Pivot Points

10 July 2022

By John Grochowski

QUESTION: At roulette, this guy a couple of spots down from me was making $5 minimum bets on red or black. Then No. 22 came up, and the guy said, "That's my pivot," and he shifted gears. Now he bet his $5 on 22 on every spin.

I'd never heard of a pivot in roulette. Why 22? Is that supposed to be a magic number?

ANSWER: The other player was using a pivot system in which he bets on repeating numbers. Any number could have been his pivot.

No doubt 22 had come up a short time earlier. Pivot systems call for the player to observe a sequence of numbers, then climb aboard when one repeats. That repeating number becomes his pivot.

The player bets on his pivot either until he wins or until he's lost 36 bets in a row.

With a 35-1 payoff on single numbers, the player makes a profit if the pivot comes up within 35 bets or breaks even if the pivot comes up on spin No. 36. The earlier the win, the bigger the profit.

Pivot players do not go beyond spin No. 36. If you're making your 37th bet, one win can't recoup earlier losses.

With any winner or with 36 losses, the bettor resets and stops the sequence. Instead, he waits for a new repeating number to become his pivot.

The reasoning is that in a sequence as short as 36 numbers, about a third will be repeaters and about a third won't come up at all. Over a longer time, the odds of the game will even out short-term deviations. In 10,000 spins, each number will turn up somewhere close to the same percentage of the time, and in 1 million spins, the percentages will be even closer.

Pivot players are just trying to find the right repeater that will come up a third time in short order.

Does it work? Sometimes, over time the system will lose more money than it wins.

On a zero wheel, it'll average 5.26 percent loss of total wagers, the same house edge as on all wagers except the 7.89 percent on the five-number bucket.

That a number has turned up twice in a short time doesn't affect the odds going forward. On a double-zero wheel, there are 38 numbers, and each number has a 1 in 38 chance of turning up on every spin. Past results don't change that.


QUESTION: Playing Double Double Bonus Poker, I couldn't draw a flush. I counted. In a fairly short time, I had six hands where I held four cards of the same suit, and missed on the flush every time.

That doesn't seem right. Do you suppose there was something wrong with the machine?

ANSWER: When you hold four suited cards, nine of the remaining 47 cards will complete your flush. There is an 81 percent chance your draw will not bring a needed flush card.

Six misses in a row? That's a 27.9 percent shot.

You have a 72.1 percent chance of getting at least one flush within six one-card draws, but you'll miss the flush on all six draws more than a quarter of the time.

Events with less than a 27.9 percent chance of happening come to pass often in any lengthy session. In 9-6 Double Double Bonus, you see three of a kind or better -- the hands that win more than your bet -- on only 11.3 percent of hands.

Without occurrences a lot less frequent than missing on six consecutive flush draws, you wouldn't win enough to keep you in the game.