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@Craig: You are comparing apples to fruit, since Eric's four Queens hand benefits from the DD bias in favor of flat hands, while most of the balanced 14's and 15's do not. Try comparing to random 4333 14's and 15's.

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Sorry, Craig, but the fact that the differences between DD and ATT results averages 3 to 4% does not make that a valid adjustment for specific hands. Most of the declarer advantage is specifically from inferior leads – which is why DD punishes weak doubletons so much, and turns the disadvantage of flat shape into an advantage. As for your “margin of error” estimates, please refer to any introductory statistics textbook. A proportion is a proportion, no matter what it represents. I don't have aa problem with sims of any size – just report the sample size, and if you are reporting average tricks taken, report the sample variance or standard deviation.

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Tomasz, the 3% referred to the probability of making 3NT, not the number of tricks. To estimate a margin of error on number of tricks, we need the standard deviation of the sample. This is basic statistics stuff – there is no sample size where one can say a sample result is the “true” answer. All inference from samples should be accompanied by a margin of error estimate. For proportions, such as the chance of making 3NT, it so happens we can estimate the MOE just from the proportion and sample size.

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And my comment that that is an artifact of double-summy sims, where they always find partner's killer suit. DD favors flat hands, real life does not. We cannot learn anything useful by comparing DD sims for different hand patterns.

We should, at this point, have decent single dummy tools. Kurt Schneider has attempted this but I have not been convinced that his results correlate well with at the table bridge. But we simply cannot make much use of DD sims where the opening lead is far better than in real life.

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An Ace, 1 point for the six-bagger and better than average intermediates. Second choice would be 1♣ followed by 2♣, but this hand looks very notrumpish to me.

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You would certainly expect to reach game opposite a 9 count whether or not you downgrade. 6, 7 and 8 will depend on partner's style and judgement, so I agree that 7 is the proper yardstick since few would invite over 1NT but almost all would bid game over a 2NT jump rebid.

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Now, what about strong hands? An 18+ pointer won't have as much room for intermediates as a 10 point hand, while weak hands will have more room. How significant is this crowding effect?

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It is obvious that an average hand contains one each A, K, Q, J, 10 and 9. A reasonable point count (for purposes of bidding 3NT) is 4.0, 2.8, 1.8, 0.8, 0.4, 0.2, which preserves the 40 point deck. (Basically, count each K, Q, or J as a minus factor, each 9 as a plus, and each ten as two plusses. Most hands will come out close to the 4321 count.) A French study determined that a 5-card suit is worth about 0.4 points at notrump; what I have not seen is how much to deduct for 4333. Minus 0.6 would roughly balance the 5332's but perhaps that is excessive.

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Demonstrating why Double Dummy analysis doesn't help much with specific hands. At DD, 4333 is the strongest balanced type because the opponents will less often have a killing lead; at the table, the opps don't always find that lead, and 4432 plays better than 4333.

On 1000 hands, the margin of error is roughly 3%, so #2 and #3 are too close to call, and #1 and #3 probably the same. That #2 appears clearly better than #1 is surprising; can't think of any DD peculiarity that would explain it. You might try 10000 hands for #1 to see if the result holds; that would reduce the margin of error to around 1%.

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What does double mean? Every time I want to make a penalty double, everyone including my partners think it's takeout. I don't believe in takeout doubles after three suits have been bid, but what do the doublers think double means? If double is clearly penalty, not DSI or such, that would be my choice.

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3♠ last round seems clear, as does double at this point. Even opposite – Kxxx KQxx xxxxx we may collect a heart, a diamond and two clubs. Opposite anything normal down two or three seems likely. Are you sure we didn't deal and open 1♦?

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Estimating that partner has 13/34 times 9 spades gives an expectation of 3.44 spades in partner's hand; and assuming opener does not have 5-5 and perhaps not 5-6 in the majors, the odds are about 50% we have a spade fit. This is distinctly higher than the odds if we were dealer with this hand. What's more, partner rates to be short in hearts and so can expect to ruff perhaps twice in hand. Spades rate to play well, and any contract rates to play better from partner's side. Against that, of course, is that 1NT quickly describes our strength and shape, and clubs might not be our best spot.

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Why “strictly limited” ? It is easy to define many types of special raises beginning with 1NT Forcing, such as a balanced 3-card game force, under the assumption opener will rebid two of something. But when the bidding reaches the 3 or 4 level thanks to interference or a jump rebid by opener, suddenly responder has no way to complete the description. Much better to start with a strength-showing 2♣ or 2♦ response, despite ambiguity about their length. Some players require 5 cards for 2♦ and use 2♣ as a catch-all game force.

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Bridge World Standard uses Semi-Forcing, but I am comfortable with either Forcing or Semi-Forcing. Either way, the bid should be strictly limited; I play 6-12 hcp. Forcing generally helps when responder has a long suit, not worth a 2/1 or (if you play them) invitational jump shift. It may also help when responder has a weak raise, where 2 of the major is better than 1NT.Semi-forcing helps when responder is relatively balanced, opener is minimum and balanced, and 1NT is the best spot (or better than 3 of the major whee responder has a balanced limit raise.) I think there is more to say for Forcing at matchpoints where playing in the major will often produce a better matchpoint score.

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Whether or not East has caught a fit, spades rate to be 3-3 or 3-2, so it looks like 16 total tricks to me. My hand looks good for offense so I'll compete.

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East likely has some values, which appear to be well located over partner. Pass does not seem likely to collect +500 unless we have game our way. I'll settle for the value bid of 3♣ and assume partner, holding extras, will tend to rebid 3♦, 3♥ or 3♠ so I can try 3NT.

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower

We should, at this point, have decent single dummy tools. Kurt Schneider has attempted this but I have not been convinced that his results correlate well with at the table bridge. But we simply cannot make much use of DD sims where the opening lead is far better than in real life.

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower

On 1000 hands, the margin of error is roughly 3%, so #2 and #3 are too close to call, and #1 and #3 probably the same. That #2 appears clearly better than #1 is surprising; can't think of any DD peculiarity that would explain it. You might try 10000 hands for #1 to see if the result holds; that would reduce the margin of error to around 1%.

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower

Paul Hightower