This push plus or minus EV

[jenson]

Hi All,

I am interested in calculating the EV for this. I posted this to the 1 table tourney forum earlier. I received some helpful comments but alas I still can't figure out how to do it. Any help is appreciated.

1 table live home game SNG tourney
Buy In $30

Blinds T150 / T300

Stack sizes (before posting blinds)
BB 1100
SB 2000
Button 2500

I'm in the BB with 56 offsuit

Folded to the Button who calls
SB completes

Pot Size now T900

I raise All In from the BB for an additional T800

Let's assume the following:

1. Button calls BB with top 50% of hands
2. SB completes with any two

1. Button calls All In with top 25% of hands
2. SB call All In with top 25% of hands

[LetYouDown]

Poker Stove (http://www.pokerstove.com)

[pzhon]

This question is underspecified.

To compare pushing with checking, you need to make some assumptions about the postflop play. If you push and are called in two places, will the players check it down? If you check, what will happen postflop?

Also, you said that the SB would call with the top 25%. Is that only if the button folds, or does the SB not care? I'll assume the SB doesn't care.

I'll use folding as a baseline.

If you push, about 3/8 of the time, you pick up the pot, gaining 900.

About 1/2 of the time, 1 player calls. You have put an extra 800 into a pot of 2500, and you expect to get back about 33.4%, according to PokerStove, 835, for a gain of 35.

About 1/8 of the time, both players call, and I'll assume they check it down. You have put an extra 800 into a pot of 3300, and you expect to get back about 24.7%, 815, for a gain of 15.

The average is a gain of about 357 chips compared with folding. If you check, you have a weak hand and a positional disadvantage, so you shouldn't expect to get 1/3 of the pot, 300. Pushing should average more chips

[jenson]

thanks very much.

Can you please provide the math / formulas behind your results. It is much appreciated.

[jenson]

Hi,

Thank you for your effort. /images/graemlins/smile.gif

I will try to be more specific:
1. Let's assume that the SB will only call my All In with top 25% and that he doesn't care what the button does.

2. Let's assume that if I push and am called in both places, both players end up seeing the showdown.

3. If I check, well I'm not quite sure. What makes sense here?

Can you assist me in understanding the methodoloy you used? This will help me to perform these calculations myself in the future.

Regards,
jenson

“Give a man a fish; you have fed him for today. Teach a man to fish; and you have fed him for a lifetime”—Author unknown

[pzhon]

[ QUOTE ]
Can you assist me in understanding the methodoloy you used?

[/ QUOTE ]
I'm not sure what methodology you mean.

To get the pot equity when called, I used PokerStove. Incidentally, I used the slider in PokerStove to choose the top 25.2% of hands. That might not be the right set of hands for overcalling.

To get the figures like a 1/2 chance that one player calls, that came from considering the 4 possibilities of whether each player would call. There was a 1/2 chance that the button would call, and I assumed that independently, there was a 1/4 chance that the SB would call. So, there was a 1/8 chance that only the SB would call, and a 3/8 chance that only the button would call.

[jenson]

[ QUOTE ]
If you push, about 3/8 of the time, you pick up the pot, gaining 900.

[/ QUOTE ]

I'm a little confused regarding the above quote.

If there is a 1/2 chance that the Button calls and a 1/4 chance that the SB calls then isn't there a 3/4 chance (1/2 + 1/4) that at least one of them calls?


Again, just trying to understand this so that I can use it in the future. Thanks for the clarification. It is much appreciated.

Regards,
jenson

[jenson]

Too late to edit my previous post but on further consideration:

If there is a 1/2 chance that the Button calls and a 1/4 chance that the SB calls and a 1/8 chance that they both call then isn't there a 7/8 chance (1/2 + 1/4 + 1/8) that at least one of them calls? Otherwise put 1/8 chance that they both fold.

Now i'm really confused. /images/graemlins/confused.gif

[Cezar]

[ QUOTE ]
If there is a 1/2 chance that the Button calls and a 1/4 chance that the SB calls and a 1/8 chance that they both call then isn't there a 7/8 chance (1/2 + 1/4 + 1/8) that at least one of them calls? Otherwise put 1/8 chance that they both fold.

Now i'm really confused. /images/graemlins/confused.gif

[/ QUOTE ]

Yeah, you are confused. You're double and triple counting the times that both SB and button call. You are supposed to substract it, not add. Here is a neat formula to remember
Event 1 has probability P1, event 2, independent of event 1, has probability P2. At least one event will occur with probability

P1 + P2 - (P1*P2)

May be this will help you understand better.

You're correct that they both call 1/8 of the time.
Now, button calls half the time, regardless of what SB does. That 1/2 already includes 1/8 chance that they both call. So, it is actually 3/8 chance that ONLY button calls and 1/8 chance they both do. Same goes for sb. 1/4 chance that SB calls is a sum of 1/8 that ONLY sb calls and 1/8 that he is overcalling button.
And the final answer is, 3/8 chance only button calls, 1/8 sb, 1/8 two calls, total 5/8 chance of getting one or two calls.

I'm awful at explaining things, do tell me if I only made it worse and need to rephrase it /images/graemlins/grin.gif

Cezar

[jenson]

Cezar,

Thanks for the great job of explaining this problem. It has really helped my understanding.

I've created a little spreadsheet that can be used to calculate the results of this play.

My wife said that I would be better off using my free time elsewhere. lol

Should anyone be interested in checking it out, I've included a jpg with this post and also a link to the xls file.

Any thoughts are appreciated.

http://V015U23GAB.maximumasp.com/hikenj/ev.jpg

EV of this play (http://V015U23GAB.maximumasp.com/hikenj/ev.xls)