is my pokerstove broken? (faulty %s)

[b33nz]

so i was playing around with pokerstove and it seems either pokerstove is way off or i am missing something.

i type into ps what the equity of this hand is:

Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img]
vs
a range of: A[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/heart.gif[/img], and A[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/heart.gif[/img] (all AA's without a spade)

on a T[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/spade.gif[/img] 4[img]/images/graemlins/heart.gif[/img] board.

pokerstove tells me:
Board: Tc 9s 4h
Dead:

equity win tie pots won pots tied
Hand 0: 36.869% 36.87% 00.00% 1095 0.00 { QsJs }
Hand 1: 63.131% 63.13% 00.00% 1875 0.00 { AcAd, AcAh, AdAh }


seeing those %s got me a little curious. so i did my own math and i came up with this:

since QJ has 8 outs for a straight + 1.5 outs for a backdoor flush my equity from the flop to the turn should be: 9.5/45 = 21.11%. my equity from the turn to the river should be: 9.5/44 = 21.59%. add those two up: 21.11 + 21.59 = 42.7%.

as you can see, ps only says that my equity is 36.87%. thats a 5.83% difference! thats huge! could someone tell me why this is? maybe my math is wrong but to be off by 5.83% is something that concerns me.

[jay_shark]

Have you heard of the 4x rule ?

Just take the number of outs multiplied by 4 .

9.5*4= 38%

Also , you cannot simply add the two probabilities since the two events are not mutually exclusive .In other words , you may hit some outs on BOTH the turn and river and so you will be overstating your probability if you simply add them .

P(AuB) =P(A) +P(B) -P(AB) .

ie , take a standard flush draw . You have 9 outs and so the probability should be 9/47+9/47 - 9c2/47c2 = 34.967 % .

Here is another way :

You may hit on the turn with probability 9/47 . Or you may miss the turn and hit on the river with probability 38/47*9/46 . These two events are mutually exclusive so we can simply add them to give us 34.967% .

[LearnedfromTV]

don't forget that a Q or J turn adds 5 river outs.

[Abbaddabba]

You're wrong for a few reasons, both which would skew the % in different directions.

You do the probability in terms of 1 minus the sum of the probability of not improving on both streets.. Otherwise you double count for the times that you hit your draw on both the turn and river.


You also didnt account for the possibility of making two pair or three of a kind.


You also are dividing by the wrong number. It is not x/45. It is x/41, since you already know that the aces are not in the deck and none are the cards that you need to improve your hand.