As akashenk mentioned, the constant growth payout model will not work for large field events because the min cash basically gets very close to zero.
To get around that, I used the following rules:
-A player finishing in position n is awarded 1/(n+1) more than the amount awarded to player in position n+1;
-a constant multiplier applied to each payout so that the aggregate projected payouts equal the prize pool;
-the min payout is known.
For example: I used the 2023 Seniors event, 8140 entries, $1,000 fee, $7,280,200 total prize pool. I set the min payout position to be 11% of the field (rounded to 9), which is 900th. I also set the min payout to $2,000.
This results in the following payout structure:
Code:
Place Proposed 2023 Actual Payout
1 $519,168 $765,731
2 $346,324 $473,212
3 $259,902 $356,166
4 $208,049 $269,841
5 $173,481 $205,799
6 $148,789 $158,006
7 $130,270 $122,130
8 $115,867 $95,040
9 $104,344 $74,464
10 $94,917 $58,744
20 $50,024 $30,067
30 $34,096 $24,390
40 $25,938 $19,927
50 $20,981 $16,396
100 $10,924 $5,931
200 $5,836 $5,138
300 $4,144 $3,946
400 $3,307 $3,498
500 $2,814 $2,813
600 $2,495 $2,553
700 $2,274 $2,153
800 $2,116 $2,001
900 $2,000 $1,751
As one can see 1st place paid 50% more than 2nd place, which paid 33% more than 3rd place, which paid 25% more than 4th place, etc.
The structure is less top-heavy, that is the final table represents 27.6% of the prize pool, compared with 34.6% for the 2023 event.
Payouts are roughly the same until about 300, then they get much juicier from there until the final table (or 7th).
Of course 327 fewer places are awarded. The min cash for 2023 event was place 1227, $1,601.