Bounties in tournaments: Addition to model

Up until now the model for performing ICM conversions in tournaments with bounties consisted out of two elements. The first was the ICM conversion itself. After that, in case an opponent was knocked out of the tournament, a bounty was awarded to the winning player.

I have come to realize that a third element should be involved in estimating the cash value of a stack in tournaments with bounties. This third element is the expected value of winning bounties in future hands. Basically, the fact that you hold chips adds value to your stack, given that it will allow you to win bounties later on in the tournament. This third element has, until now, unfortunately, been overlooked. Bounties were added as a feature request some time ago, and they were added following the specifications of the user requests at the time. I can only blame myself for not having been a bit more critical.

As of v3.2.5 the model for calculating the cash value of a stack in a tournament with bounties will be changed. For the sake of transparency the old method will be kept available as well. It can be toggled by turning OFF the option "Bounty calcs include future play" in the tournament menu. It is however strongly recommended to always have this option ON when you're working with bounties, given that the cash value of the chance of winning future bounties can not be ignored

The new model will consider the bounty part of the cash value of a stack as proportional to the size of the stack.

Example

Let's say you're in a tournament with 9 remaining players. You hold 2000 in chips, while the other players hold 1000. The prize structure is 50-30-20 and the bounty is $5. A calculation with an ICM calculator will tell you that the ICM value of your stack is $18.44. However, given that you hold 20% of the chips with $45 in bounties out there, the future EV for winning bounties will be $9. Therefore, the cash value of your stack is considered to be $27.44.

Go here for a more detailed example.