Ask the Slot Expert: Does payback increase when I increase my bet or the denomination?

Question: In reference to my e-mail of hitting only one four-of-a-kind in 10 days, it is the honest-to-god truth. I was playing Double Double Bonus Poker most of the time. I played at the Golden Nugget downtown, where we always stay.

After gambling for 50 years I assure you I don't have to make up gambling stories.

Answer: I am truly sorry that there is no exaggeration in your tale of the shy quads. There's a reason there are tails on either side of the normal curve — rare events do occur. I thought I'd never get dealt a royal flush, for example, but it happened to me a few weeks ago.

The funny thing is that I was dealt the royal a few days after I had made a mistake in holding cards on a Three-Way Action Poker machine. One of the keys was a little finicky and didn't always work. I was dealt four tens and had gotten into a rhythm, so I didn't see that one of the tens wasn't held until it was too late. I lost the four-of-a-kind, but at least I drew to a full house.

When I was dealt the royal, the machine automatically held all the cards for me. I didn't have an opportunity to screw up that hand.

I had my own experience with shy quads playing 9/6 Jacks recently. I needed to play 2,000 hands for a promotion. Not only were fours-of-a-kind refusing to appear, full houses and, really, just about any paying hand were staying away from me. I can usually play for a while on a 20-hand buy-in, but I got only 52 hands from one buy-in.

One hits a four-of-kind once every 425 hands, on the average, in 9/6 Jacks. I didn't get my first four-of-a-kind until hand 689, which is not unusual at all. The quads came more frequently after that and I ended up hitting five of them, for an average of 1 in 400 hands.

Let's assume you played 2,000 hands a day for a total of 20,000 hands during your vacation. One hits a four-of-a-kind about once very 418 hands in Double Double Bonus. The probability of hitting exactly one four-of-a-kind in 20,000 hands is 0.0000000000000000000728. Very unlikely, but not impossible.

The more you play, the more unusual events you'll see. I'm sure you've seen many weird coincidences in your 50 years of play. Too bad you couldn't have experienced a glut of quads instead of a dearth on that trip.

Question: Does the long-term payback drop the more you bet or stay the same across the board?

Question: On machines that let you choose the denomination you want to play, does the return percentage change when you change denomination?

Answer: I put both of these questions together because the answer is the same for both: Maybe.

Starting with the first question, I've never seen a machine on which the long-term payback goes down when you increase your bet. Even on Buy-a-Pay machines (machines on which an increased bet activates additional winning combinations), the long-term payback goes up when you increase your bet. If an increased bet doesn't activate any new winning combinations and it doesn't give you a bonus on one or more winning combinations, then the long-term payback is the same no matter how much you bet. On those machines, I usually bet the minimum and only increase my bet if I happen to hit a hot streak.

On multi-denomination machines, the long-term payback may increase with the denomination. We can certainly see that on multi-denomination video poker machines. The pay table for quarters and up is frequently better than that for nickels. Similarly, the dollar pay table may be better than the quarter pay table.

The potential for increased payback with increased denomination exists on a multi-denomination slot too, but unlike with video poker, we have no way of knowing whether the payback has increased.