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Wayne Burrows, Paul Barden and Paul Hightower (but also others, as appropriate): it gives me a great pleasure to confirm Wayne’s calculations. I decided to sit down at the kitchen table and work out the probability of four hits from first principles - using a pen and the back of three old envelopes. This gave me Pr = 0.000559, which is close enough (rounding errors, common).

Great work by all, and - of course - a lot of fun even if it was a trivial issue. Now, we just have to find another fun exercise to deal with. I’ve a few ideas…
Oct. 9
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Paul, I think your previous comment hit the jackpot when you wrote: “ The WBF reports a strange decline in performance among top players…they just don't seem to be concetrating very well on Bridge!“. Brilliant. And thanks for your belief in me that I’ll get the four hits.

And thanks to all for the various contributions. It was really fun. I never intended this as a serious discussion; more like a brain teaser on a rainy Monday evening. But I’m really hurt (joking) that some think I’ve missed four hits in the roughly 70000 boards I’ve played. That’s impossible, or at least improbable. I’m the type of a guy who counts the number of wheels on a passing large truck or wagons of a passing train.

I don’t know if there is a flaw in the design of the Monte Carlo simulation design and/or the theoretical conclusions but I would like to point out two important aspects that may or may not have been considered by the various contributors.

Regarding the probability of four hits (there seems to be consensus that it’s close to 0.056% rather than the lower 0.02% that my 40 year old memory gave us), I need to stress two factors that will reduce significantly the probability of four hits when taken into account. These are the concepts of dependent probability and linear dependency. I simplify a lot for the sake of clarity.

(1). Let’s say we draw first the 6 of S. There are now 51 cards left in the deck. But to satisfy the four hits criteria, four of these cards (2,3,4 and 5 of S) are now disqualified. So the probability of drawing another S is now only 8/47 = 17% instead of the 23.5% that you get without the adjustment. Needless to say, this reduction of the sample space needs to be taken explicitly into account in both theoretical and Monte Carlo specification designs. If it wasn’t, the 0.056% number would go down.

(2). Even more significant in the design of both the Monte Carlo simulation and the theoretical probability model is the “linear dependency”. Once it’s known that six cards are “taken”, only seven are now needed. This reduces the probability considerably, as a big chunk of the deck is now non-valid: the “sample space” is heavily reduced.

Anyway, this was fun. Maybe I should publish another BW article on other trivial issues, such as bridge with five suits - the fifth suit has only 12 cards; or on the magic prime number of 13.
Oct. 9
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And at the Club today (board 14, The Common Game), my second board was

Q654
63
A1074
Q83

So close, yet so far away.
Oct. 8
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Jim, this is absolutely brilliant. Maybe Florentin can find an example?!
Oct. 8
Magnus Olafsson edited this comment Oct. 8
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Damn you, Craig. And now I have to add your LCP to my task list. Trying to beat your 13-28 record is going to be nearly impossible, but I’ll give it a go. BTW, if I get 12-29; who’s the winner? Maybe we need to set up a Task Force and an Appeal Board to deal with such important matters…
Oct. 8
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Yes, void is a hit. Singleton Ace is a hit. Very good observation Paul regarding max length.
Oct. 7
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John, a really great post. In a minute I’ll tell you why it’s so great.

One of your great grandfathers, a guy called Plato (running around Athens some 2500 years ago) had this annoying tendency to ask penetrating questions beginning with “what is X”, such as: “What’s sport?” In his sincere attempts to identify a logical meaning, Plato always tried to investigate motivations. Why does a person do X; why do you do sport? And since WBF claims bridge is sport, we may want to reread Plato.

Those of us forced to study classical education back in the 1960s, know that there’re only three Plato motivations why you play bridge: (1) “Honor and Glory”. (2) “Material gains” (applies to professionals only, Plato said), and (3) “Perfection of the mind”. I never understood the last part, but that’s not relevant here.

But John Oikonomopoulos, you have given us a a true reasoning that even Plato didn’t see: FRIENDSHIP. Thank you, John.
Sept. 3
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Thanks Alan for posting. Always love to look at such a stuff.

Actually, in this case, the solution is pretty simple. East can only have two possible cases: K9 or stiff K. It’s important to realize that each case doesn’t have the same probability. The a priori probability of a stiff K in East is less than that of K9 (roughly 2.83% vs 3.4%). But there’s much more to it. Certain combinations (or cases) have been eliminated, such as both the 5-0 cases, and all five cases when E has a four-card suit. This changes drastically the a priori odds. If you go thru the math, you’ll find out that in 83% cases you make your four tricks by taking the finesse.

When we know that E always takes the trick with the K (when also having the Q), the odds improve for us. Today it is said that you cannot achieve the Nash equilibrium by such stupidity. But Borel pointed this out already 80 years ago and gave numerical values: up from 65% to 83% in this example.
June 18
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Congratulations to all. We Scandinavians love underdogs. Wolfson actually won the best bridge team ever. It was such a fun to watch these boards. I’m ever so grateful for the display.
March 31
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Thanks Barry. Your TCG posts are always interesting. After the game today, seven of us NYCpros discussed the boards - like we normally do. This board confused us. It took us a fairly long time, roughly three minutes, until Peter Trenka found the solution. It’s actually simple, but far from being the % play. But it’s always fun to figure out what DD is thinking.
Dec. 13, 2018
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Hi both and congrats on your glorious career. You have always been wonderful opponents; polite, ethical and unusually professional being so young. I often talk about you guys with your sister, Sandra, here in New York.

I often wonder how a typical Tuesday evening in this great bridge family was. Did you play bridge (Sandra says you didn’t play much at home), or did you discuss bridge issues or did you simply try to solve the murder of Olof Palme? And, of course, I’m curious to know if you’re going to Reykjavik at the end of January.
Nov. 2, 2018
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Thanks Robb. This is very useful to us who register players movements (left hand on table = 0; right hand on chin = 1; etc) to establish a database for correlation analysis. There’s no code we cannot discover - given this quality of visual evidence. Thanks again.
Aug. 19, 2018
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Hi Stefan,

I’m glad you’re interested. It was fun to play and gave good results.

3NT was always six in a M and five in a m. Less than opening, of course, but vulnerability mattered a lot. I’m not saying that we had the best system, but it was something like this:

4C: p/c. Over 4D, 4H was another p/c.
4D: FG, slam interest, asking void (1-1, LH).
4H: p/c
4S: to play is S. Slam interest if H.
4N: slam interest in the minor.
5C: p/c.

You could probably design a better system.

Good luck and all the best.

Magnus
Aug. 9, 2018
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I played the Icebreaker during a six month partnership 1991-92 in Iceland with Bjorn Eysteinsson (the NPC of the Bermuda Bowl winners of 1991). He had played it in previous partnerships for a few years. I always thought Bjorn was the creator of the Icebreaker but I’ll check on it.

It was great fun to play the Icebreaker, resulting in some serious swings. A lot of pass or correct bids but also constructive relay bidding. 3NT was 6 of M + 5 of m, while 4m was 6 of that m + 5 of a M.
Aug. 4, 2018
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Leonard is, of course, right: the curve rises very slowly. Let’s say the opponents take the first three tricks - everyone following. The probability of a 3-3 break is now barely 40%. But let’s say you now take the next seven tricks (throwing one of the important suit), The probability of a 3-3 break is clearly 100%. Well, it’s no longer probability: it’s certainty!
May 25, 2018
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The Richard Pavlicek approach is, of course, the correct one. But, as a general point of interest, in January last year, I wrote an article here on BW on this issue (Mary and John and Bayes). In short, the conclusion is that the famous 35.5% probability of a 3-3 break, which is based on 13 unknown cards of each opponent, changes as the unknown cards become fewer. In fact, if you plot the curve, it begins at 35.5% and develops exponentially to 100%.
May 25, 2018
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Bridge everywhere is a fading “business” where all numbers are going down except costs and average ages of our “customers”. This path of decline will be long and painful. In such cases, managers need to think outside the box and have a hard second look at the way in which we have been conducting our business.

Steve’s article is a serious contribution in this direction; well structured and full of relevant ideas. However, changing a governance structure based on regionalism to one based on skill sets, will not be easy or quick. Perhaps, such a change is best implemented in small but frequent steps. I might be wrong, but I’ve the feeling that the current ACBL management has been taking or considering such steps.

I like Steve’s pro forma list, although I would suggest we should have “Youth recruitment” explicitly there. The long-run return of investment of getting young players to join the game is greater than any other. Of course, youth recruitment could be a part of other skills (#3,6,9 and 10 on Steve’s list) but it deserves its own status.
May 2, 2018
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TrueDeal sounds strong, authorative and descriptive. However, True Deal seems to exist here and there around the world. And, BTW, many thanks to Hans for this important work.
April 28, 2018
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Dear Mr Damiani,

Thank you for your contribution to this issue of such a fundamental importance for our game: cheating. Allow me to say that I respect the work you have done for bridge and I admire your many innovations, especially that you are the creator, and you actually implemented, the concept of mixed pairs and teams.

You may remember, or not, that we met at one of the EBL annual meetings. Probably in Killarney in 1991, when you were President of EBL and I represented the Icelandic Bridge Federation. My friend, the late Jens Auken of Denmark, was there with me. Your idea of turning bridge into “sport” wasn’t well received. The main reason for our lack of enthusiasm was your lack of being honest: your idea was based on financial gains for bridge but not on believes in ethics or purity of competitions.

The CAS case was a disaster. But it was such an obvious road to disaster that we should have known. Just like we know the 4-1 break has 28% probability.
Feb. 17, 2018
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E/W open 1C w all bal hands (11-13; 17-19, even w 2 clubs and 5 in M; an excellent system). My partner and I got the normal 500 in 2Sx (although I would never bid 2S on the S hand, being vul). N was simply silly rather than devious in his hesitation. But the more interesting question is: can you escape 200 in 3 H? I don’t think so, but… Thanks Vigfus (Fusi) for posting this.
Jan. 31, 2018
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