Similarly, if I state my goal is either to double my money or go bust on just-dice, the chance that I double my money with one bet is 49.5%. If I bet 1/10th of that on the same bet until I either double my money or go bust, the chance is higher I go bust (not going to waste my time in R to tell you the odds...)
People keep saying that, but they are wrong. 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 0.41421356 BTC with payout 3.41421356x and chance 28.99642866% to win 1.41421356 BTC for a profit of 1 BTC
2. if you lose, bet 0.58578644 BTC at the same payout and chance to win 2 BTC for a net profit of 1 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).