Cascade Posted March 19, 2008 Report Share Posted March 19, 2008 Hmm I'm not sure what Cascade's numbers are suggesting. His first post artificially equalizes the number of hands where each contract is better, and the second doesn't seem to count situations where hearts and spades are equal. I am not sure what you mean. My first simulation made no assumptions other than the we held the hand in the opening post and I calculated double dummy tricks opposite 1000 random hands. One subsequent series of simulations tried to give information about heart and spade length for the three scenarios:More tricks were available in spades then heartsspades and hearts produced the same number of tricksmore tricks were available in hearts than spades Quote Link to comment Share on other sites More sharing options...
awm Posted March 19, 2008 Report Share Posted March 19, 2008 Okay here's what I mean. Given partner has 4+♥, what are the probabilities that hearts are better, spades are better, or they are equal? Cascade's first post just generates random hands. But obviously for some (many?) of these random hands we will always end in 4♠. So we need to condition on partner actually raising a heart rebid, which is pretty close to conditioning on partner has 4+♥. Cascade's second post comes closer to doing this, but he figures out of the hands where 4♥ is better than 4♠, what percentage include various numbers of hearts and spades in partner's hand?. This again is not what we want -- presumably most of the time that hearts are better partner has four or more hearts; the question is how often are hearts better given partner has four or more hearts versus the number of times spades are still better despite partner having four or more hearts. Cascade's third post actually gives the percentage of times hearts are better given partner has four or more hearts as 276/1000 for exactly four hearts and 505/1000 for five-plus hearts. However, the question is, of the thousand hands where partner has exactly four hearts, how often are the two contracts equal? If hearts are better 276/1000 times and they are the same the other 724/1000 times then introducing hearts is obviously a big win. If hearts are better 276/1000 times and spades are better the other 724/1000 times then introducing the hearts will lead to lots of inferior contracts. Of course the reality is somewhere between the extremes, but we need to know where it is. Quote Link to comment Share on other sites More sharing options...
Cascade Posted March 20, 2008 Report Share Posted March 20, 2008 Okay here's what I mean. Given partner has 4+♥, what are the probabilities that hearts are better, spades are better, or they are equal? Cascade's first post just generates random hands. But obviously for some (many?) of these random hands we will always end in 4♠. So we need to condition on partner actually raising a heart rebid, which is pretty close to conditioning on partner has 4+♥. Cascade's second post comes closer to doing this, but he figures out of the hands where 4♥ is better than 4♠, what percentage include various numbers of hearts and spades in partner's hand?. This again is not what we want -- presumably most of the time that hearts are better partner has four or more hearts; the question is how often are hearts better given partner has four or more hearts versus the number of times spades are still better despite partner having four or more hearts. Cascade's third post actually gives the percentage of times hearts are better given partner has four or more hearts as 276/1000 for exactly four hearts and 505/1000 for five-plus hearts. However, the question is, of the thousand hands where partner has exactly four hearts, how often are the two contracts equal? If hearts are better 276/1000 times and they are the same the other 724/1000 times then introducing hearts is obviously a big win. If hearts are better 276/1000 times and spades are better the other 724/1000 times then introducing the hearts will lead to lots of inferior contracts. Of course the reality is somewhere between the extremes, but we need to know where it is. Responder has :Four or more heartsSix or more points (perhaps this should be relaxed a little)Hearts made more tricks 364/1000 Spades made more tricks 95/1000 Quote Link to comment Share on other sites More sharing options...
hrothgar Posted March 25, 2008 Report Share Posted March 25, 2008 Out of curiousity, what happened at the table on this one? Quote Link to comment Share on other sites More sharing options...
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