Bounties in tournaments: Example




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For this example we have a tournament with 3 players left.
SB has a stack of 1000, BB has a stack of 2000 and the button has a stack of 3000.
The prize structure is 50-30-20, the bounty is $10, blinds are 10/20.

SB now decides to shove all of his hands, BB calls with all of his hands.
In this example we will show how BB's EV of 2.38 is calculated.

There's 3 outcomes that are relevant here.
We will show the resulting stacks for each outcome and the corresponding ICM value for BB.
This ICM value can be achieved with any ICM calculator
Below that the bounty value is shown, which is considered proportional to the stack size.

BB Loses

Stacks: SB:2000 BB:1000 Button: 3000
ICM values: SB:34 BB:27.5 Button:38.5

BB's stack is 16.67% of the total nr of chips.
There's 3 bounties left, worth $30
BB's bounty value is $5.

SB and BB tie

Stacks: SB:1000 BB:2000 Button: 3000
ICM values: SB:27.5 BB:34 Button:38.5

BB's stack is 33.33% of the total nr of chips.
There's 3 bounties left, worth $30
BB's bounty value is $10.

BB wins

Stacks: SB:0 BB:3000 Button: 3000
ICM values: SB:0 BB:40 Button:40

BB's stack is 50% of the total nr of chips.
There's 2 bounties left, worth $20
BB's bounty value is $10.

However, BB has also just won a bounty of $10.

The outcome

The chance of BB losing is 47.966%.
The chance of BB winning is 47.966%.
The chance of a tie is 4.067%

That makes the weighed average of the value of BB's stack:
47.966%*(27.5+5) + 4.067%*(34+10) + 47.966%*(40+10+10) = 46.15803.

The value of folding

Finally we will need to know how much BB's stack would be worth if he had folded.
Stacks: SB:1020 BB:1980 Button: 3000
ICM values: SB:27.64 BB:33.88 Button:38.49

BB's stack is 33% of the total nr of chips.
There's 3 bounties left, worth $30
BB's bounty value is $9.90.

BB's EV for calling

BB's EV for calling is therefore 46.15803 - (33.88 + 9.90) = 2.38.