Q. Tell me something about slot machine odds and bonuses. I was playing for a while, and it seemed like the bonus wasn’t happening very often. I spotted a guy with a name tag that said slot supervisor, and asked him how often a bonus was supposed to come up. He said no set time, but he thought the average was about once in 80 plays.

I went back to play and counted. It took 224 spins before I went to the bonus. How is that even possible if it’s supposed to come up once per 80?

A. Results are random, and every result is possible on every spin. If the odds are 1 in 80 of going to the bonus round when you start, they’re still 1 in 80 if you’ve gone 80 spins without a bonus, or 100 spins, or 224 spins. Over a very long time, the odds of the game will lead toward about 1 spin per 80, taking you to the bonus round.

To illustrate, I’m going to make up an oversimplified example.

Imagine you were rolling an 80-sided die, with spaces numbered one through 79 and one space marked “BONUS!”

You could have a chart giving you a slot reel combination for each number. No. 1 could be five ravens, No. 2, five unmatched symbols, and so on. When the die landed on BONUS! you’d get to play a separate game to accumulate extra credits.

The first time you rolled, chances would be equal of the die landing on each space.

The second time you rolled, your actions would be exactly the same, and the chances for each space would still be equal.

No matter how many times you rolled and how long you went without a bonus, you’d still be starting from scratch on the next roll. If you rolled 224 times without a bonus, the chances on the next would still be 1 in 80.

Slot machines are more complex, with many more possible outcomes. Instead of one face among 80 on a die, 1/18 of thousands — or even millions, in the case of big jackpot games — of combinations will take you to the bonus.

You are a 79-1 underdog of going to the bonus on each spin. That makes long bonus-less streaks not only possible, but inevitable. There’s a flip side. Given enough chances, multiple bonus events within a few spins also are not only possible, but inevitable.

Q. I was at a Three Card Poker table where the dealer kept exposing his bottom card. I could see one card on almost every hand.

There has to be a way to take advantage of this, right? Don’t tell me to warn the dealer he’s exposing his cards. That’s not happening.

A. I’ll give no such warning. In cases about hole card play, courts have upheld players’ right to use the information offered by exposed dealer cards.

Michael Shackelford has a page about Three Card Poker hole card play at WizardOfOdds.com. I won’t go into all the details here, but here’s a quick summary.

Instead of using the basic strategy of following your ante with a bet whenever you have Queen-6-4 or better, you should bet on any hand if you see the dealer has any card from two through Jack.

If the dealer has a Queen, King or Ace, then you move the bet threshold up to better hands. With a dealer Queen, bet on Queen-9-2 or better, and make that King-9-2 or better vs. a King and Ace-9-2 or better vs. an Ace.