simple ev calculation

[sebbb]

I have a disagreement with another SSNLer about ev calculations

I bet allin $5 into a $10 pot, villain always calls and wins (1-y)% ot the time.

What's the ev? ev of folding is 0. Details of calculations please.

[sebbb]

I think the ev= y(5+10)+(1-y)*(-5)

amIcorrect?

[AaronBrown]

Let me make sure I understand. You are heads up and there is $10 in the pot, with no bet to you. You go all-in for $5 and are always called, so there is always $20 in the pot. You win fraction y of the time (I'm not using %, so an even chance of winning is y = 0.5, not y = 50%), so your EV is $20y - $5. That's the same as your formula.

I just took your expected winnings ($20y) and subtracted what you have to pay to get them. You took the amount you win if you win ($10 in the pot plus $5 supplied by the other player) times the chance of winning (y) plus the amount you "win" if you lose (-$5) times the chance of losing (1-y).

[tarheeljks]

[ QUOTE ]


I just took your expected winnings ($20y) and subtracted what you have to pay to get them. You took the amount you win if you win ($10 in the pot plus $5 supplied by the other player) times the chance of winning (y) plus the amount you "win" if you lose (-$5) times the chance of losing (1-y).

[/ QUOTE ]

my problem with this calculation is that you don't always lose the $5 you that you bet. you lose it (1-y) percent of the time.

[AaronBrown]

[ QUOTE ]
my problem with this calculation is that you don't always lose the $5 you that you bet. you lose it (1-y) percent of the time.

[/ QUOTE ]
You're correct, that's why there are two ways of doing the problem.

In my way, I treated it as paying $5 to get a chance at $20. OP treated it as betting $5 against $15. So I'm buying a lottery ticket, he's making a bet. You get the same EV either way if you do the problem right.

If you win, you collect a $20 pot. I treated the entire $20 as revenue, against a $5 expense. OP paid himself his $5 back, so he said he had only $15 of revenue by winning, but he only had to pay the $5 if he lost.

So I say:

$20y - $5

and OP says:

$15y - $5(1 - y)
=$15y - $5 + $5y
=$20y - $5

and we agree.

[tarheeljks]

original disagreement was that i wanted to count the pot as $20, not $15