Casino Random Number Generator

Here’s how it works: the outcome of each round of the game is either 0 or 1.  Before the outcome is decided, players place bets on either side.  The total amounts bet on each side are confidential.

After betting is closed, the outcome is calculated as the one with the least amount bet on it.  The losers get nothing, the winners double their money, and the casino takes the rest. For example, if there is $100 bet on 0 and $120 bet on 1, the outcome would be 0, there’d be $200 in payouts, and $20 to the house.

Any conceivable pattern in the outcomes will be obliterated, and expectations by the players will become self-defeating prophesies.  In other words, if we could get people to play this game, the outcomes would be about as random as you can get.

Would this work?  What are the flaws?