What you've done looks pretty good so far. You must have filled in some other stacks to do the equity calculations, which is exactly what you have to do. The context is pretty clear that the other stacks should be close to t2000 and mostly even, with t18,000 total on the table. Using the convention in the book (?) the small blind has already been pulled out of your stack, so your actual stack is t1970 before posting. You always have to add the blinds back in, but not the antes. Good thing I'm a huge nit. The SB thing and maybe filling in the other stacks slightly differently accounts for the tiny difference between your numbers and mine.
(The ICM macro seems to be accurate to a fixed number of decimal places, rather than a certain fraction of the prize pool. I used $50/$30/$20 as my payouts instead of 0.5/0.3/0.2 to get around this.)
Let's start by looking at the exact scenario presented in the book. Your choice is between pushing and getting called by 66 or folding. For the option of folding, I like your assumption that MP1 bets the flop and everyone folds. It's not perfect, but it makes the solution much simpler. Also, it happens to give a nice lower bound for your prize pool equity, since in a qualitative sense large disparities in stack size improve the prize pool equities of those in the middle relative to more even stacks. The effect wouldn't be that big anyway, so I feel fine ignoring it and taking a probable lower bound. My number is
$EV_fold=$10.83.
If you push and he calls 100% with 66, he is a 54.6/45.4 favorite. This gives your prize pool equity if you push as:
$EV_push = 0.546*(0) + 0.454*(21.82) =
$9.91
assuming he always has 66 and he always calls with it
This, as you also showed, is a demonstration that under those exact conditions, folding is better than pushing. That doesn't really fit with our "poker instinct," nor Collin's conclusion on the hand, nor would any decent poker player ever recommend folding there. The reason is sometimes he has a different hand, and sometimes he folds to your push. So how to account for this? We need some hand ranges. Here are the next steps.
<ul type="square">[*] For simplicity, assume every other player other than MP1 always folds.[*] Decide on an open-raising range for MP1.[*] Decide on a push-calling range for MP1.[*] Use an ICM calculator to determine your prize pool equity if MP1 folds.[*] From those two ranges and the basic probabilities of being dealt certain hands, figure out how often he calls your all-in raise and how often you win the pot uncontested. Hint: SNGPT can shortcut this step for you, although it can't do the actual calculation without some twisting.[*] Using a tool like PokerStove or the
ProPokerTools Simulator, determine how often you win with AKo against his push-calling hand range.[/list]