Math/Calling Range Question

(Assume NLHE cash game with 1/2 blind structure)

40 bb stacks not including blinds, SB open pushes top 50% of hands, find a calling range for BB that makes this a -EV push please.

Edit: I obv have no idea wtf im talking about (see chat transcripts)

Originally Posted by bigspenda73

-EV for you would be calling with more than 50% of your hands, here's pokerstoves top 45% of hands:

44+,A2s+,K2s+,Q4s+,J6s+,T6s+,96s+,86s+,76s,A2o+,K6 o+,Q8o+,J8o+,T8o+,98o

However, I think you would only want to be calling here with the top 25% of your hands, therefore:
66+,A2s+,K6s+,Q8s+,J8s+,T8s+,A7o+,K9o+,QTo+,JTo

That's nice, but give me the range and calculation to show that the range you gave makes my SB push -EV.

Figured I'd post this. We talked about it in the FTR Chat and I explained to him why the 25% range is -EV. Any other takers?

Originally Posted by spoonitnow

Figured I'd post this. We talked about it in the FTR Chat and I explained to him why the 25% range is -EV (for the BB, making it +EV for the SB). Any other takers?

Edit: Here's the transcript from chat
11:04:21 pm : spoonitnow : (.437)(.25)(41.5)
11:04:45 pm : spoonitnow : 25% of the time BB calls, 43.7% of the time we win, and we
win a 41.5 bet profit
11:05:03 pm : spoonitnow : EV of BB folding = (.75)(1.5)
11:05:17 pm : spoonitnow : EV of BB calling and we lose
11:05:34 pm : spoonitnow : (.25)(.563)(-40)
11:05:55 pm : spoonitnow : sooooo with our handy dandy calculator
11:06:10 pm : spoonitnow : EV with BB folding = 1.125
11:06:38 pm : spoonitnow : EV of SB winning SD = 4.53
12:25 am: 11:06:57 pm : spoonitnow : EV of SB losing SD = -5.63
11:07:18 pm : spoonitnow : Total EV = +0.025 bb

math is for ugly ppl, u should know that spoon<3

Originally Posted by ville18

math is for ugly ppl, u should know that spoon<3

Spoon must be fucking hideous

Y'all motherfuckers need Jesus or 2+2 or something

Originally Posted by spoonitnow

Y'all motherfuckers need Jesus or 2+2 or something

That's from S.W.A.T

oh wait, this isn't the movie quotes thread

Originally Posted by spoonitnow

(Assume NLHE cash game with 1/2 blind structure)

40 bb stacks not including blinds, SB open pushes top 50% of hands, find a calling range for BB that makes this a -EV push please.

Just to clarify. Do you mean 1/2 blinds with 80 chips in stacks or 1/2 blinds with 40 chips?

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.

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

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

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

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.