BillPatch

Simulated hand an additional 200 for a sample size of 400 just on % set contract 6♠ 8.75% K♥ 8.75% 6♥ 6.5% 3♦7.5% 4♣ 7.5% dead heat between ♠ and k♥ for best lead at IMPS.

Simulated hand 200 times using Jack6. lead average tricks set contract 6♠ 2.645 8.0% K♥ 2.86 7.5% 6♥ 2.60 6.0% 3♦ 2.67 8.0% 4♣ 2.645 8.0% This sample implies that K♥ is the best lead at MP. The actual 3 way tie for setting contract with K♥ close behind implies that there is no clear leader at IMPS, but based on a similar hand in Bird/ Anthias I would bet that K♥ is best there too, with 6♠ second best.

Bird/Anthias emphasize non-Stayman auctions in their NT book. In Stayman auctions when opener shows a major there is a fair sized minor preference, and in most cases the longer minor is superior(Most of the hands they cover for this auction have 2,3, or 4 little cards. In these cases shown, the longer minor always shows superior results.) Also, if opener has 4 clubs, it is unlikely his partner was considering doubling Staymen for lead.

Since responder by passing 2♥ has shown a limited hand, his 2♣ implied values in both majors. I doubt we will win the battle in the majors.

Our par on this hand is three or four hearts for the other side with their side making 9 tricks. 2♦ can lose by 1)partner's A ♦ lead, 2) our side playing in ♦ for a bad result, or 3) their underbidding or superior play due to bad split we warned them about. I let them keep the dice.

Eddie Kantar Teaches Modern Bridge Defense(1999) on p 15 recommends the lead of the suit against NT that does not have the ace when "You have two suits of equal length and one is headed by the ace." The auction strongly suggests a minor lead, and the discrepancy between suit lengths makes it unlikely that opening leader is 5-5, so this only affects overtricks when for the leader to be 4-4 in the minors, although it may affect the contract when the leader is 3-3.

Help! I am trying to make deal319 work on Windows 8.1 machine. What is the best way to learn enough TCL to make deal functional? Have a quant MBA background most familiar with excel, SAS, SPSS and GPSS, with a limited knowledge of command prompt, but little knowledge of other programming languages.

According to Richard Pavlicek's[spelling corrected]website, the expected value from playing tens of thousands of bridge hands at three notrump by experts on vue graph championships after the opening lead is equal to the double dummy analysis value. Bird/Anthias further tens of thousands of hands from club play and several thousand hands simulated single dummy on WBridge5 with similar results. Therefore we may conclude that given adequate statistical power from our sample we may draw the inference that the expected percentage that a low spade will outscore a low diamond is 17.1%. The extra overtricks saved outweigh the reduced rate of setting the contract by eight to one. Since the preponderance of the evidence indicates that equal strength contestants will win .171 board on average by leading over a field lead of the low diamond. The diamond lead is a pure bridge error.

While I agree that the finish between low spade and low heart is inconclusive, it is customary to compare the diamond lead to the better major suit. It is debatable whether to lead second best from T8x or low(Bird/Anthias recommend low from this combination because they believe that following the conventional lead may aid partner more than the statistical gain from starting unblocking on the first round with the lead of the 8. The low spade beats contract 12.5% and produces the optimal defensive trick count 66.9%. Plugging the low spade numbers into the last sentence by Rainer: "The 2.3% you beat the contract more often has to be balanced against the 19.4% you . . . lose one or more IMPs in overtricks." 17.1 low spade better in tricks -(-2.3) low diamond better at set = 19.4% extra overtricks allowed by diamond lead.

Edgar Kaplan proposes a similar setup, but his bid for opener to show less than four card support would be 3♦, promising at least 4. If responder has both minors he has found his fit in the other minor. See Edgar Kaplan's notes on Kaplan-Sheinwold at the BridgeWorld.com website. With a holding of 4 +♣, opener rebids 3NT if both majors are stopped, or his better major.

Both vulnerable (the original problem) was the only one of the set where defending the contract by passing was indicated. Pass was leading 3♠ by .32 imps/bd, pass/double by .74 imps/bd, 3♠/double by .28 imps/bd. Sample size 54. A minimum sample size of 200/treatment(pass, double, 3♠) would be required to reach the .95 level of significance that pass was better than double. (Tech Stat Theory Two-tailed ANOVA experimental design) Neither vulnerable Double was best. It beat pass by .96 imps/bd. Double/3♠ by .56 imps/bd. 3♠/pass by .76 imps/bd. Doubling the sample size from 50 to a minimum of 100 could determine at the .95 level of significance that double was better than pass. With only the defensive bidders vulnerable Double was best. It beat pass by 1.56 imps/bd. Double/3♠ by .98 imps/bd, pass led 3♠ by .04 imps/bd. As reported on my other reopening poll post, 3♠ was best 2.9 imps/bd better than passing.

gszes is spot on. The initial simulation of 50 at this vulnerability exceeding .95 Confidence level E must take action, and 3♠ is much better than double. 3♠ beats defending 2,90 imps/bd, and beats double by 1.48 imps/bd. Double beats defending by 1.48 imps/bd. Incidentally, this appears to be the only vulnerability at which 3♠ is the best choice.

I ran a short double dummy simulation of 100 hands using Jack. The results: IMPs Contract set with standard low card lead: ♠ = 11% ♥ = 12 ♦ = 16 ♣ = 7 Best lead at IMPS is a ♦. Defensive tricks per hand: ♠ = 2.90 ♥ = 2.70 ♦ = 2.77 ♣ = 2.78 A ♠ lead appears best. Kudos to Endymion77 for suggesting the winners.

Auction N E S W Pass Pass 3♦ Pass Pass ?? East Hand AKQ96 9762 97 JT

Auction S E W N Pass Pass 3♦ Pass Pass ?? East Hand AKQ96 9762 97 JT My simulation will recommend all 3 choices as vulnerability varies. (IMPS--modified 1300edt 5/30)

My regular partner is unavailable. I also will need a partner in Toledo OH the next week, competing in 3 OH regionals in 4 weeks. I have 437 mp.

I am sure that this is a lower intermediate topic, but the authorities on 2/1 and Standard on this side of the pond recommend bypassing the weak heart suit with a good game-forcing hand. Otherwise good bidders might stretch to fit slams with insufficient trumps.

A passed hand that suggests a choice of reopening actions occur relatively rarely in an individual's bridge career. Each vulnerability poses subtle differences. A bridge expert's recommendation of the current question is based on the selective memory of a handful of cases. Through simulation we can generate dozens to thousands of sample hands which meet the conditions of the given E hand reopening after the sample action, and generate results of the bidding and play of each sample hand. Through statistical analysis we can test the likelihood of our results being due to chance, and how much more confidence we can acquire by increasing the sample size. Through another statistical test, the Bayesian, we can determine the relative likelihood of each option being superior to each other. Of equal importance to chance errors in our mathematical model using simulation are non-random errors due to errors in bridge judgement at each stage of the simulation, including the extensive use of double dummy analyser to simulate the play of the cards after opening leads, and also non-bridge errors in modeling, data entry and analysis.

I ran a short simulation using Jack (54 boards) between the three options(pass 3♠ double). As suggested by mikeh the three options are close. The results are not significant at this sample size for any reasonable p level. The order of finish was pass 3♠ double. The statistical summary of the simulation, based on IMPing 3 two way matches. pass versus 3♠ pass versus double 3♠ versus double mean imps/bd = .315 mean= .648 mean= .241 sdev.s=7.05 s= 6.41 s= 6.22 z= .3279 z= .7433 z= .2843 The lack of shortness in their suit suggests inaction at this vulnerability.

Only if you take the second club in dummy which only works on the 40% chance of 2-2 clubs, an inferior line.

If we assume that west will correctly cover with Kxx or KTx it is a three way guess between those holdings and west Kx. The advantage of playing the immediate finesse of the J is that it minimizes the number of undertricks when it fails. Leading the Q, as RunemPard has noted, will take advantage of a defensive lapse common against non-experts. You can never beat a 4-1 break.

Perhaps we should attribute some blame to partner for his double of 3♦ after we bid 3♣ forcing to game. Did not this suggest that we might not do as well in game as defending 3♦, suggesting that partner lacks a high honor in ♣, so game is odds off with current hand, and worse than that if our club suit were only AQ sixth rather than seventh?

The current expert consensus is that lying in replying to Stayman is almost always wrong. It is particularly wrong at MPs where you can lose all the matchpoints by making 3NT when 4♥ makes the extra trick. xx or Ax in your hand provide a good route to an extra ruffing trick in your hand. Stayman in his 1967 book Do You Play Stayman? recommended a suit of at least qtxx to use or reply to Stayman, for fear of bad breaks in the trump suit, but only at IMPS. It might be something to try if you need a swing at IMPS.

Sorry EGR, I made a major misestimate of the amount of 2 1/2 and 3 QT hands. A sample of 150 13 card hands reveals that for every 100 12 hcp hands 14 2/3 have less than 2 QT; 32, 2 QT; 38 2/3, 2 and 1/2 QT and 14 2/3, 3 QT. Thus, it appears that on about half of balanced hands with 12 points and a doubleton can make positive results, even though they fail the rule of 15.

When I said that my study used double dummy anlysis I meant that the last 51 cards were played using Jack's double dummy analyser, not the analysis of absolute par. During the record of play we recorded absolute par for the last 80% of the hands, so I will comment on the differences in score. Jack bid to the suit and contract level(partscore, game, slam)over 50% and 90% of the time the side with the absolute par had a plus score. Richard Pavlichek's website has an extensive comparision of results from actual play versus double dummy analysis for ach contract played in top competition. At he part score level declarer underperforms in actual play by .1 of a trick. Since in this analysi the openerer's side played about 60% of the time to the defender's 40 % to create a bias as suggested by Helenne of 2 tricks per 100 hands.