We have a strategy that has won us a fair bit of money on the roulette table and I want to try and understand the odds a bit better. The strategy is as follows:
- Select either red or black and always bet the same color
- Bet the table minimum, let's say \$10, on the first bet
- If we win the bet we double up for a total profit of \$10
- If we lose, then we triple the next bet to \$30
- Every time we win we collect our winnings and start again at the minimum bet (\$10)
- Every time we lose we triple the bet until we win again (eg. bet 1: \$10, bet 2: \$30, bet 3: \$90, bet 4: \$270 etc)
The table we're playing is an American Roulette table which has a 47.4% probability of winning a red/black bet. There is no table limit on the table and so the only way I see this being a losing strategy is if you're unable to cover your triple up (eg. you don't have sufficient bank roll) and you lose X number of times in a row.
The reason we triple up when we lose is to ensure we cover our lost bet and always make a profit from a winning bet.
The only time we would not triple up is when we get back to our starting stack (let's say we start with \$150 and have won \$300 for a total of \$450 then if our triple up was going to take us below our starting point then we would just start again at the minimum bet of \$10 - this further reduces the risk of the strategy).
To help with this I'd be keen to know what the odd's are of losing 2, 3, 4, 5, and 6 times in a row if we select the same color. I'm also keen to know if there is anything that we haven't thought of that could trip us up here.