11/09/2002 Adjustment of double dummy results for law of total tricks using Okbridge play results. For suit contracts at 2 level players make about 0.12 tricks more then double dummy; at 3 level players make about 0.08 tricks more then double dummy. At 4 level in minor suits  players make about 0.06 tricks more. At 4 level in major suits  players make about 0.01 tricks less. 10/20/2002 Analysis of final contracts using 30 million plays from OkBridge. Only 8 non-slam contracts are positive. They are 1H 1S 1NT 2H 2S 3NT 4H 4S. This is the case for both imp and mp scoring. I call them "our contracts" or "Peter's 8 contracts". If it is our hand we prefer to play in "our contracts". If it is their hand, we prefer them to not play in "our contracts" See single/Double Dummy section for more information. 7/18/2002 Analysis of >25 million plays from OKBridge and compare them with double dummy results. The most important general finding is that double dummy analysis is very accurate as compared to actual play from OKBridge. The overall total number of tricks taken by the declarer is 9.21 (9.22 for imp and 9.20 for mp).  The double dummy analysis of the same deal produce 9.11 (9.12 for imp and 9.11 for mp).  So actual play by OKBridge player takes 0.1 tricks more then the double dummy analysis result. 5/17/2002 Analysis of passing flat hands 4432 and 4333 with 11 HCP (in computer analysis/ pass flat hand section). 4443 with 3 controls and 4432 with 2 controls are below average. 5/16/2002 Analysis of passing flat hands 4432 and 4333 with 12 and 13 HCP (in computer analysis/ pass flat hand section). 99.99% of 12 and 13 HCP flat hands are above average hands. 5/15/2002 For IMP scoring I am being conservative to use 34% for vulnerable game and 42% for non-vulnerable game taking into consideration that once in a while you may get X and go down and lose more imps. A more aggressive % would be 33% and 40% if you assume you seldom get X. (in strategy/IMP game % section) 5/12/2002 Complete computer output for 1NT opening with or without stoppers and 1NT (5332 5422) with 5 spades and 5332 with 5 spades. 5/7/2002 First formal release of version 4.0.5.7 of Peter Cheung's bridge analysis program on the Web. Go to simulation/download section. The zip has an .exe and two Microsoft dll for .net C++ mfc applications. 5/4/2002 Discussion of Flannery (in computer analysis section  Flannery). 5/4/2002 Discussion of 1NT opening with or without requirements on stoppers (in computer analysis section  15-17 NT ). 5/4/2002 In 5 card minor section a complete bidding sequences for 1NT with and without interference. 5/2/2002 A new copy of my C++ windows application for bridge hand analysis is available under simulation/download section. 4/29/2002 Computer analysis of aggressive and conservative pass hand condition for rule of 15. For aggressive pass hand rule of 15 is extremely accurate. For conservative pass hands there are a few exceptions. Also almost always open with 12 HCP hands which fails the rule of 15 except very bad 12 HCP44. 4/25/2002 Computer output section for some complete output of deals. Popular opening hands. Deals NS makes 8,9,10,11,12,13 tricks. Deals NS has 25,26,27 distributional points. 4/25/2002 15 - 17 NT opening with complete analysis of game opportunities (in computer analysis section  15-17 NT ). To summarize the result opposing a 15-17 NT opening, you should force to game if you have 10 HCL points or 10 HCLS points if you have a major suit fit. Invite if you have 9 HCL points. Most 8 HCL point hands should not invite game. In imp scoring and vulnerable a few more 8 HCL hands can invite game. 3/28/2002 New section on Rule of 15 and rule of 20. 3/28/2002 Statistics for a general hand from > 2 million double dummy deals are added under the statistic section as general hand. The special point count system are used for testing of point count system. The best I found so far is 6 for A 4 for K 1.8 for Q 0.8 for J 0.4 for T and 0.2 for 9.  If you do a factor of 3/4 the result will be the same magnitude as the regular point count system. See 5 card Minor system section for explanation of short suit points and long suit points. 3/28/2002 more information in the statistic section for % of different opening hands. The number of average tricks by the partnership is also calculated. 1C is 9.75% (9.2 tricks) 1D is 10.17% (9.3 tricks) 1H is 7.3% (9.5 tricks) 1S is 7.6% (9.6 tricks) 1NT(15-17 no 5 card major) is 4.9% (9.5 tricks) 2C strong bid is 0.42% (11.3 tricks) weak 2 any specific suit 6-10 HCP 1.8% (8.5 tricks for S ) 4441 11 to 21 HCP 1.3% (9.5 tricks) 4441 or 5440 with any suit 1.85% (9.7 tricks) 2NT(20-21 no 5 card major) is 0.53% (10.6 tricks) Weak 3 any specific 7 card suit 6-10 HCP 0.4% (8.9 tricks for S ) Weak 4 any specific 8 card suit 6-10 HCP 0.23% (9.6 tricks for S ) 3/28/2002 Advance 5 card minor bidding system with a more precise and powerful 1C, 1D 2C and 2D bid which replaces the standard American 1C,1D, 2C, and 2D bid. All other bids are the same as standard American 2/1 bid and open 1H or 1S with any 5 card H or S suit. This system is especially great in match point competition. 1C include the standard American 2C strong bid, 10-21 HCP 5+/5+ in the minors, 12-14 HCP NT hand with no 5 card suit, 18-19 HCP NT hand with no 5 card suit. 1D include 11-21 HCP with exactly one 5+ card minor suit. 2C include 11-17 HCP 4441, 8-10 HCP 6 card C, 9-10 HCP 5 card D, 8-10 HCP 6 card D.  2D include 18-22 HCP 4441, 8-10 HCP 5 card H and 8-10 HCP 5 card S. 3/28/2002 Losing trick count with no adjustment is tested. The computer analysis shown it is not as good as the standard point count system in predicting how many tricks the partnership can make. (Using  linear correlation coefficients) 3/28/2002 significant improvement in the computer simulation program.  Standard deviation, and linear correlation coefficients are calculated for some parameters. This enable me to evaluate different point count or hand evaluation systems. The maximum time to process 2 million double dummy hands is 26 seconds using a 1133 MHz AMD CPU chip. 3/20/2002 Some new simulation results are based on >2 million double dummy hands. If the hands are quite unique, results are obtained by rotating the hands and all 4 hands are used. This gives an effective >8 million hands to select from. 2/22/2002 different vulnerability and % make and sacrifly. (statistic/vulnerability) With unfavorable vulnerability the computer simulation results says you should bid and make your contract 32.4% and sacrifly 1.7%. With favorable vulnerability you should bid and make 48% of the time and sacrefly 17.6 % of the time. North south cannot make any contract = 18.44% North south make partial contract = 50.80% North south make any game = 24.00% North south make any small slam = 5.29% North south make any grand slam = 1.47% 2/16/2002 new double dummy analysis result for general hands under statistics/general section. almost complete computer output in simulation/sample result section using 900,000 hands.Interesting observations:- best contract (NT or suit) average trick is 8.44 North south cannot make any contract = 18.48% North south make partial contract = 50.78% North south make any game = 23.94% North south make any small slam = 5.33% North south make any grand slam = 1.47% average long suit point is 1.9 average short suit point is 2.0 average total point is 24 2/8/2002 new double dummy analysis results for the Law of total tricks. Confirming that the law is extremely accurate for total trumps of 16 and 18.