
1146:
1144:
1130:
1110:
1105:
1097:
1089:
1088:
1076:
1075:
1051:
1036:
1034:
1033:
1028:
1026:
1024:
1011:
1010:
991:
987:
986:
976:
971:
969:
956:
955:
936:
932:
931:
921:
906:
904:
903:
898:
886:
884:
883:
878:
866:
864:
863:
858:
853:
852:
840:
839:
816:
814:
813:
808:
806:
804:
767:
766:
754:
753:
740:
733:
732:
720:
719:
706:
691:
689:
688:
683:
678:
677:
665:
664:
645:
643:
642:
637:
613:
611:
610:
605:
593:
591:
590:
585:
583:
582:
566:
564:
563:
558:
546:
544:
543:
538:
536:
535:
519:
517:
516:
511:
506:
505:
493:
492:
468:
83:
82:
21:
6188:
6187:
6183:
6182:
6181:
6179:
6178:
6177:
6163:
6162:
6161:
6148:
6132:
6116:
6104:Bridge Magazine
6097:Bridge d'Italia
6090:
6089:
6072:
6004:
6003:
5983:Bibliographies:
5982:
5981:
5955:
5936:
5732:Fishbein Trophy
5727:Fast Open Pairs
5694:
5693:
5656:
5587:WBF Youth Award
5525:
5505:
5486:
5390:
5344:
5318:
5292:
5131:
5096:
5077:
5038:Forcing defense
5026:
5014:
5013:
4885:
4884:
4834:Coup en passant
4824:Belladonna coup
4806:
4805:
4787:
4786:
4774:
4760:Trump promotion
4715:Percentage play
4649:
4630:
4614:
4540:Canapé (bridge)
4488:
4364:Inverted minors
4354:Hand evaluation
4324:Convention card
4273:
4254:
4215:Neuberg formula
4155:Contract bridge
4150:Computer bridge
4084:
4073:
4071:Contract bridge
4068:
4033:
4007:
3978:
3976:Further reading
3973:
3965:
3961:
3954:
3950:
3943:
3939:
3931:
3927:
3919:
3915:
3900:
3892:. p. 278.
3875:
3868:
3864:
3808:100,454,895,360
3797:145,394,132,760
3786:145,971,648,360
3775:104,416,332,340
3698:Number of Hands
3683:
3539:surface area of
3515:
3511:
3497:
3489:
3486:
3485:
3467:
3454:
3453:
3452:
3450:
3447:
3446:
3443:
3375:0.000000000006
3213:
3145:0.0000000000063
2641:
2340:
2271:
2268:
2267:
2203:
2200:
2199:
2168:
2164:
2109:
2071:
2069:
2062:
2047:
2041:
2040:
2039:
1983:
1980:
1979:
1956:
1952:
1943:
1939:
1937:
1934:
1933:
1927:Kronecker delta
1906:
1902:
1893:
1889:
1866:
1851:
1847:
1826:
1822:
1813:
1809:
1786:
1774:
1770:
1761:
1757:
1737:
1734:
1733:
1717:
1714:
1713:
1697:
1694:
1693:
1677:
1674:
1673:
1654:
1647:
1643:
1636:
1632:
1623:
1619:
1618:
1612:
1611:
1603:
1589:
1585:
1584:
1565:
1561:
1552:
1548:
1547:
1541:
1540:
1539:
1532:
1517:
1511:
1510:
1509:
1508:
1506:
1482:
1478:
1457:
1453:
1438:
1434:
1425:
1421:
1417:
1392:
1388:
1379:
1375:
1363:
1359:
1350:
1346:
1345:
1343:
1336:
1321:
1315:
1314:
1313:
1289:
1285:
1264:
1260:
1245:
1241:
1232:
1228:
1224:
1199:
1195:
1186:
1182:
1170:
1166:
1157:
1153:
1152:
1150:
1131:
1111:
1109:
1096:
1084:
1080:
1071:
1067:
1044:
1042:
1039:
1038:
1006:
1002:
992:
982:
978:
977:
975:
951:
947:
937:
927:
923:
922:
920:
912:
909:
908:
892:
889:
888:
872:
869:
868:
848:
844:
835:
831:
826:
823:
822:
762:
758:
749:
745:
741:
728:
724:
715:
711:
707:
705:
697:
694:
693:
673:
669:
660:
656:
651:
648:
647:
619:
616:
615:
599:
596:
595:
578:
574:
572:
569:
568:
552:
549:
548:
531:
527:
525:
522:
521:
501:
497:
488:
484:
461:
459:
456:
455:
452:
99:
48:
30:In the game of
28:
23:
22:
15:
12:
11:
5:
6186:
6176:
6175:
6158:
6157:
6154:
6153:
6150:
6149:
6147:
6146:
6140:
6138:
6137:External links
6134:
6133:
6131:
6130:
6124:
6122:
6118:
6117:
6115:
6114:
6107:
6100:
6086:
6080:
6078:
6074:
6073:
6071:
6070:
6063:
6056:
6049:
6042:
6035:
6028:
6025:The Cardturner
6021:
6014:
6000:
5995:
5990:
5978:
5973:
5967:
5965:
5957:
5956:
5946:
5945:
5942:
5941:
5938:
5937:
5935:
5934:
5929:
5924:
5919:
5914:
5909:
5904:
5899:
5894:
5889:
5884:
5879:
5874:
5869:
5864:
5859:
5854:
5849:
5844:
5839:
5834:
5829:
5824:
5819:
5814:
5809:
5804:
5799:
5794:
5789:
5784:
5779:
5774:
5769:
5764:
5759:
5754:
5749:
5744:
5739:
5734:
5729:
5724:
5719:
5714:
5709:
5704:
5699:
5690:
5685:
5680:
5675:
5673:Camrose Trophy
5670:
5664:
5662:
5658:
5657:
5655:
5654:
5649:
5644:
5639:
5634:
5629:
5624:
5619:
5614:
5609:
5604:
5599:
5594:
5589:
5584:
5579:
5574:
5569:
5564:
5559:
5554:
5549:
5544:
5539:
5533:
5531:
5527:
5526:
5524:
5523:
5517:
5515:
5507:
5506:
5496:
5495:
5492:
5491:
5488:
5487:
5485:
5484:
5479:
5474:
5469:
5464:
5459:
5454:
5449:
5444:
5439:
5434:
5429:
5424:
5419:
5414:
5409:
5404:
5398:
5396:
5392:
5391:
5389:
5388:
5383:
5378:
5373:
5368:
5363:
5361:Cavendish Club
5358:
5352:
5350:
5346:
5345:
5343:
5342:
5337:
5332:
5326:
5324:
5320:
5319:
5317:
5316:
5311:
5306:
5300:
5298:
5294:
5293:
5291:
5290:
5285:
5280:
5275:
5270:
5265:
5260:
5255:
5250:
5245:
5240:
5235:
5230:
5225:
5220:
5215:
5210:
5205:
5200:
5195:
5190:
5185:
5180:
5175:
5170:
5165:
5160:
5155:
5150:
5145:
5139:
5137:
5133:
5132:
5130:
5129:
5124:
5119:
5114:
5108:
5106:
5098:
5097:
5087:
5086:
5083:
5082:
5079:
5078:
5076:
5075:
5070:
5065:
5060:
5055:
5050:
5045:
5040:
5034:
5032:
5028:
5027:
5025:
5024:
5019:
5010:
5008:Winkle squeeze
5005:
5000:
4995:
4993:Triple squeeze
4990:
4985:
4980:
4975:
4970:
4965:
4963:Simple squeeze
4960:
4955:
4953:Pseudo-squeeze
4950:
4945:
4940:
4935:
4930:
4925:
4920:
4918:Double squeeze
4915:
4910:
4905:
4900:
4895:
4890:
4881:
4876:
4871:
4866:
4861:
4856:
4854:Loser on loser
4851:
4846:
4841:
4839:Crocodile coup
4836:
4831:
4826:
4821:
4816:
4811:
4802:
4797:
4792:
4782:
4780:
4776:
4775:
4773:
4772:
4767:
4762:
4757:
4752:
4747:
4742:
4737:
4732:
4727:
4722:
4717:
4712:
4707:
4702:
4697:
4692:
4687:
4682:
4677:
4672:
4670:Avoidance play
4667:
4661:
4659:
4651:
4650:
4640:
4639:
4636:
4635:
4632:
4631:
4629:
4628:
4622:
4620:
4616:
4615:
4613:
4612:
4607:
4602:
4597:
4592:
4587:
4585:Precision Club
4582:
4577:
4572:
4567:
4562:
4557:
4552:
4547:
4542:
4537:
4532:
4527:
4522:
4517:
4515:Bidding system
4512:
4507:
4502:
4496:
4494:
4490:
4489:
4487:
4486:
4481:
4476:
4471:
4466:
4461:
4456:
4454:Takeout double
4451:
4446:
4441:
4436:
4431:
4426:
4421:
4416:
4411:
4406:
4401:
4396:
4391:
4386:
4381:
4376:
4371:
4366:
4361:
4356:
4351:
4346:
4341:
4336:
4331:
4326:
4321:
4316:
4311:
4309:Board (bridge)
4306:
4304:Bidding system
4301:
4296:
4291:
4285:
4283:
4275:
4274:
4264:
4263:
4260:
4259:
4256:
4255:
4253:
4252:
4247:
4242:
4237:
4232:
4227:
4222:
4217:
4212:
4207:
4202:
4197:
4192:
4187:
4182:
4177:
4172:
4167:
4162:
4157:
4152:
4147:
4142:
4137:
4132:
4127:
4125:Bridge scoring
4122:
4117:
4112:
4107:
4102:
4100:Auction bridge
4096:
4094:
4086:
4085:
4075:
4074:
4067:
4066:
4059:
4052:
4044:
4038:
4037:
4031:
4015:Reese, Terence
4011:
4005:
3989:
3977:
3974:
3972:
3971:
3959:
3948:
3937:
3925:
3913:
3898:
3865:
3863:
3860:
3857:
3856:
3853:
3850:
3846:
3845:
3842:
3839:
3835:
3834:
3831:
3830:12,204,432,000
3828:
3824:
3823:
3820:
3819:45,618,822,000
3817:
3813:
3812:
3809:
3806:
3802:
3801:
3798:
3795:
3791:
3790:
3787:
3784:
3780:
3779:
3776:
3773:
3769:
3768:
3765:
3764:53,704,810,560
3762:
3758:
3757:
3754:
3753:19,749,204,780
3751:
3747:
3746:
3743:
3740:
3736:
3735:
3732:
3729:
3725:
3724:
3721:
3718:
3714:
3713:
3710:
3707:
3703:
3702:
3699:
3696:
3682:
3679:
3673:
3672:
3669:
3665:
3664:
3663:4,997,094,488
3661:
3657:
3656:
3653:
3649:
3648:
3645:
3641:
3640:
3637:
3633:
3632:
3629:
3625:
3624:
3621:
3617:
3616:
3613:
3609:
3608:
3605:
3601:
3600:
3597:
3593:
3592:
3589:
3585:
3584:
3581:
3577:
3576:
3573:
3569:
3568:
3565:
3518:
3514:
3510:
3507:
3504:
3500:
3496:
3493:
3470:
3465:
3462:
3457:
3442:
3439:
3436:
3435:
3432:
3429:
3425:
3424:
3421:
3418:
3414:
3413:
3410:
3407:
3403:
3402:
3399:
3396:
3392:
3391:
3388:
3385:
3377:
3376:
3373:
3370:
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:
3245:
3244:
3241:
3238:
3237:2 Three-suited
3234:
3233:
3230:
3227:
3223:
3222:
3219:
3215:
3209:
3208:
3205:
3202:
3198:
3197:
3194:
3191:
3170:single suiters
3166:balanced hands
3156:
3155:
3153:
3150:
3149:
3146:
3143:
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:
2993:
2990:
2989:
2986:
2983:
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:
2833:
2830:
2829:
2826:
2823:
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:
2640:
2637:
2634:
2633:
2630:
2627:
2624:
2621:
2618:
2615:
2612:
2608:
2607:
2604:
2601:
2598:
2595:
2592:
2589:
2586:
2582:
2581:
2578:
2575:
2572:
2569:
2566:
2563:
2560:
2557:
2554:
2550:
2549:
2546:
2543:
2540:
2537:
2534:
2531:
2528:
2525:
2522:
2518:
2517:
2514:
2511:
2508:
2505:
2502:
2499:
2496:
2493:
2490:
2486:
2485:
2482:
2479:
2476:
2473:
2470:
2467:
2464:
2461:
2458:
2454:
2453:
2450:
2447:
2444:
2441:
2438:
2435:
2432:
2429:
2426:
2422:
2421:
2418:
2415:
2412:
2409:
2406:
2403:
2400:
2397:
2394:
2390:
2389:
2386:
2383:
2381:
2378:
2375:
2373:
2370:
2367:
2365:
2362:
2359:
2357:
2354:
2339:
2336:
2323:
2320:
2317:
2314:
2311:
2308:
2305:
2302:
2299:
2296:
2293:
2290:
2287:
2284:
2281:
2278:
2275:
2255:
2252:
2249:
2246:
2243:
2240:
2237:
2234:
2231:
2228:
2225:
2222:
2219:
2216:
2213:
2210:
2207:
2182:
2177:
2174:
2171:
2167:
2163:
2160:
2157:
2151:
2148:
2145:
2142:
2139:
2136:
2133:
2130:
2127:
2124:
2121:
2118:
2115:
2112:
2107:
2104:
2101:
2098:
2095:
2092:
2089:
2086:
2083:
2080:
2077:
2074:
2065:
2060:
2056:
2053:
2050:
2044:
2038:
2035:
2032:
2029:
2026:
2023:
2020:
2017:
2014:
2011:
2008:
2005:
2002:
1999:
1996:
1993:
1990:
1987:
1967:
1964:
1959:
1955:
1951:
1946:
1942:
1914:
1909:
1905:
1901:
1896:
1892:
1888:
1885:
1882:
1879:
1876:
1872:
1869:
1865:
1860:
1857:
1854:
1850:
1846:
1843:
1840:
1837:
1834:
1829:
1825:
1821:
1816:
1812:
1808:
1805:
1802:
1799:
1796:
1792:
1789:
1785:
1782:
1777:
1773:
1769:
1764:
1760:
1756:
1753:
1750:
1747:
1744:
1741:
1721:
1701:
1681:
1657:
1650:
1646:
1639:
1635:
1631:
1626:
1622:
1615:
1606:
1600:
1597:
1592:
1588:
1582:
1579:
1576:
1573:
1568:
1564:
1560:
1555:
1551:
1544:
1535:
1530:
1526:
1523:
1520:
1514:
1505:
1499:
1496:
1493:
1490:
1485:
1481:
1477:
1474:
1471:
1468:
1465:
1460:
1456:
1452:
1449:
1446:
1441:
1437:
1433:
1428:
1424:
1420:
1415:
1412:
1409:
1406:
1403:
1400:
1395:
1391:
1387:
1382:
1378:
1374:
1371:
1366:
1362:
1358:
1353:
1349:
1339:
1334:
1330:
1327:
1324:
1318:
1312:
1306:
1303:
1300:
1297:
1292:
1288:
1284:
1281:
1278:
1275:
1272:
1267:
1263:
1259:
1256:
1253:
1248:
1244:
1240:
1235:
1231:
1227:
1222:
1219:
1216:
1213:
1210:
1207:
1202:
1198:
1194:
1189:
1185:
1181:
1178:
1173:
1169:
1165:
1160:
1156:
1149:
1143:
1140:
1137:
1134:
1129:
1126:
1123:
1120:
1117:
1114:
1108:
1103:
1100:
1095:
1092:
1087:
1083:
1079:
1074:
1070:
1066:
1063:
1060:
1057:
1054:
1050:
1047:
1023:
1020:
1017:
1014:
1009:
1005:
1001:
998:
995:
990:
985:
981:
974:
968:
965:
962:
959:
954:
950:
946:
943:
940:
935:
930:
926:
919:
916:
896:
876:
856:
851:
847:
843:
838:
834:
830:
803:
800:
797:
794:
791:
788:
785:
782:
779:
776:
773:
770:
765:
761:
757:
752:
748:
744:
739:
736:
731:
727:
723:
718:
714:
710:
704:
701:
681:
676:
672:
668:
663:
659:
655:
635:
632:
629:
626:
623:
603:
581:
577:
556:
534:
530:
509:
504:
500:
496:
491:
487:
483:
480:
477:
474:
471:
467:
464:
451:
448:
445:
444:
441:
438:
435:
431:
430:
427:
424:
421:
417:
416:
413:
410:
407:
403:
402:
399:
396:
393:
389:
388:
385:
382:
379:
376:
372:
371:
368:
365:
362:
358:
357:
354:
351:
348:
344:
343:
340:
337:
334:
330:
329:
326:
323:
320:
317:
313:
312:
309:
306:
303:
299:
298:
295:
292:
289:
285:
284:
281:
278:
275:
271:
270:
267:
264:
261:
258:
254:
253:
250:
247:
244:
240:
239:
236:
233:
230:
226:
225:
222:
219:
216:
213:
209:
208:
205:
202:
199:
195:
194:
191:
188:
185:
181:
180:
177:
174:
171:
168:
164:
163:
160:
157:
154:
150:
149:
146:
143:
140:
137:
133:
132:
129:
126:
123:
119:
118:
115:
112:
109:
106:
102:
101:
96:
93:
90:
87:
47:
44:
26:
9:
6:
4:
3:
2:
6185:
6174:
6171:
6170:
6168:
6145:
6142:
6141:
6139:
6135:
6129:
6126:
6125:
6123:
6119:
6113:
6112:
6108:
6106:
6105:
6101:
6099:
6098:
6094:
6087:
6085:
6082:
6081:
6079:
6075:
6069:
6068:
6064:
6062:
6061:
6057:
6055:
6054:
6050:
6048:
6047:
6043:
6041:
6040:
6036:
6034:
6033:
6029:
6027:
6026:
6022:
6020:
6019:
6015:
6013:
6012:
6008:
6001:
5999:
5996:
5994:
5991:
5989:
5986:
5979:
5977:
5974:
5972:
5969:
5968:
5966:
5962:
5958:
5951:
5947:
5933:
5930:
5928:
5925:
5923:
5920:
5918:
5915:
5913:
5910:
5908:
5905:
5903:
5900:
5898:
5895:
5893:
5890:
5888:
5885:
5883:
5880:
5878:
5875:
5873:
5870:
5868:
5865:
5863:
5860:
5858:
5855:
5853:
5850:
5848:
5845:
5843:
5840:
5838:
5835:
5833:
5830:
5828:
5825:
5823:
5820:
5818:
5815:
5813:
5810:
5808:
5805:
5803:
5800:
5798:
5797:Mini-Spingold
5795:
5793:
5790:
5788:
5785:
5783:
5780:
5778:
5775:
5773:
5770:
5768:
5765:
5763:
5760:
5758:
5755:
5753:
5750:
5748:
5745:
5743:
5740:
5738:
5735:
5733:
5730:
5728:
5725:
5723:
5720:
5718:
5715:
5713:
5710:
5708:
5705:
5703:
5700:
5698:
5691:
5689:
5686:
5684:
5681:
5679:
5676:
5674:
5671:
5669:
5666:
5665:
5663:
5659:
5653:
5650:
5648:
5645:
5643:
5640:
5638:
5635:
5633:
5630:
5628:
5625:
5623:
5620:
5618:
5615:
5613:
5610:
5608:
5605:
5603:
5600:
5598:
5595:
5593:
5590:
5588:
5585:
5583:
5580:
5578:
5575:
5573:
5570:
5568:
5567:Rosenblum Cup
5565:
5563:
5562:McConnell Cup
5560:
5558:
5555:
5553:
5550:
5548:
5545:
5543:
5540:
5538:
5535:
5534:
5532:
5528:
5522:
5519:
5518:
5516:
5512:
5508:
5504:Championships
5501:
5497:
5483:
5480:
5478:
5475:
5473:
5470:
5468:
5465:
5463:
5460:
5458:
5455:
5453:
5450:
5448:
5445:
5443:
5440:
5438:
5435:
5433:
5430:
5428:
5425:
5423:
5420:
5418:
5415:
5413:
5410:
5408:
5405:
5403:
5400:
5399:
5397:
5393:
5387:
5384:
5382:
5379:
5377:
5374:
5372:
5369:
5367:
5364:
5362:
5359:
5357:
5354:
5353:
5351:
5347:
5341:
5338:
5336:
5333:
5331:
5328:
5327:
5325:
5321:
5315:
5312:
5310:
5307:
5305:
5302:
5301:
5299:
5295:
5289:
5288:United States
5286:
5284:
5281:
5279:
5276:
5274:
5271:
5269:
5266:
5264:
5261:
5259:
5256:
5254:
5251:
5249:
5246:
5244:
5241:
5239:
5236:
5234:
5231:
5229:
5226:
5224:
5221:
5219:
5216:
5214:
5211:
5209:
5206:
5204:
5201:
5199:
5196:
5194:
5191:
5189:
5186:
5184:
5181:
5179:
5176:
5174:
5171:
5169:
5166:
5164:
5161:
5159:
5156:
5154:
5151:
5149:
5146:
5144:
5141:
5140:
5138:
5134:
5128:
5125:
5123:
5120:
5118:
5115:
5113:
5110:
5109:
5107:
5103:
5099:
5092:
5088:
5074:
5071:
5069:
5066:
5064:
5063:Rusinow leads
5061:
5059:
5056:
5054:
5053:Rule of 10-12
5051:
5049:
5046:
5044:
5041:
5039:
5036:
5035:
5033:
5031:Defender play
5029:
5023:
5020:
5018:
5011:
5009:
5006:
5004:
5001:
4999:
4998:Trump squeeze
4996:
4994:
4991:
4989:
4988:Strip squeeze
4986:
4984:
4981:
4979:
4976:
4974:
4971:
4969:
4966:
4964:
4961:
4959:
4956:
4954:
4951:
4949:
4946:
4944:
4941:
4939:
4936:
4934:
4933:Guard squeeze
4931:
4929:
4926:
4924:
4923:Entry squeeze
4921:
4919:
4916:
4914:
4911:
4909:
4906:
4904:
4903:Clash squeeze
4901:
4899:
4896:
4894:
4891:
4889:
4882:
4880:
4877:
4875:
4872:
4870:
4869:Scissors coup
4867:
4865:
4862:
4860:
4859:Merrimac coup
4857:
4855:
4852:
4850:
4847:
4845:
4842:
4840:
4837:
4835:
4832:
4830:
4827:
4825:
4822:
4820:
4817:
4815:
4814:Alcatraz coup
4812:
4810:
4803:
4801:
4798:
4796:
4793:
4791:
4784:
4783:
4781:
4779:Declarer play
4777:
4771:
4770:Vacant Places
4768:
4766:
4763:
4761:
4758:
4756:
4753:
4751:
4748:
4746:
4743:
4741:
4738:
4736:
4733:
4731:
4730:Probabilities
4728:
4726:
4723:
4721:
4718:
4716:
4713:
4711:
4708:
4706:
4703:
4701:
4698:
4696:
4693:
4691:
4688:
4686:
4683:
4681:
4678:
4676:
4673:
4671:
4668:
4666:
4663:
4662:
4660:
4656:
4652:
4645:
4641:
4627:
4624:
4623:
4621:
4617:
4611:
4608:
4606:
4603:
4601:
4598:
4596:
4593:
4591:
4588:
4586:
4583:
4581:
4578:
4576:
4573:
4571:
4568:
4566:
4563:
4561:
4558:
4556:
4553:
4551:
4548:
4546:
4543:
4541:
4538:
4536:
4533:
4531:
4528:
4526:
4523:
4521:
4518:
4516:
4513:
4511:
4508:
4506:
4503:
4501:
4498:
4497:
4495:
4491:
4485:
4482:
4480:
4477:
4475:
4472:
4470:
4467:
4465:
4462:
4460:
4457:
4455:
4452:
4450:
4447:
4445:
4442:
4440:
4439:Single suiter
4437:
4435:
4432:
4430:
4427:
4425:
4422:
4420:
4417:
4415:
4412:
4410:
4407:
4405:
4402:
4400:
4397:
4395:
4392:
4390:
4387:
4385:
4382:
4380:
4377:
4375:
4372:
4370:
4367:
4365:
4362:
4360:
4357:
4355:
4352:
4350:
4347:
4345:
4342:
4340:
4337:
4335:
4332:
4330:
4327:
4325:
4322:
4320:
4319:Brown sticker
4317:
4315:
4312:
4310:
4307:
4305:
4302:
4300:
4297:
4295:
4292:
4290:
4289:Balanced hand
4287:
4286:
4284:
4280:
4276:
4269:
4265:
4251:
4248:
4246:
4243:
4241:
4238:
4236:
4233:
4231:
4228:
4226:
4223:
4221:
4220:Rubber bridge
4218:
4216:
4213:
4211:
4208:
4206:
4203:
4201:
4198:
4196:
4193:
4191:
4188:
4186:
4183:
4181:
4178:
4176:
4173:
4171:
4168:
4166:
4163:
4161:
4158:
4156:
4153:
4151:
4148:
4146:
4143:
4141:
4138:
4136:
4133:
4131:
4128:
4126:
4123:
4121:
4118:
4116:
4115:Bridge maxims
4113:
4111:
4110:Bridge-O-Rama
4108:
4106:
4105:Bridge ethics
4103:
4101:
4098:
4097:
4095:
4091:
4087:
4080:
4076:
4072:
4065:
4060:
4058:
4053:
4051:
4046:
4045:
4042:
4034:
4032:0-575-02597-2
4028:
4024:
4020:
4019:Trézel, Roger
4016:
4012:
4008:
4006:0-575-02799-1
4002:
3998:
3994:
3990:
3985:
3980:
3979:
3968:
3963:
3957:
3952:
3946:
3941:
3935:
3929:
3923:
3917:
3909:
3905:
3901:
3899:0-943855-48-9
3895:
3891:
3887:
3886:
3881:
3873:
3871:
3866:
3854:
3851:
3848:
3847:
3843:
3841:1,451,520,000
3840:
3837:
3836:
3832:
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:
3742:5,080,948,428
3741:
3738:
3737:
3733:
3730:
3727:
3726:
3722:
3719:
3716:
3715:
3711:
3708:
3705:
3704:
3700:
3697:
3694:
3693:
3690:
3688:
3678:
3667:
3666:
3659:
3658:
3651:
3650:
3643:
3642:
3635:
3634:
3627:
3626:
3619:
3618:
3611:
3610:
3603:
3602:
3595:
3594:
3587:
3586:
3579:
3578:
3571:
3570:
3566:
3563:
3562:
3559:
3556:
3544:
3542:
3540:
3534:
3516:
3508:
3505:
3498:
3494:
3491:
3463:
3460:
3433:
3430:
3427:
3426:
3422:
3419:
3416:
3415:
3411:
3408:
3405:
3404:
3400:
3397:
3394:
3393:
3389:
3386:
3384:Shortest suit
3383:
3382:
3374:
3371:
3368:
3367:
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:
3254:
3252:
3242:
3239:
3236:
3235:
3231:
3228:
3225:
3224:
3220:
3216:
3214:Single-suited
3211:
3210:
3206:
3203:
3200:
3199:
3195:
3192:
3189:
3188:
3185:
3183:
3179:
3178:three-suiters
3175:
3171:
3167:
3163:
3154:
3144:
3141:
3140:
3136:
3133:
3130:
3129:
3125:
3122:
3119:
3118:
3114:
3111:
3108:
3107:
3103:
3100:
3097:
3096:
3089:
3086:
3085:
3081:
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:
2994:
2987:
2984:
2981:
2980:
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:
2885:
2882:
2881:
2877:
2874:
2871:
2870:
2866:
2863:
2860:
2859:
2855:
2852:
2849:
2848:
2844:
2841:
2838:
2837:
2834:
2827:
2824:
2821:
2820:
2816:
2813:
2810:
2809:
2805:
2802:
2799:
2798:
2791:
2788:
2787:
2783:
2780:
2777:
2776:
2772:
2769:
2766:
2765:
2761:
2758:
2755:
2754:
2750:
2747:
2744:
2743:
2736:
2733:
2732:
2728:
2725:
2722:
2721:
2717:
2714:
2711:
2710:
2706:
2703:
2700:
2699:
2695:
2692:
2689:
2688:
2684:
2681:
2678:
2677:
2674:
2673:
2670:
2666:
2664:
2658:
2656:
2652:
2651:
2646:
2631:
2628:
2625:
2622:
2619:
2616:
2613:
2610:
2609:
2605:
2602:
2599:
2596:
2593:
2590:
2587:
2584:
2583:
2579:
2576:
2573:
2570:
2567:
2564:
2561:
2558:
2555:
2552:
2551:
2547:
2544:
2541:
2538:
2535:
2532:
2529:
2526:
2523:
2520:
2519:
2515:
2512:
2509:
2506:
2503:
2500:
2497:
2494:
2491:
2488:
2487:
2483:
2480:
2477:
2474:
2471:
2468:
2465:
2462:
2459:
2456:
2455:
2451:
2448:
2445:
2442:
2439:
2436:
2433:
2430:
2427:
2424:
2423:
2419:
2416:
2413:
2410:
2407:
2404:
2401:
2398:
2395:
2392:
2391:
2387:
2384:
2379:
2376:
2371:
2368:
2363:
2360:
2355:
2352:
2351:
2348:
2345:
2335:
2318:
2309:
2306:
2303:
2300:
2297:
2294:
2291:
2288:
2285:
2282:
2279:
2273:
2250:
2241:
2238:
2235:
2232:
2229:
2226:
2223:
2220:
2217:
2214:
2211:
2205:
2197:
2175:
2172:
2169:
2165:
2161:
2158:
2149:
2143:
2140:
2137:
2131:
2125:
2122:
2119:
2113:
2110:
2105:
2099:
2096:
2093:
2090:
2087:
2081:
2078:
2075:
2072:
2058:
2054:
2051:
2048:
2036:
2030:
2027:
2024:
2021:
2018:
2015:
2012:
2006:
2003:
1997:
1994:
1991:
1985:
1965:
1962:
1957:
1953:
1949:
1944:
1940:
1930:
1928:
1907:
1903:
1899:
1894:
1890:
1886:
1883:
1880:
1877:
1870:
1867:
1858:
1855:
1852:
1848:
1844:
1841:
1835:
1827:
1823:
1819:
1814:
1810:
1806:
1803:
1800:
1797:
1790:
1787:
1783:
1775:
1771:
1767:
1762:
1758:
1754:
1751:
1748:
1745:
1739:
1719:
1699:
1679:
1648:
1644:
1637:
1633:
1629:
1624:
1620:
1598:
1595:
1590:
1586:
1580:
1577:
1574:
1571:
1566:
1562:
1558:
1553:
1549:
1528:
1524:
1521:
1518:
1503:
1497:
1491:
1488:
1483:
1479:
1472:
1466:
1463:
1458:
1454:
1447:
1439:
1435:
1431:
1426:
1422:
1413:
1407:
1404:
1401:
1398:
1393:
1389:
1385:
1380:
1376:
1369:
1364:
1360:
1356:
1351:
1347:
1332:
1328:
1325:
1322:
1310:
1304:
1298:
1295:
1290:
1286:
1279:
1273:
1270:
1265:
1261:
1254:
1246:
1242:
1238:
1233:
1229:
1220:
1214:
1211:
1208:
1205:
1200:
1196:
1192:
1187:
1183:
1176:
1171:
1167:
1163:
1158:
1154:
1147:
1141:
1138:
1135:
1132:
1127:
1121:
1118:
1115:
1106:
1101:
1098:
1093:
1085:
1081:
1077:
1072:
1068:
1064:
1061:
1058:
1055:
1048:
1045:
1037:. Therefore,
1021:
1015:
1012:
1007:
1003:
996:
993:
988:
983:
979:
972:
966:
960:
957:
952:
948:
941:
938:
933:
928:
924:
917:
914:
894:
874:
849:
845:
841:
836:
832:
820:
801:
795:
792:
789:
783:
777:
774:
771:
768:
763:
759:
755:
750:
746:
737:
729:
725:
721:
716:
712:
702:
699:
674:
670:
666:
661:
657:
630:
627:
624:
601:
579:
575:
554:
532:
528:
502:
498:
494:
489:
485:
481:
478:
475:
472:
465:
462:
442:
439:
436:
433:
432:
428:
425:
422:
419:
418:
414:
411:
408:
405:
404:
400:
397:
394:
391:
390:
386:
383:
380:
377:
373:
369:
366:
363:
360:
359:
355:
352:
349:
346:
345:
341:
338:
335:
332:
331:
327:
324:
321:
318:
314:
310:
307:
304:
301:
300:
296:
293:
290:
287:
286:
282:
279:
276:
273:
272:
268:
265:
262:
259:
255:
251:
248:
245:
242:
241:
237:
234:
231:
228:
227:
223:
220:
217:
214:
210:
206:
203:
200:
197:
196:
192:
189:
186:
183:
182:
178:
175:
172:
169:
165:
161:
158:
155:
152:
151:
147:
144:
141:
138:
134:
130:
127:
124:
121:
120:
116:
113:
110:
107:
103:
97:
94:
91:
88:
84:
81:
79:
78:Vacant Places
74:
71:
69:
65:
61:
57:
53:
43:
41:
36:
33:
19:
6121:TV and Radio
6109:
6102:
6095:
6088:
6065:
6058:
6051:
6044:
6037:
6030:
6023:
6016:
6009:
6002:
5980:
5737:Goren Trophy
5692:
5537:Bermuda Bowl
5073:Smith signal
5048:Opening lead
5012:
5003:Vice squeeze
4978:Squeeze play
4883:
4849:Devil's coup
4804:
4785:
4750:Smother play
4729:
4720:Pin (bridge)
4685:Card reading
4600:SĂ€ffle Spade
4595:Romex system
4570:Little Major
4479:Weak two bid
4474:Void (cards)
4459:Three suiter
4344:Forcing pass
4205:Masterpoints
4130:Bridge whist
4022:
3996:
3993:Kelsey, Hugh
3983:
3962:
3951:
3940:
3928:
3916:
3883:
3701:Probability
3684:
3676:
3557:
3545:
3536:
3532:
3444:
3390:Probability
3364:0.000000003
3265:Probability
3259:Longest suit
3250:
3248:
3226:8 Two-suited
3196:Probability
3181:
3161:
3159:
3134:0.0000000032
2667:
2662:
2659:
2648:
2645:hand pattern
2644:
2642:
2388:Probability
2341:
2195:
1931:
819:permutations
453:
100:Probability
95:Combinations
89:Distribution
75:
72:
67:
55:
51:
49:
37:
29:
5668:Buffett Cup
5366:Crockford's
5335:Dallas Aces
5297:Other lists
5278:Switzerland
5248:New Zealand
5183:Netherlands
4879:Vienna coup
4800:Safety play
4619:Conventions
4580:Polish Club
4545:Carrot Club
4525:Boring Club
4449:Strong pass
4414:Psychic bid
4339:Forcing bid
4299:Bidding box
3731:872,361,936
3671:37,478,624
3174:two suiters
3002:Probability
2842:Probability
2682:Probability
2380:Probability
2372:Probability
2364:Probability
2356:Probability
92:Probability
6091:Magazines:
5782:Marcus Cup
5582:Venice Cup
5386:Savoy Club
5058:Rule of 11
4874:Trump coup
4590:Roman Club
4484:Zar Points
4464:Two suiter
4444:Stolen bid
4384:Minor suit
4379:Major suit
4210:Minibridge
3862:References
3720:90,206,044
3712:0.000668%
3550:2 and the
3395:Three card
3353:0.0000003
3201:3 Balanced
3162:hand types
3123:0.00000011
3112:0.00000025
1925:where the
692:spaces is
98:Individual
6077:Magazines
5857:Reisinger
5340:Four Aces
5330:Blue Team
5143:Australia
4886:Squeezes:
4819:Bath coup
4675:Beer card
4648:Card play
4520:Blue Club
4135:Bridgette
3709:4,245,032
3417:Singleton
3406:Doubleton
3342:0.000017
3190:Hand type
3101:0.0000015
3090:0.0000040
3079:0.0000097
2655:doubleton
2632:1.000000
2606:0.999999
2580:1.000000
2548:1.000000
2516:1.000000
2484:1.000000
2452:1.000000
2420:1.000000
2322:%
2316:≈
2307:−
2295:−
2254:%
2248:≈
2239:−
2227:−
2166:δ
2162:−
2141:−
2123:−
2097:−
2091:−
1849:δ
1845:−
1596:−
1578:−
1572:−
1489:−
1464:−
1405:−
1399:−
1296:−
1271:−
1212:−
1206:−
1148:×
1013:−
973:×
958:−
775:−
769:−
443:0.00082~
429:0.00178~
415:0.00306~
401:0.00421~
387:0.00467~
370:0.00261~
356:0.00484~
342:0.00727~
328:0.00888~
311:0.00745~
297:0.01211~
283:0.01615~
269:0.01776~
252:0.01956~
238:0.02826~
6167:Category
5887:Spingold
5258:Pakistan
5163:Bulgaria
4765:Uppercut
4745:Shooting
4555:Fantunes
4394:Overcall
4349:Game try
4083:Overview
4021:(1986).
3908:96188639
3723:0.0142%
3387:Patterns
3372:13-0-0-0
3361:12-1-0-0
3331:0.00037
3262:Patterns
3251:a priori
3218:13-0-0-0
3193:Patterns
3182:a priori
3142:13-0-0-0
3131:12-1-0-0
3120:11-2-0-0
3109:11-1-1-0
3098:10-3-0-0
3087:10-1-1-1
3068:0.000011
3065:10-2-1-0
3057:0.000031
3046:0.000056
3035:0.000082
2626:0.998983
2620:0.902410
2614:0.285846
2600:0.997864
2594:0.858174
2588:0.205565
2574:0.999997
2568:0.995763
2562:0.801240
2556:0.140025
2542:0.999990
2536:0.991985
2530:0.732097
2524:0.088163
2510:0.999972
2504:0.985549
2498:0.651828
2492:0.049708
2478:0.999923
2472:0.975187
2466:0.562382
2460:0.025085
2446:0.999806
2440:0.959137
2434:0.468331
2428:0.011523
2414:0.999542
2408:0.935520
2402:0.374768
2396:0.003639
2196:a priori
1871:′
1791:′
1049:′
466:′
224:0.0339~
207:0.0478~
193:0.0622~
179:0.0678~
68:a priori
5514:General
5223:Ireland
5213:Hungary
5208:Germany
5198:Fiction
5193:England
5178:Denmark
5158:Britain
5148:Austria
5105:General
4795:Finesse
4710:Hold up
4695:Endplay
4658:General
4575:Moscito
4493:Systems
4399:Preempt
4329:Cue bid
4282:General
4272:Bidding
4250:Vugraph
4180:Goulash
4145:Chicago
4093:General
3844:0.229%
3734:0.137%
3434:0.0511
3423:0.3055
3412:0.5380
3401:0.1054
3398:4-3-3-3
3369:13 card
3358:12 card
3347:11 card
3336:10 card
3320:0.0047
3309:0.0353
3298:0.1655
3287:0.4434
3276:0.3508
3243:0.0423
3232:0.2902
3221:0.1915
3207:0.4761
3076:9-4-0-0
3054:8-5-0-0
3043:7-6-0-0
3032:9-2-2-0
3024:0.00010
3021:9-3-1-0
3013:0.00018
3010:9-2-1-1
2999:Pattern
2985:0.00045
2982:8-4-1-0
2974:0.00072
2971:6-6-1-0
2963:0.00109
2960:8-3-2-0
2952:0.00109
2949:7-5-1-0
2941:0.00118
2938:8-3-1-1
2930:0.00192
2927:8-2-2-1
2919:0.00265
2916:7-3-3-0
2908:0.00362
2905:7-4-2-0
2897:0.00392
2894:7-4-1-1
2886:0.00513
2883:7-2-2-2
2875:0.00651
2872:6-5-2-0
2864:0.00705
2861:6-5-1-1
2853:0.00895
2850:5-5-3-0
2839:Pattern
2825:0.01243
2822:5-4-4-0
2814:0.01326
2811:6-4-3-0
2803:0.01881
2800:7-3-2-1
2792:0.02993
2789:4-4-4-1
2781:0.03174
2778:5-5-2-1
2770:0.03448
2767:6-3-3-1
2759:0.04702
2756:6-4-2-1
2748:0.05642
2745:6-3-2-2
2737:0.10536
2734:4-3-3-3
2726:0.10580
2723:5-4-2-2
2715:0.12931
2712:5-4-3-1
2704:0.15517
2701:5-3-3-2
2693:0.21551
2690:4-4-3-2
2679:Pattern
60:bidding
6005:Books:
5283:Taiwan
5273:Sweden
5268:Russia
5263:Poland
5253:Norway
5243:Monaco
5238:Mexico
5228:Israel
5203:France
5168:Canada
5153:Brazil
5068:Signal
4807:Coups:
4788:Basic:
4735:Revoke
4225:Screen
4029:
4003:
3906:
3896:
3833:1.92%
3822:7.18%
3811:15.8%
3800:22.9%
3789:23.0%
3778:16.4%
3767:8.46%
3756:3.11%
3325:9 card
3314:8 card
3303:7 card
3292:6 card
3281:5 card
3270:4 card
32:bridge
5964:Books
5530:World
5349:Clubs
5323:Teams
5233:Italy
5218:India
5188:Egypt
5173:China
4755:Tempo
4700:Entry
4680:Caddy
4245:Trump
3745:0.8%
3541:Earth
434:8 - 0
420:7 - 1
406:6 - 2
392:5 - 3
378:4 - 4
361:7 - 0
347:6 - 1
333:5 - 2
319:4 - 3
302:6 - 0
288:5 - 1
274:4 - 2
260:3 - 3
243:5 - 0
229:4 - 1
215:3 - 2
198:4 - 0
184:3 - 1
170:2 - 2
162:0.11
153:3 - 0
148:0.13
139:2 - 1
131:0.24
122:2 - 0
117:0.26
108:1 - 1
66:, or
56:split
4829:Coup
4740:Ruff
4690:Duck
4550:EHAA
4510:Acol
4235:Suit
4027:ISBN
4001:ISBN
3934:link
3922:link
3904:LCCN
3894:ISBN
3855:N/A
3685:The
3428:Void
3176:and
2266:and
454:Let
437:0.00
423:0.03
409:0.17
395:0.47
381:0.33
364:0.01
350:0.07
336:0.30
322:0.62
305:0.01
291:0.15
277:0.48
263:0.36
246:0.04
232:0.28
218:0.68
201:0.10
187:0.50
173:0.40
156:0.22
142:0.78
125:0.48
111:0.52
64:play
62:and
3695:LTC
3137:12
3126:12
3115:12
3104:12
3082:12
3071:24
3060:12
3049:12
3038:12
3027:24
3016:12
2988:24
2977:12
2966:24
2955:24
2944:12
2933:12
2922:12
2911:24
2900:12
2878:24
2867:12
2856:12
2828:12
2817:24
2806:24
2784:12
2773:12
2762:24
2751:12
2729:12
2718:24
2707:12
2696:12
2385:HCP
2377:HCP
2369:HCP
2361:HCP
2353:HCP
821:of
398:112
70:).
54:or
52:lie
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3902:.
3869:^
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3838:12
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2643:A
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2028:,
2022:,
2019:b
2016:,
2013:a
2010:(
2007:P
2004:=
2001:)
1998:b
1995:,
1992:a
1989:(
1986:P
1963:=
1958:w
1954:n
1950:=
1945:e
1941:n
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1908:w
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675:w
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