Tournament Chop Calculation

Basic Info

50$ - 20 person tournament (no rebuy or addon)
3000 Starting Chips
60,000 Total Chips in Play

3 players remain. (P)
Player A has 20,000 Chips (33.3%)
Player B has 30,000 Chips (50.0%)
Player C has 10,000 Chips (16.7%)

Prizes (Z)
#1 $500 (50%)
#2 $300 (30%)
#3 $200 (20%)

A Chop has been suggested. What is the correct calculated equity for each player?

Incorrect Method A

(z1 * Px chip%) + (z2 * Px chip %) + (z3 * Px chip %)

Player A Equity = 250+150+100 = 500
Player B Equity = 165+100+65 = 333
Player C Equity = 84+50+33 = 167

Incorrect because it only results in a linear correlation to chip %. This makes the payouts too top heavy (and can result in a completely unequitable top payout if someone has > 50% of chips)

Incorrect Method B

(z1+z2+z3) * (Px chip%)

Player A Equity = 1000 * .50 = 500
Player B Equity = 1000 * .33 = 333
Player C Equity = 1000 * .10 = 167

This is basically the same calculation as method A, just written differently.

Correct Method

(z3) + [(z1-z3)*(Px chip%)] + [(z2-z3)*(Px chip%)]

Player A Equity =
200+[300*.50]+[100*.50]= 200+150 +50 = 400

Player B Equity =
200+[300*.33]+[100*.33]=200+100+33 = 333

Player C Equity =
200+[300*.17]+[100*.17]=200+51+17 = 267

Written more simply, z3 + [(z1+z2-z3-z3)*(Px chip%)]

Explanation

Everyone has already been guaranteed the last place prize, so begin by giving all remaining players that amount, and then subtract that amount from all remaining prize amounts. Then, sum the remaining amounts. Apply each remaining players chip percentage to the result.

Here is a simple process you can use at the table. You will need a piece of paper and a pencil. If you want to print out a pre structured form, you can go HERE.

1. Begin by asking all involved players to count their chips.
2. Draw a line separating the paper in half. The upper half will be PRIZES, the lower half will be PLAYERS
3. In the upper area, list all remaining prizes.
4. Subtract the lowest prize from all other prizes. Note the new values and cross out the last place prize.
5. Add the new values of all remaining prizes together. This number should be labeled the PRIZE POOL
6. In the lower area, list all remaining players.
7. Beside each players name, write the amount of chips they have left
8. Sum all of the amounts of chips the players gave you.
9. Multiply the initial starting stack by the total number of entrants.
10. Ensure the values of +8 and +9 are relatively equal. If grossly different, the reported values of chips will need to be validated by a floor person.
11. Once the players stacks, and the total chips in play have been verified, note the percentage of chips each player has next to their name.
12. Beside each player write the amount of the last place prize, followed by a +
13. Apply each players percentage to the PRIZE POOL amount from #5, and add it after the + sign.
14. Sum the amounts from #12 and #13 for each player to give the total resulting equity.