Expressing one variable as a function of another is unfortunately not possible. When I started writing StoxEV I intended to include this functionality but I never got around to it.
I think the best way to look at this is by using a graph with 2 variables.
I've made a tree for this hand with the following assumptions:
- Villain cold calls preflop with his top #1% of hands. However, I've discounted AA-KK and AK. He'll only cold call with these 30% of the time.
- Villain will definitely bet the flop and turn with top pair or better or a flushdraw, no matter what turncard comes off.
- Added to that he will also bluff some unknown portion of the time. I've assigned variable #2 to this. Villain will stack with his bluffs regardless of the turncard.
- If villan has missed and decides not to bluff, he wil give up on the turn unless he can beat top pair.
- If the turn comes an A you will give up the hand.
You can mail me at
stoxpoker_ev@hotmail.com for the file if you want it.
The key decisions are at the flop and you make two of them:
Decision 1: Check with the intention of calling off
Decision 2: Villain indeed bets and you decide to stack.
Decision 1:
Given these assumptions I've made a 2 variable graph. Variable 1 is villain's preflop range (with AA-KK,AK discounted), variable 2 is his bluff %. The numbers are your EV for your flop line:
The numbers are slightly jumpy because they were made with the Monte Carlo engine, but this doesn't have much of an effect on the analysis.
The numbers are expressed as a function of the prize pool, asuming a 50,30,20 prize structure.
As you can see, already at a preflop range of 6% (88+,AQo+,AJs+,KQs,QJs) the line is +EV, even if villain never blufs. This is because with this range villain will only hit the flop 29% of the time and otherwise give up (if he doesn't give up with AQ,AJs,99-QQ and blufs all in it's even more +EV).
Decision 2:
Same graph, only now for the decision to stack off after villain bets.
Ok, a slightly worse picture. The decision to stack off is only +EV if villain bluffs his misses 30% or more, almost regardless of his preflop tightness.
Given the fact that villain's range is probably looser than 6% (which is the point where you require him to bluf 30% of the time) the first decision will not be affected by this and checking with the intention of stacking should be ok,
provided of course that you expect villain to bluff more than 30% with his misses. Otherwise you need to give up. It's this bluff% that's the key in making the decision.
Last edited by scylla; 12-17-2008 at 05:17 PM.