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Old 08-30-2007, 03:46 PM
jay_shark jay_shark is offline
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Join Date: Sep 2006
Posts: 2,277
Default Re: HU SNG All in every hand

I've solved this problem a long time ago but the calculations can get tedious . The best way to work this problem is to work backwards .

I'll give you an example .

Lets play a simplified version of this game where you and your opponent have 3 BB's .

If your opponent is on the button and pushes with any two cards , then you're getting 4:2 odds which means you need to win at least 33% of the time to show a profit . This means you should call with any two cards except 3-2 o . So you should call with 1213 hands out of 1225 .

EV=1213/1225 [4*0.5016 - 2*0.4984] = 0.9997

Now say each player has 3.5BB's and you're in the sb. You would prefer to call with all hands that gives you an EV > 0.9997 . Since you're getting pot odds of 4:3 , you need 4x-3(1-x) >=0.9997
Solve for x>=0.5713 . Now use pokerstove to find all such hands with an equity versus a random hand greater than 57.13% .This range is about 24.7 % of all hands with an equity of 62.7%.

EV(3.5) = 0.247*[4*0.627 - 3*0.373] + Ev(3)
Ev(3.5) = 0.343 + Ev(3)
Ev(3.5) =~ 1.3427

Now all you have to do is continue until you reach Ev(75) [img]/images/graemlins/smile.gif[/img] which should give you your exact EV for this game assuming that you're playing optimally .
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