starting hand probability
Join Date: Mar 2009
Posts: 69
Is there anything wrong with my math here?
in holdem # of hands to expect to get AA pre flop 1 time
1 / ( (4*3) / (52*51) ) = 221
in 2-7 # of hands to expect to be dealt 23457 (without making a flush)
1 / ( (4*4*4*4*4-4) / (52*51*50*49*48) ) = 305760
Join Date: Aug 2008
Posts: 7,905
Math is right on the first one, but I think the better general solution is to use combination form instead.
C(52,2) / C(4,2) = 221
That's the same as what you wrote, but more flexible for other problem types and a lot easier for some types. It also becomes much more intuitive logically with a bit of practice.
You second one is wrong, as it specifies they be in order. It would be easier solved with combinations and avoid that pitfall. Using your method, you don't have 4 possible first cards, you have 20. Then 16 possible second cards, etc. The final chance is much more common than what you have.
Last edited by spadebidder; 11-05-2010 at 11:31 PM.
Join Date: Sep 2003
Posts: 3,208
The probability for any specific five cards of different ranks that don't make a flush is (45-4)/C(52,5) = 1/2548.
Join Date: Mar 2009
Posts: 69
thanks a lot for your replies, i understand why my 2-7 calc is wrong, I calculated 1/2538 by making the adjustment. I was a bit suspicious with the probablility I found of 1/300k. Time for me to study up on some combinatorics.
Last edited by unusual storage; 11-06-2010 at 04:32 AM.
