Hi Vincent-

I'm going to make a nice assumption about you and think you aren't a troll, despite a flood of silly posts today by you. Here's my take on the matter:

If Casinos didn't cap their bets, yes, theoretically a gambler with a giant bankroll could ruin them. Let's make this easy: Assume the game gives you a 40 % chance of winning, so it's -EV. If you have a bankroll of $1.023 trillion and the casino has $1 billion, you start by wagering $1 billion. If the casino wins, you wager $2 bil, then $4, etc, until they are broke or you are. The casino would have to beat you 10 times in a row to take your $1.023 trillion bankroll. (2^10) With a 60 % chance of beating you in any given game, the casino will succeed at this venture .6 % of the time, or 6.05 times out of 1,000. (.6^10) So, 6 times out of 1,000, the casino takes $1 trillion from you. 994 times out of 1,000, the casino gives you $1 billion. This is a net loss of $5.05 million for you, per hand of blackjack or whatever it is we're playing.

This seems like bad odds for you, and I'm sure billionaires would be lining up to bankroll the casino. This is why this theorem doesn't work. Casinos cap their bets not because it's profitable, but because they don't have a line of billionaires waiting to back them. But if someone set up an explicit deal such as yours, I'm sure there'd be a long line [img]/images/graemlins/smile.gif[/img]

This, by the way, is why Negreanu's strategy of a massive NL buyin isn't fundamentally a bad thing for the players. Whether one should be playing against Negreanu is another story, but if he's making poor plays, then it's +EV for a good player to take him on, as long as the player keeps a good amount of their bankroll off the table at any given time.