The Martingale and full-pay Deuces

21 September 2017

By John Grochowski

QUESTION: I have a question about the double-up Martingale, where you keep doubling bets until you win.

I’ve looked online and I know you recommend against it, as do lot of gambling experts. But suppose I decide to try, starting with betting $5 on black in roulette. I lose six in a row, so I lose $5, $10, $20, $40, $80 and $160.

The next bet is $320. If I win, I get all my losses back and make a $5 profit.

Wouldn’t I be insane NOT to make the $320 bet? Losing seven in a row is so unlikely that this seems like a no-brainer.

ANSWER: Losing seven in a row may be a long shot, but losing a seventh in a row after you’ve already lost six is not.

In American double-zero roulette, when you bet on black there are 18 numbers that will win and 20 that will lose. You have a 52.6% chance of losing the bet no matter how many in a row you’ve lost or won before that.

If you were to evaluate your chances before the first spin, you could say the chances of losing the next seven are only 1.12%. But after you’ve already lost six, the question becomes “What are my chances of losing my next bet?” The answer is the same as on any other spin: 52.6%.

So no, I don’t think you’d be insane not to make the $320 bet. I think it’s far less sane to put yourself in position where you need to win a $320 bet to make a $5 profit.


QUESTION: I’m used to NSU Deuces. There’s never been any full-pay Deuces near me.

In Las Vegas this summer for a nephew’s wedding, my brother insisted on taking me to a joint that had full-pay Deuces. That full-pay Deuces is supposedly the higher-paying game is the most counter-intuitive thing I’ve ever seen. Compared to NSU, it pays less on flushes, full houses, straight flushes and five-of-a-kind, and pays more only on four-of-a-kind.

What gives? I’ll take NSU every time.

ANSWER: Four-of-a-kind is an extremely important hand in Deuces Wild. A pair of 2s with another pair is four-of-a-kind. If you have three cards of one denomination, one of another and a 2, the 2 doesn’t pair with the singleton for a full house; it completes the four-of-a-kind.

The effect is that you get four-of-a-kind more often than you get all four hands you mentioned combined.

Full-pay Deuces is marked by a 5-for-1 payoff on quads vs. 4-for-1 on NSU. On the other hands you mention, the NSU edge per coin wagered is 16 vs. 15 on five of a kind, 10 vs. 9 on straight flushes, 4 vs. 3 on full houses and 3 vs. 2 on flushes.

Given expert strategy at full-pay Deuces, you’ll get four-of-a-kind once per 15.4 hands, while flushes happen once per 60.3, full houses once per 47.1, straight flushes once per 242.7 and five-of-a-kind once per 312.3.

There are some strategy adjustments to be made when playing NSU, but even there quads occur far more often that the other hands mentioned. There, you’ll get four-of-a-kind once per 16.4 hands vs. once per 48.2 on flushes, 38.3 on full houses, 194.7 on straight flushes and 321.7 on five-of-a-kind.

The bottom line is that full-pay Deuces is a 100.8% game with expert play, while NSU Deuces is a 99.7% game.