Wow thats actually pretty close.

Ive done some maths on it but I havnt quite finished yet. The best way to answer it would be to get a computer to plot it graphically. Heres what I have so far for the equation that the computer should solve. If any of you guys want to plug or program for a solution then go ahead. I have to go out soon though so I have no time.

Anyway.


Ive assumed blinds of 0.5 and 1. BB means Big blind. If this isnt quite what you ment it should be fairly easy to modify it.

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SB Pushes for 40BB

BB either calls and wins, calls and loses or folds.

Possibilities from SB perspective are:

BB calls, SB wins. +41.5 probability = A
BB calls, SB loses. -40 probability = B
BB folds. +1.5 probability = C

EV is 41.5A - 40B + 1.5C

with A + B + C =1 (since BB must either call or fold)

C = 1-A-B

so

EV = 41.5A - 40B +1.5(1-A-B) [sub in for C]

= 40A - 41.5B + 1.5

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At this point I decided it would be more useful to put the equation in terms of the BBs calling range (R) and the Equity (E) we have when called by that range.

===========================

R = A + B => B =R - A

EV = 40A - 41.5(R - A) + 1.5

=40A - 41.5R + 41.5A +1.5

=81.5A - 41.5R + 1.5

A is the chance of being called AND winning so :

A = RE

where E is our equity against BBs range.

EV = 81.5RE - 41.5R + 1.5

======================

This is where I get stuck. There is obviously a relation between R and E but I have no idea what it is. My plan for when im really bored later is to plug some numbers into pokerstove and see where it takes me.

Ideally id be good at Excel and get it to make a graph with R and E as the axis, and colour code EV as RED = -EV, GREEN = +EV, BLACK = 0EV.

If anyone here is good at programming that shouldnt take too long. The other alternative is to plug numbers into pokerstove and see what happens. I tried a BB calling range of 25% and that came up pretty much neutral which suprised me. Someone take this off my hands plskthx.