Quote from: dooglus on January 08, 2013, 09:02:32 PM

Quote from: dooglus on January 08, 2013, 07:36:06 PM

So again it's better to martingale a series of high-multiplier bets than to play a single large low-multiplier bet.

Why??

I think I found the reason:

I have to choose between two seeming equivalent betting strategies:

a) I commit to betting 1, 2, 4 on a bet that pays out 2x with a 1/2 probability of winning each time, and that the house takes 2% of everything I stake as a service charge. I'm committed to risking up to 7 to win 1.

b) I bet the 7 all at once on a bet that pays out (8/7)x and which has a 7/8 probability of winning. Again, the house takes its 2% service charge of all stakes.

In both cases I risk 7 to win 1. In both cases I have a 1/8 probability of losing 7 chips.

The difference is in the service charge. In a) there's a good (75%) chance that I won't need to bet the 4, because either the 1 or the 2 will win. So I'll be paying less service charge. In b) I pay 2% of the full 7 chips.

There's no service charge at satoshidice, but there's a house edge, which is effectively the same thing. Breaking a single low-multiplier high-stake bet up into a martingale series of high-multiplier low-stake bets means on average I'll be staking less to achieve the same result. So while it's true that martingale betting can't reduce the house edge, it's also true that martingale betting can be used to give a higher expected return than placing a single large equivalent bet by reducing the average amount that needs to be staked to achieve the desired return.

Every time I start betting over 1 I end up losing most of my money, I lost 8 48% bets in a row. I seem to have better luck with the smaller bets on 24/12% odds.