the problem is it never becomes negative EV to buy back in. Essentially, after you are booted, it is always rational to buy back in. Which means that the two people with the deepest bankroll will always be doing an expensive coinflip at the end with everyone else just suckers on the way.

Could make it more interesting by adding some probability on each round that someone gets declared a winner with no further buy-ins possible. ie- an 80% chance someone will get eliminated and game will continue as usual, a 20% chance that someone in the game will scoop the pot. So if there are 4 people playing there is an 80% chance one will get eliminated and a 5% for each of them that they will be declared the outright winner that round.

I have thought of that. That's why I came up with other ending scenarios like the game ending when the pool reaches a certain number of bitcoins per player, but your idea is pretty good. Although it is possible that a guy who put in only one bit coin at the start could make it all the way to the end without getting booted once. Another scenario that could be done is that there is a small chance every round that the game comes to and end and the pot is split up between the remaining players.