Streaks in Roulette

2 January 2022

By John Grochowski

QUESTION: I have a question about the odds of streaks in roulette. This was brought on by a brother who insists Martingales are good bets. He bets red or black, and if he loses, he doubles his bet, and he keeps doubling until he wins.

When he wins, it wipes out the losses and gives him a profit equal to his first bet. I say a losing streak means he has to risk A LOT of money, and he says losing streaks long enough to hurt him just don't happen.

So, what are the chances of a long losing streak, like five in a row or six in a row, where he has to be sweating with the amount of money he's betting.

ANSWER: In double-zero roulette, when you bet on red or black, there are 20 losing numbers and only 18 winners. With a bet on black, you would lose on 0, 00 and on the 18 red numbers and win on the 18 black numbers.

Your chances of losing the bet are 20/38, which reduces to 10/19. That's .526, and when you multiply by 100 to convert to percent, it shows a 52.6 percent chance of losing one bet.

For a string of consecutive losses, the formula is (10/19)^n, where n represents the number of losses. You divide 10 by 19, then raise the result to the nth power.

For three losses in a row, it's .526 to the third power, or .146. Converted to percent, you have a 14.6 percent chance of losing three bets in a row.

You have a 7.7 percent chance of losing four in a row, 4.0 of five in a row and 2.1 of six in a row,

A 2.1 chance is nothing to sneeze at. It means per 100 trials; you'd see that streak an average of twice. Sometimes it will happen more, sometimes less, but it happens.

If you're at a table with a $10 minimum and you start with a minimum bet and lose six in a row, you'd lose $10, $20, $40, $80, $160 and $320 for total of $630. If you want to continue to a seventh step, you'd need to bet $640 and hope for a win to bring you back to a $10 profit.

When you bet that $640, the odds that apply are for winning one bet, where you have a 52.6 percent chance of losing. Once you're at that point, your losses will climb to $1,270 more often than you'll salvage a $10 profit.


QUESTION: I was playing nickel Hundred Play Poker, Double Double Bonus Poker. It was a pretty bad pay table, just 7-5, but I was having fun with all those hands.

I got lucky and caught a big one. I was dealt four parts of a royal, and got the royal eight times. There were some other small pays, so I won a whole lot of nickels.
The machine locked up and an attendant said I had to sign a tax form. No one hand was worth more than $200. I thought the cutoff was $1,200 but they wouldn't pay me without signing.

ANSWER: The IRS considers all returns for one bet on a multi-hand video poker game as one payoff, just as it lumps together all paylines on a multiline slot machine.

If all the payoffs for one bet total $1,200 or more, the IRS requires the casino to have you sign a tax form before you get paid. The eight royals total $1,600, so the casino had no choice but to have you sign before paying you.