macroxue

The Zar Points are not as accurate as other simpler methods. That's my conclusion from analyzing 700K double dummy deals (downloaded from GIB site a long time ago). Numbers below are for deals with a 9-card fit. (Results are similar for 10/11-card fit.) Columns are: points, average tricks, average error, cumulative percentages of making 8 to 12 tricks, number of deals. Each unprotected honor in a short suit is treated as the next lower-ranked honor. Distributional points are counted for both hands. 4321-531 Pts Trks Err 8 9 10 11 12 Deals 24 9.1 0.93 96 76 34 5 0 31076 25 9.4 0.93 98 86 49 11 1 30373 26 9.8 0.93 99 92 64 21 2 28169 This is the baseline with Works and 5-3-1 distributional points for void-singleton-doubleton. On average 25 points make 9.4 tricks with an error of 0.93 trick. 49% deals make 10 tricks or more. Zar Pts Trks Err 8 9 10 11 12 Deals 50 9.1 0.94 96 76 33 05 0 21882 51 9.4 0.94 98 84 45 10 1 21732 52 9.6 0.93 99 89 56 14 1 20469 53 9.8 0.93 99 92 66 21 2 19836 On average 52 Zar points make 9.6 tricks with an error of 0.93 trick. 56% deals make 10 tricks or more. The average error is comparable to the baseline. 6421-531 Pts Trks Err 8 9 10 11 12 Deals 30 9.1 0.89 97 76 31 4 0 22832 31 9.3 0.89 98 84 43 7 0 22328 32 9.6 0.89 99 90 55 13 1 21607 33 9.8 0.87 99 94 67 20 2 20705 The plain 5-3-1 evaluation for void-singleton-doubleton is more accurate than Zar's (a+b)+(a-d). The average error drops below 0.9. BUMRAP-531 Pts Trks Err 8 9 10 11 12 Deals 24 9.0 0.88 96 72 26 3 0 29724 25 9.3 0.89 98 84 42 7 0 29389 26 9.6 0.88 99 91 58 14 1 27907 Now let's turn to BUMRAP with A=4.5, K=3, Q=1.5, J=0.75 and T=0.25. 50% game is between 25 and 26 points. The average error is comparable to 6421-531. Since no bidding systems can communicate fractions of a point, the points in both hands are rounded to the nearest integers before they are added together. 5321-531 Pts Trks Err 8 9 10 11 12 Deals 26 9.1 0.89 97 76 31 4 0 27252 27 9.4 0.88 98 86 46 9 0 26679 28 9.7 0.88 99 92 60 16 1 25460 If one doesn't like dealing with fractions, a simple way is to count A as 5 points and the accuracy for a game decision is still comparable to BUMRAP. To make the point scale compatible to 4321-531, one can still count A as 4 points but compensate that by subtracting 1 point for an ace-less hand and adding 1/2/3 points for 2/3/4 aces. Results are the same except that the relevant point range for a game decision changes from 26-28 to 24-26.

南家的加倍有问题，更好的选择是2C迈克尔扣叫显示五五高花。无论同伴选择哪一门，之后南家都直接叫到局。

拿东家这手牌我会叫4NT让同伴选一门低花，同伴应该不会“短路”吧。这样的叫牌后，西家更有理由相信东家的红心首攻（无论什么牌）是单张，A拿后回一张红心是必须的。

统计了一百万副随机牌的双明手结果，数据和#74差不多。 * 大满贯：3.0% * 小满贯：10.7% * 成局：46.7% * 部分：39.6% 超过60%的牌是某一方有局或贯的。 在成局牌里： * 3NT: 27.8% * 4M: 32.9% * 5m: 12.4% （打不成3NT的只有5.1%） 因为一副牌有多种成局的可能性，所以三个百分比加起来大于46.7%。有高花成局的牌比有3NT的牌多5个百分点，高花成局优于3NT。低花成局的牌比其它两种少得多，其中打不成3NT只有5.1%。

我的处理是2NT, 不保证均型或挡张, 先建立逼叫进程再说。 同伴叫3♣, 我叫3♦显示六张以上套。同伴可以pass或试探♦成局。 同伴叫3♦, 我叫4♥红木试探♦满贯。 同伴叫3♥显示5-4高花, 我叫3♠支持。同伴可以简单进局或扣叫试探满贯。 同伴叫3♠至少五张, 我扣叫4♥显示♠配合, ♥单张和满贯兴趣。 同伴叫3NT, 我pass。 同伴最难办的牌型是4=3=3=3, 可以在3♣和3♦之间选择。♥挡张好的话, 3NT也有可能。