jogs

You need more restrictions on the side conditions. Your questions cover too much territory. 4333 generates fewer tricks than 4432. 5422 generates fewer tricks then 5431. No one has studied and published info on this topic.

Okay you got me. I went out of my way to show 5332 in the worst possible light. Also double dummy analysis has a bias favoring the defense of 0.35 to 0.5 for normalized HCP. No one in the real world can find all those killer defensive lines. 7.645 tricks/board is low. Expect approximately 8. Is 5332 a flat pattern? It is relative. 5332 is the third flattest of 39 possible patterns. Only 4333 and 4432 are flatter. When pard knows you hold five in the suit 5332 IS the flattest possible pattern. 1M-4M with 5332 must have netted some poor results. With normalized HCP and a known 5-4 trump fit 5332 will generate less than 9 tricks. a) 5332 // 4243 b) 5332 // 4234 Do these two joint patterns generate the same expected tricks? I don't know. Guessing it will be close with a) slightly higher. c) 5431 // 4333 Does c) generate more or less tricks than a) and b)? All SST=4 are not equal. Expect fewer than 9 tricks whenever the SST => 4. Expect more the 9 tricks whenever the SST =< 3. Joint patterns which generate fewer tricks than trumps are arbitrarily defined as flat.

Assuming a contested auction in the majors. Yes, if you are 5332 with a doubleton in a minor pard is likely to have a doubleton or singleton in the other major. Actually I am claiming that 5332 is a flat pattern which is detrimental to tricks. If it is right to bid 3 over 3, it will be because pard has a skewed pattern. Meaning the flat pattern should pass and allow the pard to make the final contested decision. In the case where there are two doubletons in different suits with normalized points the expected tricks was 8.66 in my small sample. Really needed a singleton somewhere before it was clear to go 3 over 3. LoTT should be E(tricks) = trumps + e where e is N(u,σ²) for trumps =< 18 u = 0 for trumps > 18 u < 0 meaning expected tricks is less than total trumps whenever total trumps is 19 or greater. *Had to change the last two lines.

Don't know which 32519 thread you're referring to.

On Chapter 9 p216 Cohen listed many adjustment factors. He provided no statistical analysis. It is really difficult to isolate the effects of any particular parameter.

Read his article. Neither Cohen or Bloom posted expected value or variance for any of their data.

Okay, I copied and pasted the app and a line or two disappeared. Rechecked it after gwnn disagreed with my numbers. Now it is 1642 total tricks. 8.21 ave tricks. 1.037 std dev.

Recalculated these. ave trks = 7.645 std dev. = 0.948

I rechecked everything and now have your numbers. Sorry.

You better add them up. 1600 total tricks. It is the nature of variance. The outliers have a greater effect on the variance than those lumped in the middle. The LoTT statement is too powerful. Total tricks equal total trumps less than 40% of the time. Cohen backed off and later stated the average tricks equal total trumps. He needed to weaken the statement more. The expected number of tricks equals total trumps. Now we 'know' when tricks is less than trumps. And when tricks is more than trumps. Flat patterns produced fewer tricks. Skewed patterns, those with singletons, voids, and long second suits, produce more tricks than trumps.

Sample size = 200 total tricks = 1430 ave tricks = 7.15

Thanks, no problem. Have app in excel to solve variance. Averaged only 7.15 tricks. This is much lower than I expected. The bias for the defense in double dummy must be huge. I was expecting 8 to 8.25 tricks. ave trks = 7.115 std dev. = 2.365 ave trks = 7.150 std dev. = 2.312

Thanks, inquiry. average tricks = 8.000 standard deviation = 1.794 ave trks = 7.965 std dev. = 1.787 Was surprised by the high std dev. Notice that 9 trumps produced only 8 tricks. 8 tricks was what I found from my small sample. Lawrence/Wirgren was right. Flat patterns produce fewer tricks. This blind bid up to the level of your trumps is wrong. Bergen raises aren't protected by any physical law. Should add that there is a minor bias favoring the defense in double dummy. In live play declarer may do 1/4 of a trick better.

simulation needed Can anyone help? TIA Conditions. Both sides hold 20 HCP. NS has 5-4 spades. EW has 9 hearts. Restrict patterns for NS to 5233 // 4243 and 5233 // 4234 100 iterations. List tricks made by NS with spades as trumps. Need list of distribution. I will calculate the variance. 12 - 11 - 10 - 9 - 8 - 7 - 6 - 5 - 4 - thanks, jogs

Power and Pattern Review of the material. Power and pattern are two multi-dimensional independent random variables used to estimate tricks. Power is high card points, the location of those HCP, and how they interact with each other. This would require a complex polynomial too difficult to solve at the table. HCP is the component of power which is roughly proportional to tricks. HCP will be used as a proxy for power in the our tricks model. Pattern is the ordered configuration of the four suits in one hand. Joint pattern is the joint pattern of the two partnership hands. All four suits have effects on tricks. Combined trumps is the component of pattern which is roughly proportional to tricks. Trumps is the proxy for pattern. E(tricks) = trumps + (HCP-20)/3 + e Skewness/flatness. Singletons and voids increases the expected tricks. The absence of singletons and voids(or flatness) reduces the expected tricks. Singletons and voids are components of pattern, not power. E(tricks) = trumps + (HCP-20)/3 + SF + e Interaction. There are effects due directly to each individual parameter. There are also effects due to the interaction of those parameters. Most systems assign a fixed value to a singleton. Singletons are components of pattern, not power. The true value of a singleton is dependent on how it reacts with other parameters. Therefore a singleton should have a variable value expressed in expected tricks. 5431 // 3343 The singleton is valuable when we play in spades. Singletons in the hand with the long trumps limits opponents to one trick in that suit. The ruffing in spades is probably tricks we already had. 5431 // 3523 Singletons in the hand with the short trumps are additional trump tricks, provided there are sufficient trumps. Played in the 5-4 heart fit we are able to ruff clubs with the short hearts. That is potentially seven trump tricks with hearts as trumps. These examples show that singletons do have a variable value depending on how it interacts with other parameters and in the general case that value should be measured in expected tricks. On any particular board attempt to count the actual tricks during the auction.

Bidding is an inexact science. Some hands just don't fix our bidding methods. This time 2♦ works. Can we really cater a system to unlikely 6-5 hands?

With 5+ diamonds, wouldn't pard bid 5♦ himself?

Don't understand this sequence. Why didn't we just pass and defend 2♥?

There will be no proposed detailed complete evaluation system presented here. The theme of this thread is think in terms of tricks for our partnership rather than points in our hand.. These statistical models are for the general case. Often completed by the third bid of the auction. Our expected tricks is X +/- e. All estimates come with errors and this e >=1. There are three phases to the evaluation process. The first phase is the initial point count. The two our tricks models are the second phase. By using the model which consist of HCP, trumps, and skewness/flatness one can improve his starting point for the third phase. The first two phases are for the general case. This third phase is counting the tricks for the actual board. This will require uncovering the effects of addtional parameters. This thread will make no suggestions on how to accomplish this task of counting. Future posts will suggest how to utilize the models for better bidding decisions, often at the part score level.

It's hands like this which demonstrates that advancer should give interventor lots of leeway.

Nice bidding by East and West.

The objective of hand valuation should be to find the best contract for the partnership. It is not to find the most precise valuation of my hand in a vacuum. The initial point count is just a transitory value which will be readjusted with every successive bid in the auction. Power is the independent random variable used to estimate tricks. Point count is a dependent component of power. Example 1. I have an ace, two kings and a jack. My pattern is 1=5=4=3. In work count I have 11 points regardless of the location of the honors. a) ♠2 ♥AK752 ♦KJ82 ♣642 b) ♠K ♥J8752 ♦K852 ♣A42 Many would open hand 'a' 1♥. Few would open hand 'b'. Yet both are 11 point hands. The location of the honors and whether they are working together does affect the ability of a hand to generate tricks. Hand valuation is about how honors interact with one another. Hand valuation is more complex than assigning a fixed value to each honor. Example 2. [hv=pc=n&w=s2hak752dkj82c642&e=s653hqj98daq53c98]266|200[/hv] West has 11 points. East has 9 points. 4♥ should make nearly every time. The joint pattern 1543//3442 fits well. No wasted honors in the short suits. Example 3. [hv=pc=n&w=s2hak752dkj82c642&e=sqj98h64d975caq93]266|200[/hv] West has the same 11. East still has 9 points. 1543//4234 This pair of hands do not fit nicely. If everything goes wrong west may make only 3 or 4 tricks in hearts. It is about power, points, location of those points, and how those points fit together. It is also about joint pattern. Too many systems go to great pains to evaluate individual hands to too many decimal places. It isn't about points. Taking tricks depends on how well those points are working together and how well the patterns of the partnership hands fit. ............. The main theme is this thread is The best method to achieve this objective is to estimate partnership tricks. Finding a more precise initial point count will do little to help us achieve this objective. We need better methods to determine the fit of the partnership, and thus would be better able to estimate the partnership tricks. We must realize that expected tricks may vary radically with every successive bid. E(tricks) = trumps + (HCP-20)/3 + e Std dev is about 1.25 tricks/board. E(tricks) = trumps + (HCP-20)/3 + SF + e For flat hands the std dev can be as low as 1 trick/board. There are four models for expected tricks, one for each suit. Expected tricks fluctuate wildly depending on strain of the final contract. We want to be in the strain which maximizes our expected tricks.

Are ppl still playing 100% game forcing? Haven't many switched to forcing to 3NT or 4 of a suit?

That's a 6 card suit. Notice that I stated with a 5 card suit. Should add that the valuation model utilizes both trumps and HCP. E(tricks) = trumps + (HCP-20)/3 + e And can be improved by considering skewness/flatness E(tricks) = trumps + (HCP-20)/3 + SF + e

PATTERN Pattern is the ordered configuration of the four suits in one hand. Joint pattern is the joint pattern of the two partnership hands. Trumps is usually the suit with the longest combined length. Larry Cohen has chosen trumps as his parameter from estimating tricks. SST(short suit totals) is the sum of the two shortest suit holdings of the partnership. Lawrence/Wirgren uses the shorter suit holding of each partner. Cohen and Lawrence/Wirgren are just using a different end of the same variable(pattern) to estimate tricks. Trumps is the coarse estimate. SST is the fine tuning. Using both gives us better estimates than either on a stand alone basis. Now for a naive test of joint pattern. Each side will be given 20 points with all points in two suits. [hv=pc=n&s=sakt76h42daqtc642&w=s42hakt76d642caqt&n=sqj98h53dkj98c753&e=s53hqj98d753ckj98]399|300[/hv] This example has 18 trumps and only 16 tricks. [hv=pc=n&s=sakt76h2daqtc7642&w=s42hakt76d642caqt&n=sqj98h543dkj98c53&e=s53hqj98d753ckj98]399|300[/hv] Do not assume that when we hold flat patterns, opponents will also hold flat patterns. In this example EW is 2434//2533, while NS is 4342//5134. EW makes 8 tricks in hearts. NS makes 10 tricks in spades. 18 trumps producing to 18 tricks. This is compensating errors. LoTT is credited for being 'right' when it is 'right' for the 'wrong' reasons. [hv=pc=n&s=sakt76h2d853caqt9&w=s42hakt76daqtc642&n=sqj98h543d7642ckj&e=s53hqj98dkj9c8753]399|300[/hv] In this example the points between the diamonds and clubs have been exchanged. EW is 2434//2533, while NS remains 4342//5134. EW makes 8 tricks in hearts. NS makes 9 tricks in spades. 18 trumps producing to 17 tricks. [hv=pc=n&w=s42hakt76d642caqt&e=s53hqj98d753ckj98]266|200[/hv] On all three examples EW held 9 hearts and made only 8 tricks. So maybe the expected tricks are usually only dependent on our power and pattern. Their pattern and trump length has little effect on our tricks. There are exceptions where their pattern reduces out tricks. Usually a singleton to an ace, followed by a ruff. It is rare. We should just ignore their hands and use only ours to estimate tricks. E(tricks) = trumps + (HCP-20)/3 + SF + e ----------------- Aside: this model applies mostly to when we expect to win 7 to 10 tricks. Very useful for making contested part score auctions. At higher levels controls play a larger role. Examined hand records from BBO minis, most part score boards had a std dev between 0.5 to 1 when played in the same strain. Admittedly the range of playing abilities on these minis was huge. Even in flight A events it was rare to see the std dev fall under 0.5. Could not find any evidence knowing their trump length assisted us in better competitive decisions. Knowing their joint distribution would have been useful.