Wasted royals?

I hit a royal flush while playing video poker on my home computer last night. Did I waste one of my royals?

I hear this question once in a while. Some people say that they don't want to practice playing video poker on their home computers because they're afraid that they'll use up their "royal allotment" while playing for free.

Video poker columnist and teacher Bob Dancer described a similar situation in one of his columns. Bob wrote that one of his students said that he hopes that he doesn't hit a royal when he has fewer than five coins bet on a hand so he doesn't waste one of his royals.

The logic goes something like this: Royals occur only once out of about 40,000 hands. If I hit a royal at home or when I'm playing short-coin, I'll have to play another 40,000 hands before I'm due for my next royal.

It is true that the odds of hitting a royal are about 1 in 40,000 hands in most video poker games. But it is important to note that the odds are an average, not a hard-and-fast rule. Out of many hundreds of thousands or millions of video poker hands, 1 in 40,000 will be a royal flush. Any particular set of 40,000 hands may have zero, one, two, or even more royal flushes.

Here are more examples of thinking of the odds as an average:

• Of all the hands played on any particular video poker machine, 1 in 40,000 will be a royal flush.
• Of all the people playing video poker this very second, 1 in 40,000 will get a royal flush.
• Of all the hands of video poker you will play in your lifetime, 1 in 40,000 will be a royal flush.
• Of all the hands of video poker you play on a real video poker machine, 1 in 40,000 will be a royal flush.
• Of all the hands of video poker you play on your home computer, 1 in 40,000 will be a royal flush.
• Of all the hands of video poker you play at short-coin, 1 in 40,000 will be a royal flush.

Here's one more way to look at the odds as an average: Of the next 40,000 hands played at your favorite casino, we expect to see 1 royal. We may see 0. We may see 2 or more. But we know that when we look at the number of royals in this group of 40,000 hands, and the number of royals in the next group of 40,000 hands, and the number of royals in the next group, and the next, and the next, ad infinitum, the number of royals per 40,000 hands will keep getting closer and closer to 1.

The odds of hitting a royal are the same on every hand you play. The odds don't change based on how many royals you've hit this day, this week, this month, or this year. The odds also don't change based on how long it's been since you've hit your last royal. So practice playing video poker at home; you won't be wasting any of your royals.

I found myself making the mistake of wishing for a lower-paying hand this past weekend. My favorite game is 9/6 Jacks or Better. The best game this casino offered was 8/5 Jacks, so I had to play that machine. (Yes, I had to play. I was evaluating the casino's slot club.)

A few times when I was dealt two-pair, I found myself hoping that I didn't get the full house. I didn't want to be reminded that I could have been paid $45 for the full house had the pay table been better. Then it occurred to me how stupid it was to wish for a $10 payout instead of a $40 payout. It's not like any full house I hit on this machine would be one less full house I would hit on a 9/6 or 10/7 Double Bonus machine. So I started rooting for the full houses and flushes and even got a few, too.

By the way, I have had some sessions in which I never hit a flush or full house at an 8/5 machine. For these sessions, it didn't matter whether the machine was a 9/6, an 8/5, or even a 6/5 machine. I would have won (lost, actually) the same amount of money regardless of the pay table.

Over the long run, you'll win more money from the higher-paying machine. Over the short run, the volatility inherent in video poker has more of an effect on your results than the pay table.