The d'Alembert system is a very simple system for all games that pay-out as much as your original stake return, such as Blackjack or outside bets in Roulette. The system is named after the French mathematician Jean Le Rond d'Alembert. The system basically involves adding one unit to your bet each time you lose and removing a unit every time you win.
1. If you bet $10 on black. Red comes up, you lose $10.
2. If you bet $20 on black, red comes up, you lose $20.
3. If you bet $30 on black, black comes up, you win $30.
4. If you bet $20 on black, black comes up, you win $20.
5. If you bet $10 on black, red comes up, you lose $10.
You have now bet 6 times where you have won two and lost three. This brings your winnings to (30+20)-(10-20-10) = $10. You can, of course, make the first bet as much as you like, as long as you stick to raising by 1 when you lose and subtracting by 1 when you win.