[DWarrior]

Stacked rebuys (as in, being able to rebuy when you still have chips in front of you at or below starting chip amount) and addons aside, I think you're misunderstanding ROI calculation of rebuys.

If there was a $10+1 tournament where your only option was to rebuy if you went broke (no stacked rebuys or addons) and the rebuy would also be $10+1, rebuying would be the same as putting money down for a different tournament (your $10 added to the prize pool wouldn't make any real difference in a large enough field)

There would, however, be one significant difference: you'd be starting with a stack that's below the average. In that instance it would be a better idea to go into a different tournament instead. However, you wouldn't take the rebuy not because your ROI is based off a $22 investment as opposed to an $11 investment, but because it is -EV to spend the second $11 rebuying as opposed to spending $11 on another tournament.

What affects the EV of rebuys are the fact that sometimes you don't have to pay rake on rebuys and all the strategy changes: starting with a bigger stack, being able to add onto your stack during the tournament, being able to play a tournament where you normally wouldn't be able to (as in, if this was the only tournament around), the psychological effect of having the rebuy cushion for other players, and hte fact that most of the early chips lost will be going to the lucky bad players.

Basically, if you are going to come up with a formula for how much to spend on a tournament, it shouldn't compute a total amount of money you can spend. Instead, it should analyze each time you have to rebuy to calculate the EV of spending the money on the rebuy versus playing another tournament for the same money instead. If it shows that taking the rebuy is outright -EV, or if you're higher EV going to another tournament, then you should quit; otherwise take the rebuy.

It's more or less a general consensus that you should rebuy all the time. Besides, even if such formula were to be created, the values you'll be inputting into it will not be precise, so the results will have to be calculated with a certain degree of error and I suspect the highest expected value of that error would always be positive.

EDIT: I think ROI is a pretty useless statistic when calculating profitability, it's all about EV and SD.