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The most equitable way to chop, not taking player strength into account, is to offer everyone Xth place money where X is number of players left, and divide remaining prize pool by chip count.
So, 4 players left. Prize pool is 10%, 20%, 30%, 40% - Total of $20,000.
Stacks are:
1 - 45,000
2 - 30,000
3 - 15,000
4 - 10,000
All players get $2,000 + their equity in remaining pool of $12,000
1 - $2,000 + (45% of $12,000) = $7,400 (versus $8,000 otherwise)
2 - $2,000 + (30% of $12,000) = $5,600 (versus $6,000 otherwise)
3 - $2,000 + (15% of $12,000) = $3,800 (versus $4,000 otherwise)
4 - $2,000 + (10% of $12,000) = $3,200 (versus $2,000 otherwise)
You can see that in this skewed example, the smallest stack makes out the best, and that will always happen, because he's locking in his equity when it's lowest. If he doubles up, he has more equity, and therefore could move up the prize pool. This will be less skewed if the pay structure is steeper, though, making the deal less favorable to the bottom stack (though still more $$ than 4th would otherwise pay).
You can rework the numbers for any scenario.
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