For an example of a better strategy, try:
bet 0.5 at 33%
if you win, you get 99/33 = 3x, so you get 1.5 back, a profit of 1 - you've doubled your money
if you lose, bet the other 0.5 at 24.75%
if you win, you get 99/24.75 = 4x, so you get 2 back - you've doubled your money
the only way it goes wrong is if you lose both the 33% and the 24.75% - the chance of that is (1-0.33) * (1-0.2475) = 0.504175
so the chance of success is 1 - 0.504175 = 0.495825 = 49.5825% - a fraction higher than 49.5
bet 0.5 at 33%
if you win, you get 99/33 = 3x, so you get 1.5 back, a profit of 1 - you've doubled your money
if you lose, bet the other 0.5 at 24.75%
if you win, you get 99/24.75 = 4x, so you get 2 back - you've doubled your money
the only way it goes wrong is if you lose both the 33% and the 24.75% - the chance of that is (1-0.33) * (1-0.2475) = 0.504175
so the chance of success is 1 - 0.504175 = 0.495825 = 49.5825% - a fraction higher than 49.5
I also seen something about a single martingale sequence being better than going all in on a certain % How does this exactly happened, if your chances are 49.5% how are you actually able to improve them, slightly. Is the math on casinos not perfect when calculating odds and results?
I gave an example of how the chance of doubling up can be higher than 49.5% - check the bold number in the quoted text.
It's nothing to do with imperfect calculations, it's a true effect. The strategy I outlined has a chance of doubling up that is closer to 49.6% than it is to 49.5%.
The trick is to risk less on average. If you always bet your whole bankroll on a single event, you expect to lose 1% of it all. If you sometimes double it up without having to bet it all, on average you risk less than all of it, and so expect to lose 1% of less than all of it.
