### Boredom Takes Hold

OK, so it isn't really boredom so much as curiosity mixed with something that's been nagging me for a couple of years, but it is still a little sick. I play bridge (no, an AARP card is not required), and while it is easy enough to go out and find some information on the frequency of certain combinations of cards and such, it's tough to find it all collected in one place. So I decided to collect it.

First off, while I enjoy playing with numbers, so long as the formulae don't get too crazy, I was not quite certain how I would derive everything I needed, so I poked about until I found confirmation of the base formula I needed. I wanted to know how many hands, using Charles Goren's point count system (4 per ace, 3 per king, 2 per queen, and 1 per jack), how many 13-card hands would have each High Card Point (HCP) total from 0 to 37.

I basically made a 4-digit base-5 number that represented every combination of the zero to four of each card rank, ace down to jack. I had my spreadsheet total the number of cards in each combination and eliminated all that had more than 13. Then I had it calculate the HCP for each combination and sorted based on that number. Another column calculated the number of 13-card combinations for each such arrangements, and then I totaled up each group that represented a given HCP figure. It makes a pretty chart.

Then I went crazy and did the same thing for suit distribution (number of cards in each suit) so that I could see which combinations were most common (though I had seen the numbers for the top five before). The chart for that is a little wilder, which for someone as damaged as I can be quite cool.

Oh, brother. I need serious help. On the other hand, if you happen to want the data, just let me know where to send it.

## 1 Comments:

Hi Andrew,

Would it be possible for you to send me your data? I'm personally interested in what percentage of 13 card hands have between 11 and 14 points inclusive, but it would be good to see all your data. My email is gib_alpha@yahoo.co.uk

Thanks in advance,

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