Calculating expectation in a tournament situation

[avisco01]

Suppose you're involved in a tournament whereby the prize structure is as follows:

1st: $200.00
2nd: $100.00
3rd: $ 40.00

Three players remain:

CL: 7,000
You: 4,500
SS: 900

Blinds are 300/600 and you're in the small blind. CL raises to 1800 preflop. Suppose you could see CL's cards and knew you had him beat:

CL: QJo
You: AKs

Supposing in this example, we're reasonably sure we'll finish 2nd close to 100% of the time should we fold given SS's low chip count. Now, what is our expectation in terms of place of finish, of raising all-in, if we knew CL would definitely call, making us a 66% - 33% favorite? I'm not sure how to do the formula, please help if possible, thank you. As an aside, on a personal level, assuming we can't see CL's cards, can anyone actually fold the AKs in this situation, or can it possibly be positive expectation to indeed fold?

[fiskebent]

You can use the Independent Chip Model to figure out how much your stack is worth in dollars. There's a calculator here: http://sharnett.bol.ucla.edu/ICM/ICM.html

You need to set up the different scenarios and calculate the stack sizes.
If you fold, the stacks are 7900, 4200 and 300. That gives your stack a value of $130.37.

If you go all-in and win, the stacks are 2500, 9600, 300 which gives your stack a value of $176.75.

If you go all-in and lose you're out and win $40.

So the $EV of going all-in vs folding is 0.66*176.75+0.33*40 - 130.37 = -$0.42.

So going all-in is very, very close to even money, dollar-wise. It's slightly -$EV, so you should fold here.

[KJ o]

In the situation described in the OP, there is a chance that the CL will fold if you push.

Unless you know CL very well or want to reduce variance, this should be a push.

If CL had pushed, removing your folding equity, it's a fold.