Of course "works" is a relative term, depending on what your goal is. When playing a negative expectation game, the one progression that maximizes winnings/minimizes losses as compared to other schemes for betting negative expectation games is the devil's staircase.
The devil's staircase is a progression that says to parley all winnings until a win goal is reached or until you go broke, in either case you stop playing. We'll call the win goal, the amount that you want to reach, K. If your bank is less than K/2 then you bet your bank, otherwise you bet K-bank. This means that you will parley all winnings until your bank is > K/2.
This results in a function called the devil's staircase, which is an extremely interesting function, some professional gamblers who play negative expectation games like craps and roulette use the devil's staircase when trying to break the bank.
The logic to this approach is that the more hands (or throws of the dice or spins of the roulette wheel) that are played at negative expectation, the more likely that the entire bankroll will be lost, so the intention of the devil's staircase is to limit the number of hands played (or dice throws or roulette wheel spins).
Let's say that your goal is to increase your bank by a factor of 16 and you use the devil's staircase, we'll call the bank B.
First bet B
Win and parley, second bet 2B
win and parley, third bet 4B
win and parley, fourth bet 8B
win and parley, B now equals 16B stop playing
what are the odds that you will win 4 in a row in a 50/50 game? 1/2*1/2*1/2*1/2 or 1/16, of course that means that the odds that you will go broke before hitting 16B are 15/16.
Of course you can't get 50/50 games in a casino, but you can get close, the pass line with 100X odds, a roulette wheel with a single zero, a single deck blackjack game with excellent penetration and excellent rules.
So, if you want to double your money and you intend on flat betting a negative expectation game, you are better off to bet it all on one hand, you have a 50% chance (more or less) of doubling your money. Flat betting a negative expectation game comes no where near close to that.
Steve
