EV+?

[Guernica4000]

Playing last night I made a deal that I think was good but how can I calculate EV+ on the spot?

I am heads up with 25,000 chips vs. 5,000 I offered the other player 2nd place plus $10 he accepted. It was a $60 buy-in with 10 players.

First paid $300 (so $290 after the deal)
Second paid $180 (so $190 after the deal)

I would say that both of us are at the same skill level.

[Greeksquared]

Assuming your chances at winning are equal to the proportion of chips you have in play. Then you have a 5/6 chance at first and a 1/6 chance at second.

SO your EV is 5/6*300 + 1/6 * 180 = 280. So the deal was good for you.

[BruceZ]

[ QUOTE ]
Playing last night I made a deal that I think was good but how can I calculate EV+ on the spot?

I am heads up with 25,000 chips vs. 5,000 I offered the other player 2nd place plus $10 he accepted. It was a $60 buy-in with 10 players.

First paid $300 (so $290 after the deal)
Second paid $180 (so $190 after the deal)

I would say that both of us are at the same skill level.

[/ QUOTE ]

These numbers work out nice, so you can do this quickly on the spot. There is $120 on the line, and you are a 5:1 favorite to win, so your opponent will win 1/6 of the time, or an average of $20 of the $120. Since you only paid him $10, you made a good deal.

[Absolution]

This assumes there's a linear relationship between chip count and probability of winning.

[BruceZ]

[ QUOTE ]
This assumes there's a linear relationship between chip count and probability of winning.

[/ QUOTE ]

There is. When the players are equally matched, the probability of a player winning is equal to the ratio of his chips to all of the chips in play.

To prove this, note that when the player with 25,000 chips wins, he gains 5000 chips, but when the player with 5000 chips wins, he gains 25,000 chips or 5 times more. If you run this a billion times, since the players are of equal ability, they must win an equal number of chips on average. Therefore the player with 25000 chips must win 5 times more often than the player with 5000 chips.

[Guernica4000]

Thanks!

[Absolution]

I was just thinking that maybe the dynamics of the game make it more and more difficult to win as the difference in stacks gets larger and/or the shortstack gets smaller. Maybe it doesn't matter.