EV Question

[rayrns]

Let me set up the example, then I'll ask my question.

You are HU while drawing to the nut flush, which will win if you hit.
There is $20 in the pot and your opponent bets $20 bringing the pot to $40.

The EV of this situation can be found 2 ways. I am using one.
(+$40 x 9) + ( -$20 x 38 ) = -$400/47 = -$8.51

Now on to the question. If we are using the theory that once money is put in the pot it is no longer ours, then why do we not add the $20 we will have to call to the pot and make the equation:
(+$60 x 9) + ( -$20 x 38 ) = -$220/47 = -$4.68

We would have to put the $20 in the 38 times we are losing, why are we not putting it in on the 9 times that we are going to win the pot?

While in the example both are negative EV, it is less negative when we add the amount we have to call to both sides of the equation. This would mean that in situations that would be very close, if we use the second equation we would have more positive equations than using the first.

Thanks in advance as I am sure there is a simple reason that I am just not seeing .

Ray

[nsidestrate]

[emmapeel]

I certainly defer to Nside on this.

It does look like a good question and I must admit that I am not sure of a clear answer myself; I only know that it works.

But look at it this way.

If you include the amount you use to call as you say then when you hit your flush and win the pot your stack will then be $80. But there is only $40 in the pot and $20 used to call so where does the extra $20 come from?

You're adding your $40 win on to the $20 anyway when you win. You can't count that $20 twice.

EP

[janeg]

If you win, you get your $20 back so all that matters is how often you will lose the $20. Think it's a litte easier to see if you do

.2($40) - .8(20) = 8 - 16 = -8

20% of the time you win the existing pot, and 80% of the time you will lose the $20 bet.

[Bugsbunny]

If you want to always include the 20 into the pot you go to an equity calculation:

Your equity in this pot (assuming you always win when you hit the flush, and never do otherwise) is 9/47 = 0.191489362, or about 19.15%

So your "fair share" of the pot is:
60 * 0.191489362 = $11.489361702, or just about 11.49

You're investing $20 so your expected net is 11.49 - 20 = -8.51