Some math that's supposed to help me figure out SNGs

[eastbay]

[ QUOTE ]
Okay so Bones and I have been talking about that 77 ITM hand I posted a little while ago. Here is a hypothetical situation that we're using to try and figure it out.

You: 2000
SB: 2000
Button: 4000

Blinds 100/200


SB shows AKo and pushes. You look down and see 77. ICM says a call here is correct (+1.3%).

The main reason the call is correct because of the payout weights.

So here's what we were thinking. In a $22 SNG, your profit for finishing 3rd will be $18. Winning this hand will give you a 50% chance of winning the tourney, ignoring difference in skill level. So when you go heads up, you have a profit EV of $58 ((78 + 38) * .5).

45% of the time you make $18, and 55% of the time you make $58.

58/18 = 3.22, so you need to finish 3rd place a little more than 3 times to equal the profit you gain from getting heads up once.


[/ QUOTE ]

You were fine until this last sentence I think, and then you took a left turn into nonsenseland.

What you are trying to do is to estimate the equity of each of your possible moves. The two moves you're considering are calling and folding.

For folding, you get this from ICM'ing the chip stacks if you fold out (and assume that it's folded around for simplicity.)

For calling, you need to use the numbers you just quoted to get the overall EV. You do this by weighting each outcome by its probability. (.45)(18) +(.55)(58) = X.

The key concept is that the overall EV of some decision is the average of the possible outcomes weighted by the probability of each. Your ratio 58/18 isn't relevant. What you want is the overall EV of calling, so that you can compare it to folding (or the EV of any other possible move, if you have some way of estimating it.)

Then you compare X to whatever you got for folding, and this helps you make your decision.

eastbay