A shuffle through the Gaming mailbag:

Q. I was at a roulette table where black numbers came up 15 times in 18 spins. It was all up there on the board to check — black was red hot.

If you were coming to the table and noticed that on the board, would you start betting red because it hadn’t been hitting and was due, or would you bet black because it was hot?

A. I’d bet black and try to ride the streak, but it would be just for fun. There’s nothing in the odds of the game that would make it more or less likely for black to keep winning.

Every spin is an independent trial, and past results have no effect on future outcomes.

If you had told me one number had shown up repeatedly or that several numbers clustered close together on the wheel were dominating the results board, I’d have said I’d play those numbers on the long-shot chance they indicated a biased wheel.

It’s extremely unlikely such short-term results indicated a bias, but at worst, the odds against you are the same as on other numbers.

With a preponderance of black numbers, however, it’s difficult for me to imagine even a long-shot chance at a bias. The black numbers are distributed all around the wheel, and a wheel biased in favor of 18 widely spaced numbers would be something to see.

Q. I found a craps machine game with bouncing dice, and the odds looked pretty enticing. Instead of 30-1 on 2 or 12, it pays 31-1, and instead of 15-1 on 3 or 11 it pays 16-1. Hardways pay 10-1 and 8-1 instead of 9-1 and 7-1.

What does that do to the house edge? Does that make these viable bets, instead of sucker bets?

A. Before getting into edges with higher than usual payoffs, let me caution you to check whether you’re getting odds-to-1, and not odds-for-1.

It’s common for machine games to pay odds-for-1 because the game has already taken your bet before the roll takes place. On a table that pays 30-1, if you win your bet on 12, you keep your 1-unit bet and get 30 units in winnings, for a total of 31. On a machine that pays 31-for-1, the machine keeps your bet when you make it, but pays 31 units on a win — still a total of 31 on your side after a win.

So 31-for-1 is the same as 30-to-1, 10-for-1 is the same as 9-to-1, and so on.

With that caution aside, let’s check out some house edges in the event the game is paying odds-to-1.

The higher payoffs make a difference, but not enough to turn bad bets into good ones.

With the standard 30-1 you’d get at most craps tables, bets on 2, 12 or hard hop bets give the house a 13.89 percent edge. If the payoff is 31-1, the edge drops only to 11.11 percent. True odds are 35-1, so there’s a long way to go from 30-1 before these become viable bets.

On the hardways, when your payoff is 9-1 on hard 6 or 8, the house edge is 9.09 percent, and when you’re paid 7-1 on hard 4 or 10, the house edge is 11.1 percent.

What if you were paid the 10-1 and 8-1 you describe? Those happen to be the true odds of winning these bets. The house edge would be zero.

That reinforces the likelihood that the game is paying in odds-for-1.