## Questions and Answers

## Question 1

I am curious to know what probability distributions were used in the computer programs that generated the sample hands used in your analysis. Computers typically use pseudo-random sequences designed to generate random numbers that conform to a uniform probability distribution, and my assumption is that the hand generation programs use these generators to create sample deals. Does this mimic the real-world setting where cards are shuffled by people, especially in matchpoint events where the decks of cards are assembled from boards where the hands are typically not organized in a truly random fashion? It occurs to me that this could skew the statistics, although I have no idea whether this has any chance of being significant.

Robbie Robertson

Arvada, CO

**Answer**

In our analysis we have used mostly deals generated by computer programs. The mathematicians say you have to shuffle a deck six or seven times; otherwise, you will get more balanced distributions than the probabilities say you should. Most people don't. So if you shuffle manually, the resulting deals will often differ from deals generated by computer programs. We haven't taken that into account in our work, simply because it is difficult to add that factor to the equation.

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