Weird roulette results

6 July 2014

By John Grochowski

QUESTION: I have one for your strange happenings file. I was playing roulette, $5 table, $1 chips, mixing up inside and outside bets – colors, single numbers, streets and corners. I was about holding my own, and then this weird streak happened.

I wasn’t on it from the beginning, but the ball landed on No. 1. The next time, it came up on No. 2. Somebody said, “1, 2 … is 3 next?” A couple of people bet on 3, and I included it in a street. Up came No. 3.

Now everybody bet singles number on 4. I know better, I guess, but I just had to. I’d been betting only $1 on each of my inside bets, spreading $5 around the layout. But this time I bet $5 on 4. Up came No. 4.

You never heard cheering like that at a roulette table. You don’t usually get everybody rooting for the same number. Of course, we had to bet No. 5, but that was the end of the streak. The next number was 28.

Every player at the table made money on the streak. I’d never seen anything like it.

ANSWER: I’ve never seen a streak like that, either. I’ve seen the same number hit three times in a row and five times out of six. But I’ve never seen four consecutive numbers win in sequence.

The chances of any four specific numbers coming up on consecutive spins are 1 in 38 to the fourth power, or 2,085,136. Regardless of whether you’re asking, “What are the chances of the next four numbers being 1-2-3-4,” “What are the chances of the next four being 4-4-4-4” or “What are the chances of the next four being 28-12-3-35,” the answer is 1 in 2,085,136.

Once the streak has begun and partial results are in hand, the odds shorten. After No. 1 was in the bank, the chances of the next three being 2-3-4 were 1 in 54,982. After 1-2, the chances of 3-4 were 1 in 1,444, and after 1-2-3, the chances of the next begin 4 were the 1 in 38 that applies to any number on any spin.

On every step of the streak, the chances of the next sequence number were 1 in 38, because the specific number needed is 1 in 38 numbers on the wheel, including 0 and 00.

Had I been playing, there’s a fair chance I’d have gone along with the crowd and bet on 4 and 5, just for the fun of winning together if it happened. But it would have been with the full knowledge that the sequence numbers were no more and no less likely to turn up than any other number.


QUESTION: I found a Three-Card Poker game that paid 50-1 on a three-card royal instead of the 40-1 on a straight flush. All the games I’d seen before just treated Ace-King-Queen the same as any other straight flush. Other than that, it looked pretty normal, with 30 for three-of-a-kind, 6 for a straight, 3 for a flush and 1 for a pair. How much does that lower the house edge?

ANSWER: Without the mini-royal, the game you describe is the most common among the many pay tables offered on the Pair Plus portion of Three-Card Poker. The house edge is 7.28 percent. If the 50-1 payoff on a mini-royal is added, the house edge drops just a bit, to 7.10 percent.

In 22,100 possible three-card combinations, 48 are straight flushes, so straight flushes occur an average of once per 460.42 hands.

Of those 48 possible straight flushes, four are mini royals – Ace-King-Queen of each suit. So mini royals happen once per 5,525 hands. Giving the player an extra $10 per $1 wagered once per 5,525 hands reduces the house edge, but not by much.