Help Me Make Sense of This

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I received the following email. It was originally intended for the Gambling with an Edge mailbag, but I felt it was too technical to be discussed over a podcast:

I know video poker has a ton of variance, but I recently endured a hellish series of events on $5 NSU Deuces Wild at a tribal casino. 

I played 67,800 hands ($1,695,000) and lost $102,375. I hit zero royals and two sets of four deuces.

The variance of this game is supposed to be 28.78. How does this translate to dollars and cents?

Losing five royals worth of money in 67,800 seems impossible. 

I think I’m playing perfectly. I’ve been a successful AP pro for 13 years, so we can assume I’m not making beginner mistakes.

Please help me make sense of this.

Wow, you’ve run very badly. Let’s look at how badly.

Most of the variance in NSU Deuces comes from royals and quad deuces. Let’s look at them individually. The royal cycle is 43,456 hands. You’ve played approximately 1.5 royal cycles. Having zero success in 1.5 cycles happens about 22% of the time. No big deal, especially if you’re hand-picking a session after it’s over. All players go through many 1.5 cycle dry spells over their playing career.

Now let’s look at quad deuces. The cycle here is 5,356 hands, and 67,800 hands is 12.65 cycles. Having two or fewer successes in 12.65 cycles happens about one time in 3,900. This is pretty unusual. 

Having this level of bad luck at royals at the same time as this level of bad luck at quad deuces is about 1-in-17,700 event. Pretty unlikely. Keep in mind, though, that whenever you’ve held two royal cards and drawn the three perfect cards to complete the royal is a 1-in-16,215 event. These two events are of similar size. Over my career I’ve connected on several hundreds of these royals. I don’t know how much video poker you’ve played, but I’m willing to bet you’ve had lots of these too. Play enough and these rare events come about a number of times.

You mentioned this game has a variance of 28.78. That’s true, except that’s the one-coin variance, which is the typical way video poker variances are displayed. To compute the variance for five coins at a time, you need to multiply by five, giving you about 144.

Being down 1.5 royals is worth $30,000 on this game. Being down 10.6 sets of deuces is worth another $53,000. The total of $83,000 in the dumpster is about 80% of what you’re down. That’s also a lot of wild royals (at $625 per), quints (at $400 per), and smaller hands that you didn’t show up on your machine. Unusual to be down that much, but obviously not impossible

All told, it’s a lot to be down. (You already knew that.)

The next question that probably comes to your mind is: Is the machine fair? Does the fact that it’s at a tribal casino suggest more chances for casino hanky-panky?

First of all, these are IGT machines. I trust them. A casino can change the pay schedule on them, but it can’t open up the machine and turn a “tighten up this sucker” switch.

Although you’ve run bad, this was “only” one and a half royal cycles. We’ve all had longer dry spells than that, although perhaps not accompanied by such a long deuce-less result as well. I’ve played at that same casino, about 45,000 hands on those machines, and am slightly ahead on this game. I’ve hit one royal (pretty much spot on expectation), and ten sets of deuces (which is slightly more than expected.) I know other players who regularly play there, and their results seem to be “within reason.”

So, I would conclude that you hit a “once in a very blue moon” dry spell. It happens. It will happen again. If you’re not broke (losing $100,000 can do that to somebody), there’s no reason to cease playing that same game at that same casino.

As it happens, my latest trip to that casino playing that game generated a negative score. (Offset by a positive score the earlier time I played this game there.) On our next trips, yours and mine and others, if the negative scores continue to happen more than usual, I’ll begin to believe that something had changed, and it may no longer be a good play. But I’m nowhere near that conclusion yet. I’m planning considerable play on these machines in 2023. This is definitely a case of me putting my money where my mouth is.

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