Can we trust the statistical analysis in the Bridge?

The ability to analyze the game of a hand in Bridge has made outstanding progress, especially with regard to infallibility and speed, using powerful information technology.

For several years there have been programs able to calculate almost instantly, in every deal, the number of tricks available "a priori" for both lines in all contracts.

Someone thought to use these tools to provide answers to both the bidding questions and the problems of card games through statistical analysis.

We see in a nutshell, for those who were unaware of it, what the main instrument of this analysis consists of statistical simulation. Initially, a "large" sample of random hands is generated by an "ad hoc" program on the basis of specific characteristics provided carefully by the operator with reference to the particular problem examined; in general, one hand is kept fixed and the others change randomly, but compatibly with what each has shown the bidding. Subsequently the exact number of tricks obtained in each hand in a given contract and not only, is calculated in very reasonable times. Furthermore, using the same sample, the same operation can be repeated, both at the same time and at different times to probe for the maintenance of other contracts. From the comparison and from the intersections of the obtained results a series of important indications can be obtained.

It should be noted that this method it is, and has been, applied for identifying the best opening lead.

At first glance, one has the feeling of having come into possession of a tool capable of resolving if not all, but many problems.

However, with a more careful evaluation, this method presents a serious defect: the results obtained do not refer to what occurs in the reality of the gaming table, but in an ideal game, where each player has behaved to its maximum possible by playing with full possession of all the playing techniques and cards viewed: that is, double dummy.

Do we therefore have to give up this fascinating but maybe fake method?

To solve this problem, it is necessary to answer the following question: what is the difference between the "double dummy" game and the "real" game?For this we must turn again to the statistic that on a sample of hands is able to follow the trend of a relative number that expresses the difference between the tricks obtained at the table by a given declarer and those obtained with double dummy, under varying conditions. The number in question called Declarer's Advantage, which expresses the advantage (+) or disadvantage (-) of the declarer compared to the defenders.Recently in the article "Statistical analysis of DA" by Ian Casselton has been well identified from more convergent research. I will try to make an extreme synthesis of the most important results common to all the participants in this statistical survey.

In general the DA is moderately positive and is larger in the contracts at SA and at lower levels; in fact, in the 1SA contracts, the maximum DA is reached (approximately +0.37), while the level decreases and becomes even negative for the slams ( approximately -0.1). Another interesting fact is that the DA favorable to the declarer is almost entirely due to the opening lead.

From this reasoning comes the remarkable statement: any kind of investigation carried out on bridge hands using double-dummy analysis is sufficiently accurate and the results obtained can be applied to the real game. To be more rigorous, however, an adjustment of about -0.1 should be made for slam contracts and +0.15 taken for contracts at level 2 and level 3.

So let's safely use statistical simulations and accept their answers as good.