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.
All of the software that I have shows the 1 coin variance at 25.7803. Why are you showing it at 3 points higher? Was this a 3 point hiccup? This should put your 5 coin total variance at 128.9.
I’m just not a big fan of deuces wild.
I hear it’s a lower variance game but I like 8/5 bonus poker.
Put another way,: He played 67,800 hands at $25/hand on a game with standard deviation per play of about 5.077.(sqrt of variance)
Standard deviation of the total session is $25*5.077*SQRT(67,800) = $33k
Your expected loss for the play would have been about $4,600
So, your actual result is about 3 Standard Deviations unlucky.
This happens about 0.15% of the time, if memory serves.
Pretty rare. Assuming you play a lot, such results will happen, but at some point a more likely conclusion is something funny about the game, whether it be the machine itself or your play.
The victim in this story seems typical of the many VP players whose attitude is that the result of play is going to be right on the EV. They are not really thinking that a horrible result can occur. So when a horrible result does occur, they are surprised, and get emotionally wiped out. Instead, we all should NOT expect the EV or a plus-result to happen, but rather should have the attitude that ANYTHING can happen, and might happen. That way, nothing will surprise us, and we won’t get emotionally blindsided.
Is this at n.Carolina by any chance ??
And I thought I was running bad by not hitting a royal flush after about 40’000 hands I played during my last trip and “only about 7x deuces” in different variations of Deuces Wild. Fact is, I lost big playing the dollar denom and won my average sets of deuces in the quarter denom afternoon game before raising the stakes. That was the mistake I did. I should have played nothing but 50 cents denom to get a proper result. I would not like to go through such a big amount of money within 67’000 hands played. I bet this was a very frustrating experience.
From Switzerland
Boris
When you multiply the bet by 5, you multiply the variance by 25. The standard deviation is multiplied by 5, which is the unit relevant measure of volatility.
You could use the central limit theorem to estimate the probability of being this far below your ev. I’m not sure if this is enough observations to make the approximation accurate.
According to wizard of odds, the standard deviation of NSU is 5.077845 units. The standard deviation of 67,800 hands is 5.077845*sqrt(67,800)=1322.19 units. The emailer lost 4095 units. The EV of the number of hands of NSU is -184.21 units. The number of units below expectation is -3910.79. This is -2.96 standard deviations below expectation. A result this extreme or more happens 1 in 649 times assuming a normal approximation.
Apologies if any of this math is wrong, I didn’t spend a lot of time double checking it. But it should show someone the steps necessary to figure this out.
Have any of you guys been able to mathematically convince yourself that the casino had been altering the randomness?
If so, we’d all love to know the story and what you did about it.
I remember a while back Bob telling a story about a pizza chain or some kind of mom and pop chain that were altering the possibility of a royal coming. I believe they were jailed.
Any other stories?
To Al “The victim in this story seems typical of the many VP players whose attitude is that the result of play is going to be right on the EV…..(continued) ”
This entire comment is completely false. I am the “victim” here. And I am not claiming to be any victim. I am not concerned about a bad run. My only concern is that IS THE GAME FAIR? I was not quite sure how to calculate the SD on this game so that is why I was unsure of exactly how bad this run has been. Knowing now that it is -3 SD makes me feel a tad better (was thinking it was much higher), but -3 SD is still on the cusp. My attitude is fine. Trust me, I am much more used to variance than you. I am just not clear on SD when it comes to VP and this run felt “worse than it should” in my mind. This post by Bob clears up some of the math and concern, but if after 20x this sample and the SD gets to -3.5, then something might actually be funky with these machines.