Quote from: dooglus on August 09, 2013, 08:15:47 PM

Quote from: HollowIP on August 09, 2013, 04:42:34 PM

So the martingale has a better probability for turning 1000 into 1010, but how does the math change if you were to try to go from 1000 to 2000? I wonder if the martingale would still have a higher chance of winning than a single bet?

Yes. No matter what you're trying to do, two bets are better than one. I posted previously about how to turn 1 BTC into 2 BTC, and have modified the quote here, multiplying everything by 1000:

Quote from: dooglus on August 08, 2013, 04:52:38 PM

If you want to double your money, you have a higher chance if you place multiple bets than if you place a single bet. You have to pick the right multiple bets of course.

It's really quite easy to demonstrate:

If you place a single bet, then the chance of doubling your money is 49.5%.

Now consider this 2 bet sequence:

1. bet 414.21356 BTC with payout 3.41421356x and chance 28.99642866% to win 1414.21356 BTC for a profit of 1000 BTC
2. if you lose, bet 585.78644 BTC at the same payout and chance to win 2000 BTC for a net profit of 1000 BTC.

Your overall chance of success is 49.58492857%. That is higher than 49.5%.

(Note that those bets aren't exactly available on Just-Dice, since chance is only available to 4 significant figures, but that's just a nit-pick. It's still possible to double your money with a higher than 49.5% chance using 2 bets, and not using 1 bet).

In both cases you're going to run into the 'max profit' limit on Just-Dice, but we can ignore that for the purposes of this discussion.

Ah, I see and understand more clearly now. Thanks for putting it that way, and I apologize for missing it previously.

Now speaking just about martingales, eliminating the all-in, 1 bet approach. Is it more profitable to have a shorter martingale such as the 2 bet sequence, or say have a 10 bet sequence? Logic is telling me that perhaps the 2 bet sequence is better than the 10 bet sequence, but I could just be misled. For all I know, they have the same probability factor.