Join Bridge Winners
All comments by Tony Iannino
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Suppose you pick up the hand given by Mr. Willenken and hear the given auction. What would you be leading? I'm not an expert but my choice would be heart and I would be picking heart all the time unless I discover that a spade would be better over the long haul. Then I would be leading a spade all of the time. I'm surely not going to pick the suit I lead randomly.

So if we plant this deal multiple times (changing spot card, randomizing the other hands as much as possible, etc) in every major tournament in the world and discover that a pair picks a lead inconsistently what would that suggest to you? Perhaps nothing. Suppose this inconsistent lead is always the best choice? Still nothing?

In any event, since all pairs are being “monitored” a statistical test can easily be done to find the cheaters.
Aug. 19, 2015
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While not relevant to the matter at hand I wonder what sort of explanations the foreign players gave to the American players. Was it usually, never, 95%, no 4M, etc, or something completely different?
Oct. 31, 2014
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It seems to me that once partner hesitates you can no longer play bridge. A pass always seems to be a LA at least in the cases that come up with me. The poll taken by the director might be flawed. How does he decide who is in my peer group, what information to pose in the question, what system information is relevant, etc?

What I don't like is what happened last time to us. Partner (played with only once before) hesitates with a slow double and I bid 3nt. They call the director who said to call back after the hand. A spade lead beats 3nt but a safe suit was played. On trick 2 my partner stole a heart trick. If the defense won with the Ace a spade shift beats us again. Having now failed to beat us twice they called the director back. The result was rolled back. I know some are going to argue that it doesn't matter how many chances they miss. Some would see fit to give me a penalty for the 3nt bid. Why should they have so many chances at a good board knowing that they have a rollback likely coming? Yes we are the offending side but how much punishment is a hesitation worth?
April 28, 2014
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Sacrificing at IMPs is “easier” than at MPs. In the former you must only worry about what your teammates are doing while in the latter you have a much larger and often times unpredictable field to worry about. So if a save improves your score 2/3 of the time against a game contract it may be poor MP strategy if the rest of the field stops below game. Your only chance for a good score is to defeat the contract; -650 is the same as -500. As more pairs bid game the better the save becomes.
Feb. 22, 2013
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I read the write up in the bulletin and there was a comment along the lines that if a different pair of players were involved the decision of the committee might have have different. What does this mean? If Meckwell were sitting EW they would get away with it because they know their agreements so well? Also, players have been know to forget their agreements written or otherwise.

This matter of tempo is also a little disturbing. Do experts really spend 10 seconds making automatic/obvious bids in the first round or two? I don't so and as Oleg mentioned I would be more suspicious if they did.
Dec. 1, 2012
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Thanks Eugene. I had missed the earlier reference and appreciate your “review” of the book. Like all things of this nature there is no substitute for personal experience and/or peer review. Perhaps you and/or Andrew could offer advice on some the of situations covered in the book. For example, 1N - 4N; 6N and you hold an Ace and a couple of Jacks - would you always cash (at MP) as the book might tend to imply, etc?
Aug. 16, 2012
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There is a recent book "Winning notrump leads' by David Bird and Taf Anthias that covers this topic and more. Simulations were done with many thousands of hands and the results can be illuminating from just how strong the major suit bias in various types of auctions (1n-3n; 1N - 2C; 1n - transfer, etc) to leading a high honor from a short sequence (AKx, KQx, OJx) to leading from your shorter major rather than your longer major, leading a Ace againt 6N, etc. IMHO it is well worth the price.

Aug. 16, 2012
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I'd like to second Barry's suggestion about detailed analysis. In addition, being a math/stats guy I'd like to see things like a) the distribution of member ages presented at different times over several decades, b) distribution of ages when first joining the ACBL, c) total membership over time, etc. If you can get the data I'm sure I or other BW math guys would like to study it.
Feb. 9, 2012
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Jason - Yes, results are before North's bid.

I attempted a simulation after North's 3D bid but a lot depends on the constraints one puts on the bid. I modeled these constraints somewhat after the North's actual hand, that is, I gave him 0-14 HCP, 3 or 4 diamonds, 4 card major(s) possible, up to 5-clubs possible and I included a singleton. We could of course refine these constraints. Working from this partner can be expected to have heart support about 80% of the time (compared to about 70% before the 3D bid) and you could expect to make 4H somewhere around 45% of the time (compared to 16% before the 3D bid). Other assumptions for Norths hand may result in different conclusions.
Oct. 18, 2011
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I think the experts may have it right. First the good news. One can expect advancer to have Heart support (3 or more) about 70% of the time . The bad news is that if advancer is a passed hand your chances of making 4 Hearts is a dismal 16% (even including compenstation for declarers advantage). If advancer is not a passed hand then prospects are much better. You can expect to make 4H at least 40% the time; add to this the cases of other game contracts, e.g., 3N (which was making many times that 4H is going down) and you should be well over 50%.
Oct. 17, 2011
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Bob -

No results for Jxx(x) and xxx(x).

Borel was a world famous mathematician who did this entire work (over 400 pages) by hand (no computers to run simulations) back in the 1930's.
Oct. 2, 2011
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Paul -

The name of the book is “The Mathematical Theory of Bridge”. It was translated into English by Alec Traub. It is 365 pages plus another 70 pages of tables. You'll need a good math background and some time to get through some of the material. Their are quite a number of bridge situations presented. Following is a list of the various sections. It is really an amazing piece of work done before the age of computers.

1. The Shuffle.
2. The Distribution of the Cards after the Deal.
3. Period of the Auction -
how probabilities are modified when one player has seen his hand, division of residues between 3 hidden hands, probability of a short suit when we see our 13 cards, defensive values of honors, certain opening leads, etc.
4. The Play of the Cards -
division of residues between the two hidden hands, division of two residues between two hidden hands, divsion of three residues between two hidden hands, etc.
5. The Score and the Best Line of Play
choice between risk and safety, value of game at contract (pairs equal strength), declarer's choice, defender's choice, choice between a part score or game, penalty doubles and redoubles, etc.
6. Further Theory on the Shuffle
7. Enumeration of Permutations of a Deal
8. Remarks on the play of the Cards - On the general theory of finesses
9. On pairs of unequal strength
10. On the Variation of Probabilities During Play
11. On the Problem of the Finesse
12. Practical Application of Baye's Formula
13. 131 Tables
Oct. 1, 2011
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Bob -

Here are the results for leading low from Axx, Kxx, Qxx; and also for leading the K from KQ7 and KQ10. The assumptions made by the authors are interesting and I reproduce them below. Due credt is given to Borel and Cheron.

Assumptions (Diamonds is assumed the suit being lead from).
1. Declaring side will not be able to discard any losers in Diamonds and so save a trick.
2. Declarers side cannot squeeze the defence in Diamonds and another suit, nor be able to endplay the defenders to lead Diamonds against their will.
3. After the opening lead the four players play perfectly.
4. If one opponent is short in Diamonds (0, 1, or 2) the authors assume that he has sufficient number of trumps to ruff Diamonds as many times as necessary and that he will do so.
5. Any small trumps that leaders partner can make by ruffing or overruffing Diamonds cannot be counted as tricks made in Diamonds by the Defence. The loss of a trick in Diamonds cannot therefore be compensated by a ruff made by the defence.
6. Authors have not taken into account any qualifications to the probabilities due to the auction for this would result in impossible complications.

Axx (x less than 8)
Lead x: 10.8 tricks lost per 100 hands
Lead A: 5.6 tricks
Kxx (x less than 8)
Lead x: 11.3 tricks
Qxx (x less than 7)
Lead x: 7.0 tricks
KQ7
Lead K: 13.6 tricks
KQ10
Lead K: 7.7 tricks

If one is to lead low then doing so from Qxx is least costly. Low from Axx and Kxx about equal in risk.

The worst lead seems to be from KQ7 so I think that NYC expert was right. I'm not fond of the lead myself.
Oct. 1, 2011
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Bob -

Just to be clear that the results in this book (loaded with just about anything you would ever want to know) were all done by hand (no computers back then) by authors who apparently had a lot of time available. This particular anaylsis does assume that declarer guesses perfectly in those cases were a guess is involved and your comments are quite correct; just so much a human or computer can do. I could go through the enumeration of the cases where a trick is lost and see what happens if declarer guesses wrong. If you are really interested I could also post results from other combinations (I particularly like the KQ(x) combination as this comes up frequently.
Sept. 29, 2011
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(x is 7 or less)

Consider the Axx case. Leading low can cost a trick in a number of cases, e.g.,
……….10xx………
Axx……………..QJ9
……….Kxxx………

Leading the Ace can cost a trick in a number of cases, e.g.,
……….xxxx………
Axx…………….Q109
………..KJx

The net defference between leading and not leading the Ace is 5 tricks over 100 hands. One could now analyze all the enumerated cases where the chosen lead costs a trick and determine how likely they are given the particular situation, e.g, partner is busted, dummy is loaded, etc. If there is interest this can be done.
Sept. 28, 2011
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Part of my comment got truncated. Here is the rest.

(x
Sept. 28, 2011
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Some probabilistic data regarding underleading an Ace exists in an old book (1939; by Borel and Cheron).

West Holds……West Leads…..The lead will lose for his side in 100 hands
Axx……………..x……………..10.8 tricks
Axx……………..A………………5.6 tricks
Axxx…………….x……………..13.3 tricks
Axxx…………….A………………4.6 tricks

(x
Sept. 28, 2011
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I finally got a chance to redo the simulations. I'm going to define “declarers advantage” to be the success rate that declarer enjoys in contracts that theoretically (double-dummy) should go down. For example, contracts that “should” go one down will be made a certain percentage of the time. It doesn't matter if the defense blows one trick or three tricks - the contract will be made and the IMPS gained by an overtick can be ignored. This advantage varies by the theoretical amount a contract should go down. For the simulation, I used Kit's 1/4 trick restated as 1 hand in 4 declarer gets to make a contract that would otherwise go one down. For the contracts that in theory go two down I used 1 hand in 8 as decalarers advantage; for those that go down 3 tricks I used 1 hand in 16.

For good measure I added a certain rate for declarers imperfect play in contracts that make exactly. That is declarer will go wrong and go down once in awhile. I made this relatively small; 1 hand in 20. For that contracts that should make overtricks no penalty was assigned for imperfect play.

Simulation Pararemters:
Responder has 10 HCP; no 5-card Major; no singletons or voids; at most 1 doubleton.
1000 hands were simulated for each example hand.
Average IMPS were computed based on a comparision of 3N vs 1N.

Hand…………….Percent Making……IMPS won non-vul…IMPS won vul.
AQJ Ax Qxx Jxxxx 47 0.35 1.40
AQJ Ax Jxx Qxxxx 45 0.08 1.01
AQJ Jx Qxx Axxxx 41 -0.30 0.41
Jxx Ax Qxx AQJxx 46 0.14 1.19
AQJ Jx Qxx A109xx 52 0.87 2.25
K109 Q98 10xx AKQ10 51 0.70 2.07
Jxx KQ AJxxx QJx 35 -0.91 -0.51
AK10x 10x xxx AQJx 49 0.51 1.72
10xxx AK AQJ 10xxx 48 0.33 1.52
Kxx Qxx xxx AKQx 34 -1.12 -0.78

All of the hands have their peak (or mode) at 8 tricks except Hand 5 (the one with A109xx) which evenly split between 8 and tricks. So declarers advantage at the one-down level operates on about 30 to 40% of simulated hands.
Sept. 18, 2011
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Kit -

Thanks for the suggestions.

1. The parameters I used for responding hand were exactly those you suggested - so we are on the same wavelength here.

2. I will rerun the simulations and convert to IMPs. Should be interesting.

3. I know declarer has an advantange but quantifying it is difficult. I did look at one of the hands and determined by inspection that about 1/4 of the time the lead required to defeat 3N by one trick is very unlikely to be found (at least by me). It is interesting that this matches your experience. Do you feel that this is also a reasonable estimate for live-action?
Sept. 16, 2011
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Joshua, I'm assuming they break even because there is no way to quantify one way or the other. I agree that declarer has a advantage and I assign that to the notion of “declarers advantage”. I have no idea how much the advantage is and as you argue a good suit would often cause the defense problems (not necessarily experienced by the computer since discarding will also be perfect) and increase declarers advantage. Do you have a judgement as to how much the advantage is (1/4, 1/2 trick) and how much a good suit would increase that? Would you alter declarers advantage based on the playing strenght of the opposition?

In any event, Brian's point seems to be spot on. I took a closer look at hand number 3 to see what sort of leads were required to set 3N by one trick. 100 hands were simulated with 3N making 36% of the time and going one down 30% of time. It appears that about 1/4 of the time the optimal lead (in the absence of opp bidding) is very unlikely to be found by mere mortals (4th best leads beat 11 contracts and any lead beat 8 tricks). This increases the making percentage to 44% without considering the two donw contracts and perhaps more importantly declarers advantage.
Sept. 14, 2011
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