This push plus or minus EV

[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. [img]/images/graemlins/confused.gif[/img]

[/ 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 [img]/images/graemlins/grin.gif[/img]

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.



EV of this play