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#1
03-09-2006, 03:34 PM
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Studugi question
What percentage of seven-card hands contain a badugi? I've written a sim to montecarlo an answer, but wonder if anyone has calculated this, or can think of an elegant way to do so.
Whenever I try to enumerate hands that do, or do not, contain a bugugi, it seems I'm a few bricks short of a load. Side questions: can anyone think of seven-card hands that contain N badugis, 0<N<4? N>8? 
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#3
03-09-2006, 04:24 PM
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Re: Studugi question
Ok, I figured out what a badugi is. There are C(52,7) possible 7 card hands. For a hand NOT to contain a badugi, it would have to contain only 3 or fewer suits. So, if we exclude one suit (13 cards) that leaves us with C(39,7) hands which are 3-suited or less. So the percentage of hands which DO contain a badugi would be 1-[C(39,7)/C(52,7)]=88.5%. Doest that sound right?
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#4
03-09-2006, 07:32 PM
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Re: Studugi question
It could contain all four suits, yet not contain a badugi if two or more suits were represented by a single card, and those single cards were of the same rank. But I like your approach, it's exceptions and redundicies might be easier to quantify than any of the ways I was trying.
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#5
03-09-2006, 08:49 PM
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Re: Studugi question
There are four of these groups of 39 cards--one for each suit that we omit. So we have to multiply that figure by four. But then we have double and treble counting, because the group consisting of spades, hearts & diamonds may produce a hand consisting of the seven lowest hearts, as might the groups that omit spades and diamonds.
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