[1eyedjack]

We know that on a given hand the double-dummy result is not necessarily the best single-dummy result.
Consequently, it is dangerous (on a given hand) to rely on a comparison of the actual result against the DD result as being a guide to how well the hand was managed.
It is also fairly obvious (to me) that over the long term, both opposing sides will benefit or lose out to the same extent from such discrepancies.
I should expect, therefore that if you calculate your average IMP per board against the double dummy result it will give a fair approximation to how well you have played, and, furthermore, the larger the hand population over which the average is calculated, so the closer will be the approximation to the true measure.

What interests me (and is beyond my capability) is to arrive at an approximate function that shows how that discrepancy varies with the population size.

Any takers?

[hotShot]

First of all you should be aware (and I'm sure you are) that the deviation, gets generally smaller, the higher the contract is.
This is caused by the fact that the opening lead will be better, the more information is available at the time of the lead.
Since the DD-Solver has perfect information and the human player does not know much (e.g. 1NT p p p).


The function you are looking for does not only depend on the population size. A key factor is the question you want to answer.
If you want do generate informations about something equally likely, than a small sample will be enough.
If you want to analyze 2 possible lines of play and one has 68% and the other has 70%, you will need big sample size to be sure that there is a significant difference between the 2.

[helene_t]

If the SD for TOTPOINTS_TO_IMPS(DDresult-actualresult) for a single board is s then for the average IMPs across n boards it is s/sqrt(n).

As hotshot explains, s is not the same for each board, but the formula still holds. However, the s you should use is sqrt(E(s^2)), i.e. the squareroot of the average variance (variance = squared standard deviation)*.

*Assuming the mean difference of the two is independent of the variance. If you play against a weaker team then the mean of TOTPOINTS_TO_IMPS(DDresult-actualresult) will be positive but it could be that you are more likely to have a flat board against them when the actual result at your table is likely to be the same as the DD.

[FrancesHinden]

 1eyedjack, on 2011-July-02, 06:34, said:

I should expect, therefore that if you calculate your average IMP per board against the double dummy result it will give a fair approximation to how well you have played..

All other debates apart, I would correct that to "a fair approximation of how much better you have played than your opponents"

[nigel_k]

I don't necessarily think this is a terrible idea but you need to be aware that for high level contracts, you will need to overbid to maximize your score in comparison to the double dummy result.

For example, suppose there is a slam that needs a two way guess for a queen and another suit not to break 4-0 (90%). Single dummy this is a 45% slam and double dummy it is a 90% slam. Let's say you are non-vulnerable. If you stay out of the slam, your expectation against the double dummy result is -8.8 IMPS. If you bid the slam your expectation is -7.4 IMPS.

Or you could just not use the double dummy comparison for slam hands. Instead work out the chance of making and award yourself zero if the slam is 50% or better and otherwise your expected IMP loss assuming they stay out at the other table.

[inquiry]

You may want to consider the study by Peter Cheung's 2002 study using bridge hands from OKbridge (using bridgebrowser) and actual results at the table and compared to double dummy analysis.


This was his summary

"The most important general finding is that double dummy analysis is very accurate as compared to actual play from OKBridge. The overall total number of tricks taken by the declarer is 9.21 (9.22 for imp and 9.20 for mp). The double dummy analysis of the same deal produce 9.11 (9.12 for imp and 9.11 for mp). So actual play by OKBridge player takes 0.1 tricks more then the double dummy analysis result. This is from 383,000 deals and over 25 million plays."

See Peter Cheung's website for more delatils (click here)

[jogs]

 inquiry, on 2011-July-03, 17:22, said:

You may want to consider the study by Peter Cheung's 2002 study using bridge hands from OKbridge (using bridgebrowser) and actual results at the table and compared to double dummy analysis.


This was his summary

"The most important general finding is that double dummy analysis is very accurate as compared to actual play from OKBridge. The overall total number of tricks taken by the declarer is 9.21 (9.22 for imp and 9.20 for mp). The double dummy analysis of the same deal produce 9.11 (9.12 for imp and 9.11 for mp). So actual play by OKBridge player takes 0.1 tricks more then the double dummy analysis result. This is from 383,000 deals and over 25 million plays."

See Peter Cheung's website for more delatils (click here)

http://crystalwebsit...ouble_dummy.htm

Cheung didn't show a valid proof of that conclusion. Those means only show that the error biases balance out. He needs to show that the errors of the estimates are small and the variances or the errors are small.

[1eyedjack]

 nigel_k, on 2011-July-03, 15:08, said:

I don't necessarily think this is a terrible idea but you need to be aware that for high level contracts, you will need to overbid to maximize your score in comparison to the double dummy result.

For example, suppose there is a slam that needs a two way guess for a queen and another suit not to break 4-0 (90%). Single dummy this is a 45% slam and double dummy it is a 90% slam. Let's say you are non-vulnerable. If you stay out of the slam, your expectation against the double dummy result is -8.8 IMPS. If you bid the slam your expectation is -7.4 IMPS.

Or you could just not use the double dummy comparison for slam hands. Instead work out the chance of making and award yourself zero if the slam is 50% or better and otherwise your expected IMP loss assuming they stay out at the other table.

Instinctively, on balance I think you are right. But it is not all one-way traffic. You don't always have a 2-way finesse in a slam, and DD they will always find the killing lead if there is one to be found.

[helene_t]

 jogs, on 2011-July-03, 21:40, said:

http://crystalwebsit...ouble_dummy.htm

Cheung didn't show a valid proof of that conclusion. Those means only show that the error biases balance out. He needs to show that the errors of the estimates are small and the variances or the errors are small.

I think that an interesting hypothesis to test would be if the mean result for each board is generally close the DD result. And if not, if there are particular subsets of the deals on which the declarer has an advantage relative to DD.

[hotShot]

Has anybody read this?

http://ieeexplore.ie...rnumber=4749256

[jogs]

Cheung said in 2002.

Quote

It is likely within the next 3-5 years such a bidding system used by a computer program will be able to beat the best player in the world.

That hasn't happened. It's unlikely any bidding system by computers would be that successful until someone is willing to spend as much money on bridge as IBM has spent studying chess.

[Wackojack]

As Frances said your comparison with the double dummy result reflects your ability compared with that of your opponents. Although I don't think it gets near to answering your question and I am not sure what your question really was; FWIIW I kept a record of playing a forcing pass system on BBO. The fact that we were up in imps was probably our opps not having the luxury of working out how to defend against it.
Imps as Imps as
The forcing pass record to 30 March 2010
376 Hands played 376
Imps per hand against field 0.33
As Declarer 0.41
As defender 0.23
Imps per hand against Par 0.42

The gains against par were mainly phantom sacs by opps and better sacs by us.

[jogs]

 helene_t, on 2011-July-04, 02:28, said:

I think that an interesting hypothesis to test would be if the mean result for each board is generally close the DD result. And if not, if there are particular subsets of the deals on which the declarer has an advantage relative to DD.

Have only seen a study on 1NT when both sides have 20 HCP. DD Declarer made less than 6.2 tricks. Author didn't publish that declarer made in actual play. But suspect declarer's mean tricks would be between 6.8 to 7. In this contract defense has a huge opening lead advantage DD.