Answer: If there is NO COOPERATION among the other players, and the OBJECTIVE is to last for as long as possible, you can say with 100% certainty a bet of $19,999 will keep you around until the next turn.

Why is this so?

The only way to "lose" would be if everyone bet $20,000 (I am not sure if this would mean they all zero out anyway) which would imply massive cooperation, which would mean criterion #3 for unravelling the strategy has been evoked.

Granted, this is a ridiculous example, but you can go through a RETROGRADE ANALYSIS of survival through N rounds, then determine a bound you need never cross, then work your way back, then come up with a betting plan.

It is easier than you think, just play with it on paper (or in Excel) and you will see what I mean.