msjennifer Posted November 18, 2018 Report Share Posted November 18, 2018 Sir. as it boils down it all depends upon 1) the type of event.2)the maths of a 3/0 break 3 ) how many of that will west who has already shown both AK of clubs likely to hold a singleton King of spades..4)How many times will East hold a singleton King,when playing the A will win.5)How may times will East hold KJx when leading a small one from dummy and making the safety play wins is likely.. Sir.as I go by the book plus the table feel, if playing a MP event I shall cash the Ace.However in a IMP or team event I shall take the safety play at the cost of one IMP. A friend of mine, missing KQx did not take the safety play when playing in a small slam and lost a handful of IMPS and gained quite a few jeers. Quote Link to comment Share on other sites More sharing options...
nullve Posted November 18, 2018 Report Share Posted November 18, 2018 At IMPs, you take the safety play for one loser in trumps. What do you do at Match-point Pairs (mixed field)?I'm not sure I would play safe even at IMPs! Well, I actually think it is safe to lay down the ace, because a 0-3 trump split must be almost Fukushima-rare given the auction and the vulnerability. (The a priori probability of a 0-3 trump split most definitely doesn't apply!) Quote Link to comment Share on other sites More sharing options...
Cyberyeti Posted November 18, 2018 Report Share Posted November 18, 2018 I'm not sure I would play safe even at IMPs! Well, I actually think it is safe to lay down the ace, because a 0-3 trump split must be almost Fukushima-rare given the auction and the vulnerability. (The a priori probability of a 0-3 trump split most definitely doesn't apply!)Â Not really, how attractive do you think it is to make a 2 suited bid with something like void, xxxxx, xxxxx, AKx or overcall with the 6-4 version Quote Link to comment Share on other sites More sharing options...
Winstonm Posted November 18, 2018 Report Share Posted November 18, 2018 At MPs not making the overtrick other people are making is losing. Yes, but that assumes everyone else is in the same contract and they do not take the safety play. My experience finds few hands of that type. But, they do exist and field quality has much to do with it. At the same time, my choice probably shows my bias against MPs. Quote Link to comment Share on other sites More sharing options...
Stephen Tu Posted November 18, 2018 Report Share Posted November 18, 2018 The number of people taking safety play is irrelevant. Each one taking a safety play just changes your dropping a stiff k into a win a mp instead of tying, rather than tying instead of losing a mp. Or if void, vice versa. The math works out the same. The relevant number is the number of alt scores between -100 and 620, rather than those in game. 1 Quote Link to comment Share on other sites More sharing options...
Povratnik Posted November 20, 2018 Report Share Posted November 20, 2018 In every deal, a percentage advantage (if exists) of chasing an overtrick is fixed, always the same. Points advantage of making a game (or slam) tends to grow in bigger and more heterogeneous fields...This isn't correct. The percentage advantage of the overtrick grows proportional to the number of people in the same contract. As more people play the same, overtricks value goes up, the advantage of just being plus goes down. Here, the edge of the overtrick is rather small over the safety play, so you need > 80 percent in game. But if the edge were larger, e.g. a safety play to guard against a 4-1 break, rather than just playing for 3-2, the breakeven point would be much, much lower. If you are in habit of playing safe when in normal contracts your mp score will usually suffer. What isn't correct? I reread my statement and it's short, clear and entirely correct. And yet you somehow managed to misunderstand me. And I don't understand you (talking about the red part). When I say "percentage advantage of chasing an overtrick", I am talking about the frequency. The probability that LHO has a singleton king is greater than the probability that he has a void. The difference is about 2.63 percentile points. That's the advantage of chasing an overtrick that remains the same, regardless of the size or other attributes of the field.If you have in mind some other "percentage advantage of chasing an overtrick", unknown to me, please specify. I was talking about percentage advantage and points disadvantage of chasing the overtrick. You claim that my statement isn't correct and repeat my phrase, but with the word "chasing" removed. Now the question is - whether you're talking about the same thing (and the important word is missing, for any reasons)OR (more probably)you're trying to prove the incorrectness of my statement by talking about something else... The latter approach doesn't look entirely healthy, but I'll not be petty, I'll try to understand your statement. The percentage advantage of the overtrick grows proportional to the number of people in the same contract.  If you wanted to say:The POINTS DISadvantage of (chasing) the overtrick SHRINKS proportional to the number of people in the same contract. That's plausible for discussion. If that's what you meant, we can continue. If you wanted to say:The percentage advantage ... grows ... in the sense of probabilities That's obvious nonsense, the field has no influence on probabilities of card distributions. If you wanted to say:Some OTHER percentage advantage ... grows ... You should first introduce the very existence of the thing you're talking about and THEN claim that "the thing" grows... If you wanted to say something entirely different, please specify. As more people play the same, overtricks value goes up, the advantage of just being plus goes down. Before I try to interpret this sentence, let me notice one small, but absolute flow:We weren't talking about "just being plus", we're talking about making a GOOD contract. In this particular case, 4s is the very best contract available to NS; 620 can't be bad and can be a great result (most of the time, it will be a VERY good result).Making 170 or 140 would be "just being plus"... Did you want to say - when more people play the same, the overtrick will get you a better result? If so:- The whole setup is wrong (I don't elaborate, because it's far from certain that I'm correctly guessing your claim)- Specifically, if you watch that parameter alone (the number of pairs playing the same contract), overtricks value (if we're talking about the result) doesn't go UP, it goes DOWN. You're more than qualified to check that... * * * I could (and perhaps should) just say "I don't understand you", instead of writing 900 hundred miles long post, but I didn't want to be perceived as arrogant. I hope you'll be less obscure next time...Apologies to everybody, for low efficiency. Quote Link to comment Share on other sites More sharing options...
smerriman Posted November 20, 2018 Report Share Posted November 20, 2018 The probability you can make an overtrick is constant. The advantage of going for the overtrick (how much you benefit, compared with not going for it) is not constant. I think the confusion was in your use of the word advantage. Quote Link to comment Share on other sites More sharing options...
Stephen Tu Posted November 20, 2018 Report Share Posted November 20, 2018 Matchpoint scores can be expressed as either raw point totals, or as percentages of maximum available. Your matchpoint expectation of one action vs another, depends on BOTH frequency of gain (this part fixed, for a particular hand, I agree) AND the number of points swung by the action (NOT fixed, field dependent, one won't know until scores posted, but you can try to estimate based on hand and experience) Yes the frequency of gain of the uptrick in this case is small edge vs the losing case, but this is multiplied by the number of people in the same contract. So total gain (or non-loss, if the field is all playing for overtrick) is more, the more in game. Let's say 90 percent of field plays 4s, the rest are plus some amount < 620. Half the field decides to play safe, half goes for the uptrick. The king is stiff offside. So playing for the overtrick scores 77.5 percent. Playing safe only scores 32.5 percent, which is bad. You lose 45 percent relative to me. Half times the proportion in game. Now another day, same board and players, except now void on left. Now playing safe scores 77.5 percent. I score 22.5 percent, losing 55 percent relative to you. Or half the proportion in game plus the percent not in game and below 620. So you gain more when you are right, but since my gain is more frequent, when this proportion of people are in game, I win in the long run, very slightly. 13.16% x 45 vs 10.53% x 55. But +ev is +ev, and you take every edge. Now suppose the field is crazy unrealistically bad, and half the field misses game for some reason. Now an overtrick scores 87.5 percent when it works, while safety play still scores 62.5 percent, losing only 25 percent. Again the margin is half of those in game. So as you can see, if more people are in game, you lose more when wrong about the uptrick than when fewer people are in game. 45 vs 25. And when safety play was necessary, now playing safe scores 87.5 while going down is only 12.5 percent, losing 75 percent. Under these conditions, safety play wins easily. So you can see that the amount one gains or loses depends on the percentage of field in same contract. If nearly everyone is in game, making overtricks is essential when possible, if you don't make one the field is making you can get a very poor score. 620 could be a 10 percent score, if 90 percent are scoring 650! So one has to be able to separate boards where one third or half will screw it up, vs ones where you expect nearly all to be in same contract. This board looks mostly flat to me, and original poster seemed to indicate it was so in practice. Each board will have a breakeven point for percent of field in game vs other relevant contracts, depending on the edge of the overtrick play vs the safety play. If gap is small, you need very flat board to go for the uptrick, 80+ percent as here. If the gap is huge, one needs much less. Classic example is Axx vs kqxxx and a now entryless dummy, need 4 tricks to make. If this is a normal 2nt p 3nt and you are going to take safety play of ducking when lho follows to 2nd round, at matchpoints, because of your philosophy of making game is always good in heterogeneous field, to me you are nuts. For this hand, you are less nuts because the edge is quite tiny, but you are still wrong mathematically if 81+ percent in game, of the scores in range (the 800s mentioned by Tramticket don't matter, as those are lost mp regardless, are excluded from the calculation). And you will get poor board when field is making 650. Quote Link to comment Share on other sites More sharing options...
Stephen Tu Posted November 20, 2018 Report Share Posted November 20, 2018 Oops mea culpa. I was sloppy earlier trying to do algebra on a phone without access to pen and paper, and the breakeven for this board is actually 88.9 percent of field in game which of course is why the edge for the 90 percent field examples is so low. So perhaps safety play is right on this board. How many were in game, Tramticket? But the general gist of my prior statements re Povratnik remain correct. For any given edge of overtrick vs safety play there exists some threshold, if proportion of pairs above that in same contract, the safety play should be ignored. Below that threshold, play safe. When edge is very small you need very high uniformity, like 90 percent here. When the edge is large, like playing for 3-2, not playing safe against 4-1 break, you only need very low uniformity to go for the overtrick, like 35 percent of field in same game. Quote Link to comment Share on other sites More sharing options...
Povratnik Posted November 24, 2018 Report Share Posted November 24, 2018 @Stephen TuAnother misunderstanding :). When I said "I don't understand you", I had in mind the two red sentences only. I do understand the rest of your theory. If I wanted to express in one sentence all that I learned about your views, I'd say:Mathematical expectation is Alpha&OmegaThat's my perspective too, so all these misunderstandings are only temporary...  Matchpoint scores can be expressed as either raw point totals, or as percentages of maximum available.Aaaaaah, now I understand why did you use the word "percentage". Though I still don't like the term "percentage advantage" the way you used it, it doesn't really matter. All that I wanted to ask - is answered by this one sentence. The rest of the post explains your general approach. It wasn't necessary, because I've been understanding it (and generally approved) from the very beginning.However, your long essay wasn't completely vain. It helped me to clearly see what's wrong in your set up.Please, don't understand me wrongly - you made an impression of a sound thinker and I mostly agree with you. I'm pretty sure, you'll choose the same line as me in vast majority of such cases. When we choose different lines (due to different tastes), they'll usually have the similar mathematical expectation.I don't discuss with you so intensive because I think YOU need my advice. I'm doing this because of many users who'll read your posts without understanding and harden themselves in wrong beliefs. To shorten this post, I'll cross over the rest very briefly: Paragraph No 2Your matchpoint expectation of one action vs another, depends on BOTH frequency of gain (this part fixed, for a particular hand, I agree) AND the number of points swung by the action (NOT fixed, field dependent, one won't know until scores posted, but you can try to estimate based on hand and experience) Yes the frequency of gain of the uptrick in this case is small edge vs the losing case, but this is multiplied by the number of people in the same contract. So total gain (or non-loss, if the field is all playing for overtrick) is more, the more in game.I don't know whether to call the red part wrong, incorrect, or just wrongly set - but I certainly can't accept it as correct. It will be explained... Paragraphs No 3-7They brought nothing new. Paragraph No 8So you can see that the amount one gains or loses depends on the percentage of field in same contract. If nearly everyone is in game, making overtricks is essential when possible, if you don't make one the field is making you can get a very poor score. 620 could be a 10 percent score, if 90 percent are scoring 650!That's said less sloppily than in the previous post, but IMO, it's still below the passing bar. It will be explained... Paragraphs from No 9 to the endThey cover your general approach, that I already perfectly understood. * * * So I owe you an explanation for painting some parts of your post in red. I'll do it in separate post. Just before that, I'd like to prevent remaining of any loose ends... Outside of red parts (in this and previous post), I don't see any source of potential disagreement between you and me. But I have to check that with you.Do you see anything else that needs a further discussion? If not, I'll write an essay of my own in the very next post. Quote Link to comment Share on other sites More sharing options...
Stephen Tu Posted November 24, 2018 Report Share Posted November 24, 2018 Whatever, tell me exactly where you think I'm wrong. Other than my initial blunder calculating the breakeven point which I corrected. Quote Link to comment Share on other sites More sharing options...
nullve Posted November 24, 2018 Report Share Posted November 24, 2018 Not really, how attractive do you think it is to make a 2 suited bid with something like void, xxxxx, xxxxx, AKx or overcall with the 6-4 versionVery attractive if I have the system for it. Balancing over (1♠)-P-(4♠)-P; (P), too. Not that I expect a random West player to be like me, but... Quote Link to comment Share on other sites More sharing options...
nige1 Posted November 24, 2018 Report Share Posted November 24, 2018 Stephen Tu's argument seems correct: At match-points, your decision whether to take the safety-play largely depends on your estimate of how many people will play in 5 or more â™ s rather than in part-scores. If you judge that significantly more people will play in part-scores, then you should take the safety-play.If you judge that significantly more people will play in 5+ â™ , then you should cash â™ A.If you judge the numbers about equal, then you should cash â™ A. Quote Link to comment Share on other sites More sharing options...
Povratnik Posted November 24, 2018 Report Share Posted November 24, 2018 Whatever, tell me exactly where you think I'm wrong. Other than my initial blunder calculating the breakeven point which I corrected.On it!  Stephen Tu's argument seems correctIt does and it almost is. Yet the way it's written, it somewhat blurs the reality. Wait for my answer to him. Anyway, I mainly disagree with your post as a whole, but I wouldn't comment before I answer to Stephen, if there wasn't this blunder:[*]If you judge that significantly more people will play in 5+ ♠, then you should cash ♠A.Is this lapsus calami or what?The very existence of this group guarantees that I easily beat all who cash the Ace, even if they play only 4s! Quote Link to comment Share on other sites More sharing options...
Povratnik Posted December 18, 2018 Report Share Posted December 18, 2018 Sorry, before I finished this post, a RL issue had forced me to abandon the works for the time being. It turned out to be good, though, since the longer time usually makes a shorter and nicer post :). This post has to be big and ugly, but if there wasn't a sufficiently long pause, it would be MONSTROUS! Whatever, tell me exactly where you think I'm wrong. Other than my initial blunder calculating the breakeven point which I corrected.God, if I was practical enough to just ask you that, a lot of yours and my time and effort would be saved...OK, I'll give you what you're asking for, but I would really like to shorten yours and my further posts, so I'll try to crystallize the things on global level first. It's by far more important than petty mistakes. About the process, for Stephen Tu exclusively. Of course, others also can read, but can and will be heavily bored... My first objection is a certain layer of vagueness, indetermination... English is not my native language, so I don't know what word is the most appropriate. Let's see... You're trying to prove that trying to drop the West's king is clearly a better line than safety play, without EVER actually saying it. And you know what? Not only that you failed to convince me that your line is better; you didn't even convince me that it's your real opinion! I seriously tend to think that the main reason for your efforts is sheer inertia. How this chain of misunderstandings began? You and Cyberyeti sent me about the same message. In my words: There are certain boards where you may risk the game having only a slight frequency advantage; such line can even bring some +EV. This board is one of them.I answered to both, without expressing any disagreement. But you somehow misunderstood me and mistakenly said (error No 0) that my final statement wasn't correct. In the next post you've stiffly withdrawn this qualification, but continued to discuss as if I'm somewhere wrong. Not only you didn't say where do you thought I'm wrong, you haven't even pointed in the direction of my apparent wrongness. You're explaining general things - probabilities, mathematical expectation, mechanism of pair tournaments... I never asked, but I am asking you now - what made you to assume that I didn't know all that stuff you're writing about?All in all, you've written a lot, but didn't offer one single useful conclusion.I'm not saying that vagueness (or whatever is the right word) is a mistake, but have a mild objection. I'd really like to clarify - what are we actually talking about. I also see a certain layer of one-sidedness, that's my second objection. In the desire to make this post as short as possible, I'd try to skip the elaboration of this one, maybe just a comment or two in the rest of the post.Lets go to real mistakes... The first one is only hypothetical. I am not claiming the very next statement as a fact - it's just my humble opinion: Your first mistakeYou are trying to prove the hypothesis that you aren't deeply convinced of. If I'm right, this job was never very promising. It's no wonder that you faced difficulties... Now lets go to to open part of the post. Your second mistake (a MAJOR one)You aren't splitting the questions "MAY I" and "SHOULD I". You MAY choose a certain line of play if it's reasonably good; if it has similar mathematical expectation as other lines. You SHOULD choose a certain line of play if it's clearly the best; if it has the greatest mathematical expectation or is clearly the best for some other needs that you consider important (it's the wisest, the most practical... or whatever). In this case you correctly estimated that, due to extraordinary high percentage of pairs who'll bid the same contract, you can afford to risk the game. There is no need to repeat your arguments, you did a proper job. Cashing the ace has about the same expectation as safety play, so you can play it.But SHOULD you? That's a new question, yet you're using the same old means. That means served you well with the old question (may I, could I), but are powerless with the new one (should I). Your writings mainly consist of general considerations and (far from correct) focusing of (wrong) parameters. That gave us satisfactory (over)proof that risking the game is legitimate choice, but I see nothing that could even moderately corroborate the new thesis - that cashing the ace is actually a better line.Using the common language, I'll just say:You're looking for answers at wrong place. THAT's your main mistake. All specific errors are just natural consequences of this one. So I'll not try to determine whether any of your deep convictions are wrong (they probably aren't). I'll concentrate on positive story that I have to tell - how these things really operate... * * * But first I need to introduce some terms. They aren't recognized in theory, I just coined them for this occasion. OUR group - The group of NSs who played the same contract as we didLocal TOP, ZERO - The best/worst result in OUR group800 group - The group of NSs who made better result than our best possible (4s+3)300 group - The group of NSs who made better result than our worst possible (4s-1), but worse than 4s=BOTTOM group - The group of NSs who made worse result than our worst possible (4s-1)INNER group - The group that consists of OUR group and 300 group We can't reach 800 group under any circumstances. With any normal line of play, bottom group is also out of reach. So 300 is obviously the most important. More about that, later. * * * In your two large posts, there are four parts that I painted red, because (very) wrong conclusions could be implied from them. I'll cross over them, not necessarily in chronological order.Once again - whether you meant it wrongly, or were you just sloppy - isn't nearly as important, as positive story that I'm going to tell... As more people play the same, overtricks value goes up, the advantage of just being plus goes down.I already partly commented this. Whatever my previous comment is missing, will be made up by my further story... Before I try to interpret this sentence, let me notice one small, but absolute flow:We weren't talking about "just being plus", we're talking about making a GOOD contract. In this particular case, 4s is the very best contract available to NS; 620 can't be bad and can be a great result (most of the time, it will be a VERY good result).Making 170 or 140 would be "just being plus"... Did you want to say - when more people play the same, the overtrick will get you a better result? If so:- The whole setup is wrong (I don't elaborate, because it's far from certain that I'm correctly guessing your claim)- Specifically, if you watch that parameter alone (the number of pairs playing the same contract), overtricks value (if we're talking about the result) doesn't go UP, it goes DOWN. You're more than qualified to check that...   Yes the frequency of gain of the uptrick in this case is small edge vs the losing case, but this is multiplied by the number of people in the same contract. So total gain (or non-loss, if the field is all playing for overtrick) is more, the more in game.It would be actually correct, if you could keep it totally isolated, "frozen in time and space". But you can't.You have a subtle feeling about the matter, but you neglected the rest of the picture. Continue to read, it will be clear... The percentage advantage of the overtrick grows proportional to the number of people in the same contract.No, it doesn't. It can grow or shrink and neither is proportional to the number of people in the same contract....Let's assume that every NS pair played the same contract. As it's already said - you have frequency advantage, I have points advantage. In this case, my advantage is clean ZERO. So your frequency advantage, no matter how small, literally guarantees you +EV.The severest case is a team match. Your f-ad works in its fullest, giving you the maximal 2.63 percentile points of +EV. Small, but relevant.Now, lets add the third table, making it a pair tournament. Now you can't beat me for 100%, because of sharing results. If you have clean TOP, I don't have ZERO, but 25%. If I have clean ZERO, you don't have TOP, but 75%. So whenever I'm wrong, you beat me for 75%. Your +EV is now 2.63%*75%=1.97%.Let's add the fourth table. Now you beat me for two thirds (formula is n/2(n-1), n is the number of tables where the board is played on). Your +EV is now 2.63%*2/3=1.75%.And so on... Your original example (ten tables) gives you +EV of 1.46%; 16 tables ~1.4%. So we can see that your advantage haven't grown, it shrank. And not proportionally, but fast in the beginning, then slower and slower. In the range typical for club tournaments (8-16 tables per board) it shrinks only a promil - from ~1.5% to ~1.4%. So what's the truth then? Does the number of people in the same contract work in my favor?No, it just pushes your EV toward the LIMES. I chose this particular case, because it's the only one simple enough to allow us comfortable monitoring; more complicated cases also have a limes, not necessarily the same. In this case limes is 1/76 = 1.316% (Exactly one tenth of original probability! I do believe it's only coincidence, but I'm not 210% sure. I need to check similar problem, with different probabilities...).So whenever your EV is above 1/76, it will fall in smaller and smaller steps down to 1/76, never reaching it. Whenever it's below 1/76, it will raise in smaller and smaller steps up to 1/76, never reaching it. So it works for me or for you, depending whether your current mathematical expectation is above or below the limes. Specific truthExact number that serves as limes varies depending on parameters, but when number of pairs that plays the same contract grows - it invariably pushes your mathematical expectation toward the limes - whether it's good or bad for you. General truthUseful answers are elsewhere. You corrected yourself in the next post. Or at least I thought so... So you can see that the amount one gains or loses depends on the percentage of field in same contract.I reread your post (this time more carefully) and realized that this silly statement is offered as some kind of point after several entirely sound and correct paragraphs (in spirit, I didn't check the numbers).Until then, I presumed that it was correction of the blunder from previous post.So what did you try - to make a correction, to make a new statement, or both? If I take your statement literally, it's technically correct, but meaningless. My answer is:Yes, everybody's gains or loses depend on percentage of the field in every contract that was played in the board. So what? If I take it as correction of previous statement, I already told - it's better, but still not good enough. Let me continue my story and all will be revealed... In your original example, the board has been played on ten tables. Everybody bid 4s, but one pair faced successful sacrifice. Our group has impressive 90% of the field, but your EV is far from impressive - only +0.146%, TEN (!) times smaller than when it has 100% of the field. Lets drop the percentage once again, to see what's going to happen... Case AIf we remove a pair that was in 300 group and add two pairs to bottom group and two pairs to 800 group, our group will have 9 of 13 or 69.23%. Your EV is now +0.98% - much BIGGER than with 90%... Case BThis time we'll just add another three pairs to 300 group. Our group again has 9 of 13 or 69.23% of the field. But now, your EV is -2.52%... So with nearly 70% of the field, your EV could be +0.98%, but could also be -2.52%. What's wrong?The METHOD is deeply wrong. Save the few complete but limited examples that you gave us, you're trying to achieve something by analyzing our group in isolation. That's bound to failure. In this particular case, you're referring to size/percentage of our group (in the field) as if it's somehow possible to change it, without also changing the percentage of other groups. No wonder results are so erratic... Specific truthWhen the percentage of our group changes, the outcome depends on what happened to OTHER groups. General truthUseful answers are elsewhere. * * * As I already hinted - the key group is 300 group. The influence of all other parameters put together is practically negligible, in comparison with influence of the ROW NUMBER of pairs in 300 group. Yes, our mutual result depends on percentage of our group. But in INNER field, not in entire field. And even that is only theoretically. In practice, the only thing that really matters is - whether 300 group has 0, 1, 2 or MANY members. (MANY = 3, 4, 5...) We could say that row number of pairs in 300 group decides the ORDER of MAGNITUDE. Sizes of other groups in the field (including ours) decide only where we are in the same class of magnitude. In normal live tournaments, there are only four classes of magnitude - 0, 1, 2 and MANY. Lets say that p0, p1, p2 and p4 are their respective probabilities. If you're writing a book, you'd have to find the credible way to estimate and compare these probabilities.In practice, you can ignore p1 and p4. On bigger tournaments, you can also ignore p2. But you can never, ever forget about P0. Class 0 is bread and butter of your "collecting small profits" strategy. Lets return to the beginning. You just estimated that cashing the ace is legitimate line of play. Fine. You're done with phase 1 and can immediately play the move if you like it. We do play bridge primarily for enjoyment, after all.But if you have greater ambitions (want to judge whether this line is actually better), you're already in the phase 2. Now you should entirely change the perspective and take a view from the opposite side. Forget all obsolete arguments and immediately focus on the most essential question:What's the probability THATNOBODY stopped in wrong contract ANDNOBODY faced a successful sacrifice? Estimate p0 and if you're impressed - go for it! If you aren't - maybe you should just make the game your partner bid...How could you convince the audience that your decision is right? No idea, I don't think you can. But any sensible try has to be heavily leaned on your estimation of p0. Any other aproach is just mumbo jumbo... * * * If you remain biased in the favor of cashing the ace, I'm not worried. I know you're able to take care of yourself. I just feel sorry for many others who'll risk a good game not only when you do it, but also in many other cases when they clearly shouldn't... Disclaimers:  Disclaimer 1I planned to explain things in much greater detail, but sheer size of the task has overwhelmed me. This post (in severely shortened version!) is still extremely long and I am very tired... Disclaimer 2Maybe I made some error(s) in the math, but wholeness is sound. If someone finds an error, I'll correct it and all my conclusions will remain valid... Disclaimer 3All my discussion applies on cases when we bid a slam or game. And not just a game, but a really good game.When I play e.g. 2 in minor, I'm at least as aggressive as Stephen Tu. I'll frequently try suspicious chances, like some unpromising finesse, just to somehow force an overtrick. When I go down, I accept -50 (or even -100) with philosophical calmness, because I know they have 110. So partial scores are entirely different story...  Quote Link to comment Share on other sites More sharing options...
Stephen Tu Posted December 19, 2018 Report Share Posted December 19, 2018 Good god you use a ton of words to say not much. I will try to edit it down to the core of the argument. You're trying to prove that trying to drop the West's king is clearly a better line than safety play, without EVER actually saying it. And you know what? Not only that you failed to convince me that your line is better; you didn't even convince me that it's your real opinion! I seriously tend to think that the main reason for your efforts is sheer inertia. How this chain of misunderstandings began?Huh? I thought I already stated this many times, fairly clearly. This is my claim:trying to drop west's stiff K yields more matchpoints than taking the safety play in the long run, if >= 89% of the relevant field is in 4S.  Or in other words, "IF 89+% of the field is in 4S, you SHOULD play for the drop", but "if <89 % of the field is in 4s, the others being in contracts yielding plus scores < 620, you SHOULD play safe".Clear enough for you? I really don't get your complaints about my clarity or "may vs.should". Most everyone else on the thread understands what I meant.  You and Cyberyeti sent me about the same message. In my words: There are certain boards where you may risk the game having only a slight frequency advantage; such line can even bring some +EV. This board is one of them.I answered to both, without expressing any disagreement. But you somehow misunderstood me and mistakenly said (error No 0) that my final statement wasn't correct. In the next post you've stiffly withdrawn this qualification, but continued to discuss as if I'm somewhere wrong. Not only you didn't say where do you thought I'm wrong, you haven't even pointed in the direction of my apparent wrongness. You're explaining general things - probabilities, mathematical expectation, mechanism of pair tournaments... I never asked, but I am asking you now - what made you to assume that I didn't know all that stuff you're writing about?You basically claimed it's always right to take the safety play to make game if available on any board. A blanket statement, not restricting yourself to this particular board where the edges are small and thus a small number of outlier contracts should favor the safety play. That the field always has enough outlier contracts that the safety play is always right. You said if that if you score 620 when 650 and -100 are also possible that you will always score well above 50%. These just aren't true statements. Some fields are more homogeneous than others, and some boards are flatter than others. One has to be able to estimate how flat a board will be based on the board itself and knowledge of the field, to guess how many will be in the same contract. The more people are in the same contract, the more that favors eschewing safety plays even for very small edges. And if the edge is larger for the overtrick, then one needs less flatness to justify not playing safe. My general claim is don't play safe at matchpoints when in normal contracts. Only when edges are very small as here should one even consider playing safe, if you feel there are enough outlier contracts (> 11% on this board). Your initial posts read to most as "always play safe, making game always > 50%" which is just not true in my experience. This board is close because the edge is small, it's not clear if 90+% are going to be in game or only say 85%. We weren't talking about "just being plus", we're talking about making a GOOD contract. In this particular case, 4s is the very best contract available to NS; 620 can't be bad and can be a great result (most of the time, it will be a VERY good result).620 CAN BE BAD. If the K is stiff offside, and 90% of the field is bidding the contract and banging down the ace, you get a 10% score. Wouldn't you much rather have 55% making 5 like everyone else? Is a 10% score not bad? - Specifically, if you watch that parameter alone (the number of pairs playing the same contract), overtricks value (if we're talking about the result) doesn't go UP, it goes DOWN. You're more than qualified to check that...I don't get this argument at all. If a ton of people miss game, overtricks don't matter at all. You get a fantastic score for bidding and making game, and it's right to play safe. But if a ton of people are in the exact same game contract, the overtrick matters A LOT. If everyone is dropping the stiff K offside, you get a near bottom if you don't. The more people that are in the same contract, the more MP are swung by getting the overtrick or not. If people are in different contracts then the overtrick swing doesn't matter, the making vs. going down does.You are just wrong here.  Let's assume that every NS pair played the same contract. As it's already said - you have frequency advantage, I have points advantage. In this case, my advantage is clean ZERO. So your frequency advantage, no matter how small, literally guarantees you +EV.Huh? WTF frequency vs. points? Let's say there are 100 other pairs, all in 4s, all play for the drop. You win 100 MP when you are right, when LHO is void. You lose 100 MP when you are wrong, when LHO has stiff K. There is no "point advantage" when everyone is in the same contract. It's just pure frequencies.  There would be a point advantage if the scoring were total points or IMPs, because you only lose 50 pts/1 IMP when wrong but gain 600+/13+ when right. But at MP it's simply moving tie to loss either way, there's no "point advantage".Your point advantage comes into play *when there are outlier contracts*. This is because now when you win, you swing a half matchpoint point against the overtrick players AND a matchpoint against outlier contracts, while the overtrick players don't gain anything extra against the outlier contracts when the overtrick was available. So thus the more outliers, the more that favors the safety play, and vice versa. *PROPORTION OF FIELD IN SAME CONTRACT IS WHAT MATTERS*. Proportion, not raw number. nonsense about board-a-match teams vs pairsBunch of math arguing that I win a full board at board-a-match but only say half a board at pairs. This stuff is cancelled out by the same phenomenon in the other direction; when you beat me you gain full board at board-a-match but less at pairs. It's irrelevant. My statement is that going for overtrick is right if >89% of the field is in game, absolute size of the field, whether 3 tables, 30, tables, 300 is basically irrelevant. Smaller field favors going safe because single outliers equate to a bigger chunk of the field; if one table in 8 is weird you want to play safe; if it's only one table in 13 then you don't.Yes, everybody's gains or loses depend on percentage of the field in every contract that was played in the board. So what?So what? So your strategy should change depending on your estimate of what percent of the field is in what contract.The correct answer is not to "always play safe" as your initial post appears to suggest.It is not to "never play safe" either.One has to estimate how much of the field is in the same contract, and compare the edge of the safety play vs. the overtrick play, and make your choice based on all the numbers. The METHOD is deeply wrong. Save the few complete but limited examples that you gave us, you're trying to achieve something by analyzing our group in isolation. That's bound to failure. In this particular case, you're referring to size/percentage of our group (in the field) as if it's somehow possible to change it, without also changing the percentage of other groups. No wonder results are so erratic...My method was fine. If the pair drops out of the same contract (favoring drop), it was assumed to drop into the relevant safety play group (I specifically excluded +800 group, out of reach). And I calculated the breakeven percentage. I just was sloppy with the algebra earlier and came up with a number smaller than reality the first time. Quote Link to comment Share on other sites More sharing options...
Povratnik Posted December 22, 2018 Report Share Posted December 22, 2018 @Stephen Tu Stephen, you are VERY quick on trigger! There is no way you could read and assimilate such a big post in an hour, yet you immediately wrote a fairly long "answer". The result is very disappointing...Your post consists of 9 segments and virtually (literally?) each one has a flow. Most of them I can knock down without saying anything new, just by putting a quote from some of my previous posts... Good god you use a ton of words to say not much.That's precisely my objection to most of your posts :). Of course, since I am using foreign language, my posts could be even worse. But I wasn't much active on this forum so far; so you can check all my posts and convince yourself that my posts are usually short and to the point... Unless I am writing to YOU.Generally, your posts are the hell of a mess. Specifically, when I am writing to you, I tend to fall in one and the same trap - I assume what are trying to say, instead of just asking you that. But my last post had to be that long, because I want to stop inefficient practice and correct procedural mistakes made by both of us. I wrote ALL that had to be written but, unfortunately, most of the content remained undigested by you. So we have a problem again... I will try to edit it down to the core of the argument.Well, you missed it, I hope not deliberately... The core of the argument is my claim that you're looking at the wrong side of proportion. I explained it in the last part of my post. You ignored it totally.A guide for reading my previous post:  My post consists of three parts.In the first part, I am exposing my dissatisfaction with the very process of our discussion. You made a few comments of that part, but totally ignored my (I believe - legitimate) wishes. I'll return to that.At the end of first part and beginning of second part, I said:...So I'll not try to determine whether any of your deep convictions are wrong (they probably aren't). I'll concentrate on positive story that I have to tell - how these things really operate......In your two large posts, there are four parts that I painted red, because (very) wrong conclusions could be implied from them. I'll cross over them, not necessarily in chronological order.Once again - whether you meant it wrongly, or were you just sloppy - isn't nearly as important, as positive story that I'm going to tell......In the second part, I explained why the red paint (less important) and how these thing really operate (MUCH more important). And built the apparatus, so I can speak freely in the third part, which is THE GOAL of the second part.But you dedicated majority of your post to petty mistakes and misunderstandings from second part, without dedicate ONE SINGLE WORD to the third part. As if you haven't read it at all...I understand, you were exhausted because of the length of second part, but you REALLY SHOULD read the third part carefuly.It's significantly clearer and shorter that your average post.   At the beginning of the post, I said: OK, I'll give you what you're asking for, but I would really like to shorten yours and my further posts, so I'll try to crystallize the things on global level first. It's by far more important than petty mistakes.I continued to explain the reasons of my dissatisfaction. See a few quotes:...You're trying to prove that trying to drop the West's king is clearly a better line than safety play, without EVER actually saying it....You're explaining general things - probabilities, mathematical expectation, mechanism of pair tournaments... I never asked, but I am asking you now - what made you to assume that I didn't know all that stuff you're writing about?All in all, you've written a lot, but didn't offer one single useful conclusion....And what have I got? More of the same. You're still giving lectures to those ones who overslept lower grades of elementary school. You still haven't made a relevant claim. You still haven't offered one single useful conclusion. The few productive parts of your post address third grade problems... Don't understand me wrongly - not reading carefully the post you criticize - is the sin we're both guilty of. But this time you crossed all boundaries. You pick a few sentences to quote and neglect to properly read even that tiny portion of text. Look at this: Let's assume that every NS pair played the same contract. As it's already said - you have frequency advantage, I have points advantage. In this case, my advantage is clean ZERO. So your frequency advantage, no matter how small, literally guarantees you +EV.Huh? WTF frequency vs. points? Let's say there are 100 other pairs, all in 4s, all play for the drop. You win 100 MP when you are right, when LHO is void. You lose 100 MP when you are wrong, when LHO has stiff K. There is no "point advantage" when everyone is in the same contract. It's just pure frequencies.You're "correcting" me by saying in two sentences what I said in one! Yeah, I know, it was hidden in the middle. In sandwich between first and last sentence... There is a comment where the first your sentence is "I don't get this argument at all.". In the last sentemce you said I was wrong. How do you know I'm wrong if you don't get it? And this one really pissed me of: You're trying to prove that trying to drop the West's king is clearly a better line than safety play, without EVER actually saying it. And you know what? Not only that you failed to convince me that your line is better; you didn't even convince me that it's your real opinion! I seriously tend to think that the main reason for your efforts is sheer inertia.Huh? I thought I already stated this many times, fairly clearly. This is my claim:trying to drop west's stiff K yields more matchpoints than taking the safety play in the long run, if >= 89% of the relevant field is in 4S. Or in other words, "IF 89+% of the field is in 4S, you SHOULD play for the drop", but "if <89 % of the field is in 4s, the others being in contracts yielding plus scores < 620, you SHOULD play safe".Clear enough for you? I really don't get your complaints about my clarity or "may vs.should". Most everyone else on the thread understands what I meant.A proper answer HAS to contain a clear message:a) Yes, I AM claiming that cashing the ace is better line than safety play.ORb) No, I am NOT claiming that cashing the ace is better line than safety play. Not only you haven't given a proper answer, you completely ignored everything that was said in the quote you picked yourself. You could well choose some other piece of my text and glue your mumbo jumbo as an "answer".You're "claiming" that a player should always pick the line with greater mathematical expectancy. Really?That's an insult. You should better not answer at all then "answer" this way. I never gave you an excuse (not to mention a real cause) to talk to me like that."I claim nothing. I am just making fun by discussing.", would be a disappointing, but honest answer. I would appreciate it. There are some productive parts in your post, but they can wait. Now I have to ask you a direct question. (With the hope that I'll get a direct answer.) Besides obvious generalities, the only thing you properly articulated was the claim that cashing the ace is legitimate line of play. Nobody disagreed.Have you ever (in this thread) been trying to prove (or at least claim) ANYTHING more than that? If the answer is affirmative, PLEASE be as precise and specific as you can.If the answer is negative, PLEASE say it explicitely. I BEG you - don't throw at me another pile of trivial generalities as a replacement for direct and honest answer. And finally, I'd appreciate if you don't answer immediately, but make at least a 24h delay... (Frankly, I am afraid of another mess) Thank you for your time Quote Link to comment Share on other sites More sharing options...
johnu Posted December 22, 2018 Report Share Posted December 22, 2018 Excuse me for intruding into this discussion but here are a couple of observations Stephen, you are VERY quick on trigger! There is no way you could read and assimilate such a big post in an hour, yet you immediately wrote a fairly long "answer". The result is very disappointing... The timestamp on your big post was "Posted 2018-December-18, 17:09"while Stephen Tu's response was "Posted 2018-December-18, 19:26" That looks like 2 hours 17 minutes to me. That only tells me that Stephen is probably a fast typist, nothing more, nothing less. Quote Link to comment Share on other sites More sharing options...
nige1 Posted December 22, 2018 Report Share Posted December 22, 2018 Arithmetic isn't my long suit, so masochists are welcome to check my calculations.. Assume...101 tables Match-pointed pairs .(American scoring: 1 for a win 0.5 for a tie)You, South, declare 4♠.The other 100 declarers also sit South.All defenders lead ♣AK and another.Declarer wins with dummy's ♣J.Dummy leads ♠x and RHO follows low.p of the other pairs bid 3♠and go up ♠A.q of the other pairs bid 5♠and go up ♠A.r of the other pairs bid 4♠and go up ♠A.s of the other pairs bid 4♠and take the safety-play.Note that p+q+r+s = 100. Suppose you go up ♠A as Stephen Tu recommends 11% of the time, LHO is void, so you make 9 tricks and- lose to p pairs, in 3♠.- beat q pairs, in 5♠.- tie r pairs, who go up ♠A in 4♠.- lose to s pairs, who safety-play 4♠. 13% of the time, LHO has singleton ♠K, so you make 11 tricks and- beat p pairs in 3♠.- tie q pairs in 5♠.- tie r pairs, who go up ♠A in 4♠.- beat s pairs, who safety-play 4♠. 76% of the time, you take 10 tricks and- beat p pairs in 3♠.- beat q pairs in 5♠.- tie r+s pairs in 4♠. Hence, if you go up ♠A, then you score... 0.11 * (q + r/2)+ 0.13 * (p + q/2 + r/2 + s)+ 0.76 * (p + q + r/2 + s/2)= 0.5 * ((0.26+1.52)*p + (0.22+0.13+1.52)*q + (0.11+0.13+0.76)*r + (0.26+0.76)*s)= 0.5*(1.78*p + 1.87*q + 1.00*r + 1.02*s)= 0.89*p + 0.935*q + 0.51*s + 0.50*r= 0.89*p + 0.935*q + 0.51*s + 0.50*(100-p-q-s) (because p+q+r+s = 100)= 0.89*p + 0.935*q + 0.51*s + 50 - 0.5*p - 0.5*q - 0.5*s= 0.39*p + 0.435*q + 0.01*s + 50 MP Suppose you take the safety-play as Povratnik recommends 11% of the time, LHO is void, so you make 10 tricks and- beat p pairs, in 3♠.- beat q pairs, in 5♠.- beat r pairs, who go up ♠A in 4♠.- tie s pairs, who also safety-play 4♠. 13% of the time, LHO has singleton ♠K, so you make 10 tricks and- beat p pairs in 3♠.- lose to q pairs in 5♠.- lose to r pairs, who go up ♠A in 4♠.- tie s pairs, who safety-play 4♠. 76% of the time, you take 10 tricks and- beat p pairs in 3♠.- beat q pairs in 5♠.- tie r+s pairs in 4♠. Hence, if you take the safety play, then you score 0.11 * (p + q + r + s/2)+ 0.13 * (p + s/2)+ 0.76 * (p + q + r/2 +s/2) = 0.5 * (0.22+0.26+1.52)p + (0.22+1.52)*q + (0.22+0.76)*r + (0.11+0.13+0.76)*s)= 0.5 * (2.00*p + 1.78*q + 0.98*r + 1.00*s)= p + 0.87*q + 0.49*r + 0.5*s = p + 0.87*q + 0.5*s + 0.49*(100-p-q-s) (because p+q+r+s = 100)= p + 0.87*q + 0.5*s + 49 - 0.49*p - 0.49*q - 0.49*s= 0.51*p + 0.38*q + 0.01*s + 49 MP Thus, the safety play beats going up ♠A when0.51*p + 0.38*q + 0.01*s + 49 > 0.39*p + 0.435*q + 0.01*s + 50 i.e... 0.12*p - 0.055*q > 1 If you judge that the field will play 4♠, then you should go up ♠A.Also, If you judge that other pairs are likely to overbid, then you should go up ♠A.Otherwise, you should take the safety-play when you guess that more than 8% of other pairs play in a partscore. Quote Link to comment Share on other sites More sharing options...
Stephen Tu Posted December 22, 2018 Report Share Posted December 22, 2018 Knock down without saying anything new, just by putting a quote from some of my previous posts... Your attempts to knock down things are incredibly ineffective because of so much rambling and tangents. It's not clear what statement you are attempting to knock down at all. Quote a specific claim of mine, get directly to the point of why it is wrong, say how you would rewrite the sentence so that it is correct. From my point of view you haven't knocked anything down. Just made complaints about my writing style. Other people here don't seem to think it's unclear. A proper answer HAS to contain a clear message:a) Yes, I AM claiming that cashing the ace is better line than safety play.ORb) No, I am NOT claiming that cashing the ace is better line than safety play. Wtf? I made my clear statement already, multiple times:  Don't play safe if >= 89% of relevant field playing 4s, for this particular board.  Do you agree with this statement or not, if yes, what are we arguing about; if no, rewrite the statement to what you think is correct. You're "claiming" that a player should always pick the line with greater mathematical expectancy. Really?That's an insult.  ??? Why is that insulting? It's the correct answer to the question posed by the thread. And I attempted to show how to go about calculating it.  What am I supposed to claim instead?  Your "third part", I didn't address because I think I agree with it, at least the parts of it I was able to parse. But at the same time, since I was agreeing with it, I can't see that it was knocking down anything I said previously.  Mainly I am objecting to two claims of yours, which IMO are incorrect. I am not quite sure if you believe them in an absolute sense as you wrote then, or simply neglected to include appropriate caveats that would bring us into agreement.  One is that playing safe guarantees a good score regardless of field. And maybe regardless of board also, even when going for overtrick has bigger edge. Are you still claiming this, or did you not intend to mean this?   Your claim on surface appears to be "always play safe for games at matchpoints". Is this what you mean or not?   Also you seem to dispute that more people playing the same 4s contract as you does not favor the drop. Are you claiming this number has no effect at all, or the opposite, that more people in same contract favors playing safe? My claim here is that the more people who are in 4s, the more points you gain not playing safe, when the drop was the right play, when k stiff offside. You are always comparing how many points you gain when you are right vs how many you lose when you are wrong, and the relative frequencies. Playing safe will swing more matchpoints when it is right due to outliers, vs what it loses when it is wrong, but that edge goes down as the number in 4s goes up, because that means the number of outliers is going down. Playing safe or not is a board and field dependent decision. During play you can only guess at what the contract distribution is going to be. Only after scores are published do you find out whether your estimate was right or not.  Do you agree with this statement or not, or do you think it's always right to play safe, regardless of board or field? Quote Link to comment Share on other sites More sharing options...
nullve Posted December 22, 2018 Report Share Posted December 22, 2018 I'm still surprised that people think a priori probabilities apply here. If they do apply, then they also apply to the diamond suit, so there's a non-zero probability that West passed 1♠with  ♦QJT9876432 that has nothing to do with whether he was misbidding in some way. Hard to believe, isn't it? Quote Link to comment Share on other sites More sharing options...
Povratnik Posted December 22, 2018 Report Share Posted December 22, 2018 @nige1 Sorry, you lost me at the very beginning. I don't understand that type of tournament. Against WHOM I can have win, tie or loss?If that's essentially the same as team match with MPs counting, then your math is unnecessary, Stephen's line is definitely better. Can you make corresponding arithmetic for standard pairs tournaments? @Stephen Tu Since I have to write a short message to nige1, I'll take an opportunity to write one to you, in the same post. ??? Why is that insulting?If you're so insensitive to insults, then it's a no brainer to me. I have a very effective answer: "IF 89+% of the field is in 4S, you SHOULD play for the drop", but "if <89 % of the field is in 4s, the others being in contracts yielding plus scores < 620, you SHOULD play safe".Nah, that's primitive. You should cover East's card when West is void, and put an ace when West has a king. This way you'll have MUCH better results!If you turn out to be succesful in finding the flaws of my answer, but unsuccesful in finding the flaws of your statement, just report what have you found. I'll help you to find more.Please don't write about anything else in your very next post. Just your thoughts about your statement and my answer. EDIT: I am putting another message in this post @nullve You are trying to say that bridge inferences are more important than pure math?I agree, but in this board you can't find anything useful, so we have to rely on good, old math... Quote Link to comment Share on other sites More sharing options...
Stephen Tu Posted December 23, 2018 Report Share Posted December 23, 2018 The flaw of this particular statement (drop if stiff K if offside, play safe if lho void) is obviously that it requires omniscience. One can't take this (clearly optimal!) approach accurately unless you are a god and just know, or have unauthorized information about the board, from overhearing or perhaps seeing someone's scoresheet. You are apparently implying that my approach also requires omniscience. This is not true. One can estimate the flatness of a board through experience. One can tell whether you or partner had borderline decisions, whether alternate contracts are particularly likely to be reached or not. Now certainly, one's estimate can turn out wrong, which can only be determined after the fact. More people can find a successful sac than you anticipated, which would make playing safe better. So what? Use the experience to refine your estimating skills, play safe the next time against similar board and field. Surely taking such an estimate is the approach to deciding whether to play safe, rather than making blanket false statements about how playing safe for the contract will absolutely guarantee a good score, can never be bad, will always be above 50%, all of which you claimed. None of this is true, and is the main thing I dispute. You seem to advocate playing safe regardless of estimate of how flat the board will be, even on alternative board where playing safe costs an overtrick far more often than saving the contract, e.g. playing safe vs 4-1 breaks. Now if you were just claiming that it's right to play safe on this board, because you think for certain > 11% are finding a successful sac, I wouldn't be fighting you. I am fighting you because you seem to make blanket statements implying flatness of the board doesn't matter or is unknowable. You said +620 guarantees > 50% mp on the board which just isn't right. Quote Link to comment Share on other sites More sharing options...
Stephen Tu Posted December 23, 2018 Report Share Posted December 23, 2018 And nige1 was just analyzing a standard pairs tournament. You can win tie or lose against each other pair playing the board. 1 point for win, half for tie. Add all comparisons together to get total number of matchpoints on the board. Standard way to play matchpoint pairs (except that Europe often scores instead 2 for win, 1 for tie). My math differed from his in that I assumed group Q in 5s was zero (presence of such a group clearly favors drop over safety play, as the drop never loses vs this group), and I used percentages of success accounting for the 3-3 club break rather than a priori percentages. Quote Link to comment Share on other sites More sharing options...
nullve Posted December 23, 2018 Report Share Posted December 23, 2018 @nullve You are trying to say that bridge inferences are more important than pure math?I agree, but in this board you can't find anything useful, so we have to rely on good, old math...I'm only criticising the use of a priori probabilities here, as if the probability of a 0-3 diamond break isn't affected by the fact that West passed throughout. Here are 100 hands dealt randomly on the condition that the NS cards are as above and West has ♠---♣AKx:   West hands: 1. 2. 3. 4. - - - - 9 8 3 2 Q T 9 8 2 T 8 6 3 Q T 8 3 Q T 6 4 3 2 Q J T 6 2 J T 9 7 6 2 J 8 6 4 3 2 A K 5 A K 5 A K 2 A 6 2 5. 6. 7. 8. - - - - T 9 8 6 T 9 8 6 2 8 6 2 Q 9 8 6 Q 9 8 6 4 2 Q J T 9 2 Q T 9 7 6 4 3 9 7 6 4 3 2 A 9 2 A K 2 A 6 5 A 9 6 9. 10. 11. 12. - - - - Q T 3 2 Q T 6 2 T 8 6 2 Q T 3 J T 9 8 7 4 J T 9 7 6 2 Q J T 9 6 3 Q J 9 8 6 4 3 A K 2 A K 5 A 9 2 A 5 2 13. 14. 15. 16. - - - - Q 9 3 Q 9 3 2 Q 8 6 3 2 Q T 8 3 2 T 9 8 7 4 3 2 Q J T 9 6 3 Q J T 7 6 Q T 4 3 2 A 9 6 A 9 5 A 6 5 A K 9 17. 18. 19. 20. - - - - 9 8 3 2 T 9 8 6 2 Q 8 2 9 8 6 3 2 9 8 7 4 3 2 Q J T 7 6 Q T 8 7 6 4 2 J T 9 8 2 A K 2 A 5 2 A 9 6 A 5 2 21. 22. 23. 24. - - - - 6 2 Q 9 8 6 3 2 Q T 9 8 6 3 Q 8 J T 9 8 7 6 3 2 Q J T 7 Q J 6 2 Q J 9 8 7 6 4 3 A 9 6 A 6 2 A K 5 A K 6 25. 26. 27. 28. - - - - Q T 9 8 6 2 Q 6 2 Q T 3 2 Q T 2 J T 6 2 Q J 9 8 4 3 2 Q T 9 8 4 3 Q T 9 8 7 6 2 A 5 2 A 9 5 A 9 2 A K 9 29. 30. 31. 32. - - - - Q 9 8 6 2 Q 6 2 T 9 8 6 2 Q T 9 2 Q J 7 6 3 J 9 8 7 4 3 2 Q J T 8 4 J 9 8 7 3 2 A 6 2 A 5 2 A K 6 A 9 5 33. 34. 35. 36. - - - - Q 9 8 3 2 T 9 8 6 2 Q 9 3 2 9 6 3 J 7 6 4 3 Q T 7 6 2 Q J T 8 4 2 J T 8 6 4 3 2 A K 9 A 5 2 A 9 6 A 6 2 37. 38. 39. 40. - - - - Q T 8 3 2 Q T 6 3 Q 9 8 2 Q 6 3 2 Q J 6 4 3 J 9 7 6 4 2 Q T 8 6 4 2 Q T 9 4 3 2 A 5 2 A K 6 A 6 2 A 6 5 41. 42. 43. 44. - - - - Q 9 8 3 2 Q T 8 2 Q 9 8 6 9 8 6 3 2 Q T 8 7 3 Q J T 7 3 2 Q T 9 8 7 3 8 7 6 4 3 A 6 2 A 6 2 A 9 2 A K 2 45. 46. 47. 48. - - - - Q T 8 6 2 Q T 9 8 3 T 9 8 6 2 Q T 8 3 2 J 9 6 4 2 J 8 7 6 2 J 7 4 3 2 Q 9 8 4 3 A K 9 A 6 2 A K 6 A 6 2 49. 50. 51. 52. - - - - T 8 3 Q T 9 8 6 Q 6 Q T 3 Q J 9 8 7 6 4 Q 9 7 6 3 J 9 8 7 6 4 3 2 T 9 8 7 6 4 3 A 9 2 A 5 2 A K 2 A K 5 53. 54. 55. 56. - - - - 6 3 2 Q T 9 6 3 2 T 9 8 6 3 Q T 6 2 J T 9 7 4 3 2 J 9 6 2 Q T 8 4 2 T 9 8 7 3 2 A K 2 A K 6 A 6 5 A 9 5 57. 58. 59. 60. - - - - Q 6 3 2 T 8 6 2 Q 8 3 T 9 6 2 Q 7 6 4 3 2 J T 8 7 4 2 Q 8 7 6 4 3 2 Q J 9 6 4 2 A 9 2 A 9 2 A K 9 A 6 5 61. 62. 63. 64. - - - - T 9 6 3 Q 9 8 6 9 8 6 2 Q 9 6 3 2 Q 8 6 4 3 2 Q J 6 4 3 2 J T 9 6 3 2 9 7 4 3 2 A K 9 A K 2 A 9 6 A 6 5 65. 66. 67. 68. - - - - 9 8 2 Q 9 8 6 9 6 2 Q 9 8 3 2 T 9 8 7 6 3 2 Q T 9 8 7 2 Q T 7 6 4 3 2 Q T 9 7 2 A 6 5 A 9 6 A K 6 A 9 6 69. 70. 71. 72. - - - - T 9 8 2 Q 8 3 2 Q T 9 8 6 9 6 3 2 J T 8 4 3 2 J 9 7 6 4 2 T 9 8 7 3 Q J 9 6 4 3 A K 2 A 9 2 A 9 6 A 9 6 73. 74. 75. 76. - - - - 9 6 3 2 Q 8 6 2 T 6 2 T 8 6 3 2 Q J T 8 4 3 Q T 8 4 3 2 Q T 8 6 4 3 2 Q 8 7 3 2 A 9 6 A K 2 A K 9 A K 5 77. 78. 79. 80. - - - - Q T 6 3 2 T 9 8 6 T 9 8 6 2 Q T 8 6 3 2 Q J T 9 3 J T 8 7 4 3 8 7 6 4 2 T 7 4 3 A K 9 A 6 5 A K 6 A 9 6 81. 82. 83. 84. - - - - 9 8 3 Q 8 6 2 Q T 9 8 3 Q T 9 8 3 Q J 9 8 7 6 4 T 9 6 4 3 2 Q 8 7 6 3 Q 8 6 4 3 A K 9 A 9 6 A K 2 A 6 2 85. 86. 87. 88. - - - - Q T 6 3 Q 9 Q T 6 Q 8 3 T 9 8 7 3 2 Q T 9 8 7 6 4 3 J 9 8 7 6 3 2 Q J T 9 7 6 3 A 5 2 A 9 2 A K 9 A 6 2 89. 90. 91. 92. - - - - T 6 3 9 3 2 Q T 8 6 3 3 2 Q J T 6 4 3 2 J T 9 7 4 3 2 J 8 6 4 2 J 9 8 7 6 4 3 2 A K 6 A 6 2 A 9 5 A 6 5 93. 94. 95. 96. - - - - T 6 3 Q T 8 6 Q T 9 8 6 Q T 8 6 J T 9 8 7 6 3 J 9 7 6 4 3 Q J 8 7 3 Q J 8 6 3 2 A K 2 A 6 2 A 9 6 A 9 5 97. 98. 99. 100. - - - - Q T 6 3 T 8 6 2 T 9 8 2 Q T 8 3 Q T 9 8 7 4 Q T 9 7 6 4 Q T 8 7 6 3 J T 9 8 7 6 A 6 5 A 6 2 A 5 2 A 9 6 Generated 5471 hands Produced 100 hands   As West I would have acted on all of them at this vulnerability, either over (1♠) or over (1♠)-P-(4♠)-P; (P). You may think that's insane, but if these hands are representative and there's a chance that the actual West is anything like me, then the a priori probability of a 0-3 diamond break (~ 0.11) clearly doesn't apply, and I don't think it's even a good approximation unless the field is unrealistically timid or maybe unfamiliar with concepts like 'preempt', 'sacrifice' and (of course) 'Law of Total Tricks'. Quote Link to comment Share on other sites More sharing options...
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