is there, or has anybody worked out a formula for optimum ROI on GTD prize money v's entry fee and number of players. e.g. A $15 buy in with say 16K Gtd prize money how manny players are optimum to get the best possible chance of cashing?

If theres a formula Id love to know it so I can sit at the lobby page and enter tourney when its most profitable ( may mean playing in differant time zones though )

Um... the smallest number of players that will not result in the tourney being cancelled?

Yes, but there is a bit more that can be considered.

Given prize of P, buy-in of B and N players, all of equal capability, the expected prize amount per player is P/N and therefore the expected profit per player is P/N –B. ROI is expected profit divided by investment so ROI = (P/N –B)/B = P /(NB) – 1

Simple Examples :

T1: P = 100, B= 10, N=8: ROI = 100/80 – 1 = 20%

T2; P = 200, B = 18, N= 12: ROI = 200/ 216 – 1 = -7.4%

From a strict ROI basis, tournament 1 is preferred to tournament 2 even though T1’s fee percentage relative to the prize amount is higher (10% vs 9%).