Re: Hold Em hand types
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Wow, thats some calculation! Glad I didn't attempt it manually
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Actually, there is a lot of value in trying to estimate these manually. I couldn't think of a good estimate in the few minutes it took to type and debug the recursion, but I think there is a method.
One possibility is to estimate the amount of time it takes before all of the suited hands have been seen. As the second calculation indicates, that coincides with the time the last hand is seen over 97% of the time; if one could predict that ahead of time, you might guess that the two averages will be close, and you can estimate the average amoutn of time before every suited hand is seen relatively easily, as it is a 1-dimensional recursion and similar to the standard coupon-collecting problem.
The expected amount of time before you see all suited hands is
1326/(4*78) + 1326/(4*77) + ... + 1326/(4*1)
=
1326/4 (1/1 + 1/2 + 1/3 + ... + 1/78)
=
1637.7164...
~ 1326/4 (Euler-Mascheroni constant .5772157... + ln(78))
=
1635.5960...
These are not too far off of the exact answer I computed.
1643.1229...
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