Here is my opinion on how to gamble using the Martingale betting system. My game of choice is roulette and on an American wheel you have 18 chances out of 38 to win on red, black, odd or even. That's about 47% of the time. The longer you play with the Martingale system, the higher your chance of having a long losing streak so the idea to keep it short and the shortest is to bet how much you want to win in your first bet.
Example: You want to win $100 so bet $100 on red, black, odd or even. If you win, take your $100 and walk away. If you lose, double it to $200. If you win, you have your $100 so walk away. If you lose double it to $400 and repeat until you win or lose it all. Have enough chips to cover 5 losses and 1 winning bet as a worse case scenario. If you lose 6 times in a row, you were very unlucky since this method has a 98% chance of winning.
These would be your bets for 5 losses in a row followed by a winning bet.
$200 - 1st loss bet
$400 - 2nd loss bet
$800 - 3rd loss bet
$1,600 - 4th loss bet
$3,200 - 5th loss bet
$6,400 - 6th win - take your $100 and go home.
You need 2 times $6,400 minus $100 to cover this. That is $12,700! I call this betting high to win low. To maximize your chance of winning you need to find a table that has a high enough betting limit to allow you to bet $6,400 in one bet so you'll need to proceed to the high stakes betting area where $10,000 bets are allowed.
So the equation to figure out how much you need based on your your goal winnings is ...
Bank = FirstBet * 128 - FirstBet
Bank = 100 * 128 - 100 = $12,700
If you wanted to win $50 then
Bank = 50 * 128 - 50 = $6,350
Probability of losing streak on American Roulette wheel:
1st loss = 52.63% = ((18/38)^1)*100
2nd loss in a row = 27.70% = ((18/38)^2)*100
3rd loss in a row = 14.58% = ((18/38)^3)*100
4th loss in a row = 7.67% = ((18/38)^4)*100
5th loss in a row = 4.04% = ((18/38)^5)*100
6th loss in a row = 2.13% = ((18/38)^6)*100
Since you have a 2% chance of losing 6 times in a row you should have enough money to cover 5 losses doubling each time.
You would be tempted to keep going but remember that losing streaks do happen and picking red, black, odd or even randomly is no different from selecting red every time. Your chances are still the same. If you do hit that losing streak, you will most likely lose everything you have won so far plus a lot more! So don't be greedy and take your money and run. Also remember that you could hit that losing streak first time so be prepared to lose it all. Also remember that I'm not saying to bet $100 as your first bet. You decide how much you can afford to lose then
Let's say you can afford to lose $1000. Then the equation to figure out your first bet is roughly ...
FirstBet = Bank / 127
FirstBest = 1000 / 127 = $7.9
Round that up to $8 and run it through the Bank equation and you get
Bank = $8 * 128 - $8 = $1016
Let me be clear that in this scenario, you are risking $1016 to win $8! That's why it's risking large amount to win small amount. But the risk is small so as long as you to push your luck too many times, you'll probably walk away a winner. This system is only good for the occasional gambler. If you gamble a lot, this system will not work for you since a single loss can wipe out all of your profits and put you in debt.