Back door etc

2 q's


1 What is the probability of flopping a straight w/ JT or an open ender?


2. What is the probability of a backdoor stright if Q-7-2 or 9-2-3 flops to that same hand? I tried to calculate it but my answer didn't seem right as it just about equalled the prob of a backdoor flush.


Thanx


Joe

P(flopping a straight if you hold JT)=


P( AKQ)+ P(KQ9) +P( Q98) +P(987)=


4(64)/ 50C3


P(making a straight if you hold JT and the board is Q-7-2)=


P(AK) +P(K9) +P(98)


= 3(16)/47C2


Note P(back door flush)= 10C2/47C2= 45/47C2 so it should be close.


Ill do openended later (its more of a hassle).

what is C?


I hope this isn't a retarded question.


Joe

like... 50 choose 3...


number of ways to choose 3 things from 50.


formula is something like n!/k!(n-k)!... I believe... it's been a long time since I did any math and didn't just look up an answer.


k is the number you are choosing, 3 in this case, and n is the total number... 50 in this case.


~D

Right, or combinations.

C(50,3) = 50!/[(47!)(3!)] = 50*49*48/3! That is, there are 50 ways to choose the first, 49 ways to choose the 2nd, and 48 ways to choose the 3rd, then we divide by 3! = 6 since there are 3! ways to get the same 3 in a different order. If we didn't divide by 3! we would have

P(50,3) or "permutations of 50 things taken 3 at a time".

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.