Using contract bridge dealing for example, we have a number of ways possible to compile bridge dealing results. Which of these ways are meaningful in determining the fairness of bridge deals? In the same vein, which allow statistical evaluation
generalizing to valid hypothetical bridge deal populations?

Bridge players traditionally are most concerned with suit distributions (hand shapes), and more or less equally, high card points (HCP) in each hand they are dealt.

In my experience, hand shapes are most commonly compiled. They usually take the form of how many of each specific hand shapes occurred in some specified number of deals for at least the most commonly expected shapes.

HCP compiling is typically by percentage in each hand direction at the bridge table.

Currently there is no standard bridge dealing data compiling. What data is compiled to date has little, to no, usefulness in determining bridge dealing fairness, and statistical generalizing; for players, officials, and interested observers all.

The major obstacle to acceptedly valid descriptive and analytic bridge dealing statistics up to now is the easily noted fact that each hand in each deal is wholly dependent on what the other three hands contain.

I agree that is true for all conditions - except one. If we can reduce our variables of interest to binary (50/50) form, classical probability theory dependency no longer holds sway.

Bridge Analyser has the most extensive statistics report of any bridge application I have seen to date. It has 14 data columns from all four bridge hand directions.

Here is the first data column in Bridge Analyser’s help file subject “Print Deal Statistics.”

Pts.
South 365
West 336
North 385
East 354

Total 1440

Does anyone see how you make these four variables binary? Do not feel bad if you don’t. I didn’t see it for at least the past twenty years.

If we add South’s 365 to West’s 336, the resulting 701 is a binary variable. How is that, you say? It is because it has exactly 1/2 the expected probability (EP) of the 1440 total hands dealt.

If we add South’s 365 to North’s 385, the resulting 750 is another binary variable with the same 1/2 EP.

If we further add South’s 365 to East’s 354, the resulting 719 is another binary variable with the same 1/2 EP.

Some will think we have to add West and North, West and East, and North and East also. Because four items taken two at a time usually equals six. Well, I tried that, and all I get is mirror image p-values for these last three. This is an unexpected (but
welcome) effect from using binary variables.

When I transpose my resulting three p-values into three z-values, and take the mean value of these, I finish with 0.18. This is my bias estimate of this relatively negligible sampling of 36 bridge deals. This is merely an illustrative example, and my 0.
18 is too little data to usefully generalize from.

It is entirely possible you will get a different result for the above dealing data. There are at least seven different generally accepted ways to statistically evaluate to our p-values, resulting in at least four different unique numeric amounts!!!

Side editorial: What a mess.

We need at least one other 36 deal data column result in order to begin measuring the distribution of Bridge Analyser’s Pts. From that minimum of at least two equal statistical treatment measurements, we can begin generalizing to a specific
hypothetical bridge dealing population estimate for Bridge Analyser’s Pts.

Douglas

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