Logic correct here? (Math post)

[AlwaysWrong]

This is a hypothetical example.

I have Q [img]/images/graemlins/club.gif[/img]7 [img]/images/graemlins/spade.gif[/img]5 [img]/images/graemlins/diamond.gif[/img]3 [img]/images/graemlins/diamond.gif[/img]

My opponent has A [img]/images/graemlins/spade.gif[/img]A [img]/images/graemlins/club.gif[/img]2 [img]/images/graemlins/spade.gif[/img]J [img]/images/graemlins/diamond.gif[/img]

I open on the button, opponent re-raises pot. I call. We both have exactly 1 pot-sized bet left. My opponent will open-push 100% of the time.

On the flop I need 33% equity to call. propokertools says this happens about 56% of the time.

So what is my average equity when I call? I'm not sure how to figure this out, but just eyeballing the graph it looks like I will average less than 67% and more than 55%, so call it 62% (I could be out to lunch).

So 44% of the time I fold and lose 1 unit. 56% of the time I call and have 62% equity, for a profit of 0.86 units. That means overall on the hand I stand to profit 0.04 units (a unit = the size of the pot on the flop). So AAxx is a net loser in this proposition.

I really just shot in the dark with all these numbers. I'd like to see how someone who knows what they're doing goes about it.

[Troll_Inc]

http://forumserver.twoplustwo.com/sh...age=0&vc=1

[Silent A]

Assuming your numbers are right ...

I'm first going to call 1 unit the size of your pre-flop call. So now the pot is 3 units and you have 3 units behind. All the calculations I will show are in reference to this call.

44% of the time you fold the flop and lose 1 unit.

56% of the time you call. The total pot = 9 units and you've put 4 units in the pot since your pre-flop call. You win 62% of these hands and profit 9 - 4 = 5 units. The other 38% of the time you lose 4 units.

Total EV = (0.44)(-1) + (0.56)(0.62)(+5) + (0.56)(0.38)(-4) = +0.4448 units.

BTW, I think your equity when you can call is closer to 56%. This lowers your EV to +0.1424.

Finally, your numbers are only this high because you "know" his exact hand. Against random aces you can only call 50% of the flops and, when you do call, you'll have 55% equity. Now your EV = -0.005.

Note that you can't get enough profit to compensate for the cost of your initial raise (approx 0.5 units) even if you knew his exact hand and played perfectly.