This question is quite old and it was solved by the classical mathematicians as Jacob Bernoulli, Blaise Pascal and many more having familiar names.
It is interesting that origin of probability and statistical studies is in gambling itself. These mathematicians wish to solve gambling problems (especially focused on roulette and dice) and then their conclusions were generalized to common probability laws.
Did you know, that even the first woman programmer Ada Lovelace tried to build roulette betting system?
Among the most popular betting systems belongs Martingale, Labouchère and Fibonacci.
The most popular is Martingale. It works great but you have to have infinity bankroll to be unbeatable.
Labouchère (also know as split martingale) is less aggressive, thus more robust against loss. At first you specify the amount you want to win. Then you bet a proportion of your win goal until you loss your stake, when you start act as in Martingale system.
Fibonacci is based on familiar sequence 1, 1, 2, 3, 5, 8, 13..., where every subsequent element is sum of previous two ones. As in Martingale strategy you bet the same amount again and again until you loss when you increase your bet by factor of Fibonacci sequence element.
A little bit of my bias. I along with my colleagues were developed Dice game with implemented these betting strategies. You can try them, learn them and improve them.
For more information, please go to dedicated CoinXerox Dice thread, or Dice game itself and then Botting section.
Just while searching for other systems I found out reverse Labouchère. Was just trying it out and made a 0.04BTC profit . Here is more info on reverse labouchere http://www.roulette-games.co.uk/strategy/Reverselabouchere-system.php
Thank you stellar69 for your comment. Reverse Labouchère betting strategy was added among CoinXerox Dice bots.
Those who are interested in betting strategies should read the article which stellar69 posted here.