P(openend w/a paired board)=


P(KKQ) +P(QQK) +P( QQ 9) + P99Q) +P(998) +P(889) =48(3)/50C3


P(openended w/o a paired board)=

P(KQ X (Xnot K, Q, A or 9)+ P(Q9X) +(P98X)


=16(34) + 16(34) +16(34)/50C3= 48(34)/50C3


Finally we can also compute the probability of a double gutter ball.


P(K97) +P(AQ8) =2(64)/50C3.


SO P(openended or double gutter)=48(3) +37(48)+ 2(64) / 50C3= about 10%


and also P(straight or openended)= 48(40)+2(64)+ 6(64)/ 50C3=


2304/ 19600=about 12%.


Oh yeah pCk is the number of ways to pick k objects out of p of them. (Ex 50C3 is the number of flops if you hold 2 particular cards, so the number of flops is (50 49 48)/ 3!).


Also P(A) means the probability of event A happening.