Are You Guaranteed a 97% Return on a 97% Video Poker Machine?

I was playing video poker with a complete newbie (recent grad in economics/data science, no exposure to gaming industry) and a former physicist (not a new player, but only a few years in the past in the gaming industry) and they both claimed the following was true.

“If one plays a million hands on the same 97% paytable, one would be GUARANTEED 97% of the total bets.”

My take is this: A 97% paytable COULD pay 97% of the total bets, if one played using absolute and unwavering perfect strategy for that paytable AND one had a bit of luck. Nothing is ‘guaranteed.'”

Who’s right?

[Editor's Note: For obvious reasons, this answer is written by Bob Dancer.]

You are.

If you play one million hands, you’ll end up reasonably close to the expected return, assuming you’re playing perfect strategy. How close? Well, this is not a statistics class. Games with low variance tend to be closer to the expected return than games with high variance.

After 1,000,000 hands, approximately 25 royal cycles, the main determinant as to how close you are to the exact expected return is the number of royals you actually hit. If you hit exactly 25 royals, you’ll be really close to the 97% expected return. But you’re a big underdog to hit 25 royals exactly. You’re essentially equally likely to hit 24 royals as you are 25, and anywhere between 20 and 30 is reasonable.

Anyone who says you’re going to hit exactly 25 royals over 1,000,000 hands, guaranteed, is wrong. It doesn’t work that way.

But 25 is the still the most likely number of royals to be hit in 1,000,000 hands.

Your phrase, “Nothing is guaranteed,” is technically correct, but that’s a lot different than saying, “You don’t have any idea of how it’s going to turn out.” You do have a pretty good idea. You have about a 38% chance of being within one standard deviation, 5% chance of being within two standard deviations, and a 1% chance of being within 3 standard deviations. How close is one standard deviation? Well, it depends on the game. The standard deviation is the square root of the variance, and video poker games differ greatly in the size of their variance.

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Dave_Miller_DJTB Mar-13-2021

Math?

I'm not that big with the math of Standard Deviations and Variance, but didn't you mean to say that there's a 5% chance of getting BETWEEN ONE and two DSs, and 1% of BETWEEN TWO and 3 SDs?

Also, what neither Bob nor the questioner mentioned is that it's possible to end up with more than 97%. If fact, it's almost equally possible to end up with 98% as it is to have 96% etc.

Jerry Patey Mar-13-2021

Payback

Answer is no. However if you play to infinity you might!!! Problem you do not know where infinity is. Also there is no such thing as RNG so answer is no or at least should be

[email protected] Mar-13-2021

To Dave

Actually, the correct way to state it is that you have a 68% chance of being within plus or minus one standard deviation of the mean, 95% chance of being within two standard deviations of the mean, and 99.7% chance of being within three standard deviations of the mean.  All this is assuming a normal distribution, but for video poker a normal distribution is a reasonable assumption.  So actually the 5% is the probability of being outside of 2 standard deviations of the mean (plus or minus) and 1% (really 0.3%) of being outside of 3 standard deviations.  Since normal distributions are symmetric, the probability of being above and below the mean is equal, so in the one standard deviation case the probability of being above the mean by up to one standard deviation is 34% and the probability of being below the mean by up to one standard deviation is also 34%, for a total of 68% between plus or minus one standard deviation.  I suspect Bob's 38% number was a typo.

[email protected] Mar-13-2021

To Jerry

Actually, there are true RNGs - the machines that select Keno numbers or lottery numbers from ping pong balls are truly random.  Likewise, casinos could have a giant centrally located machine picking numbered pills from a giant tub and sending the results to all the slot and video poker machines on the floor.  However, the pseudo random number generators used in video poker machines are "close enough" so that a user is not going to be able to discern the difference.

Deke Castleman Mar-13-2021

This in from Chris via email

Love the QOD, but I think you’re close on the math, but not quite right.

You should have approximately 68% chance of being within 1 standard deviation high or low (it’s actually a 2 standard deviation span) of the mean.

The 5% chance refers to being outside +/-2 standard deviation range (again actually a 4 standard deviation span). That would be a 95% chance of being within that range.

The 1% chance of being within +/-3 standard deviations (a 6 standard deviation range) isn’t right either (and it’s rounded kind of funny). It’s actually a 99.7% chance of being within that range. More like 0.3% chance of being outside that range.

CLIFFORD Mar-13-2021

The sure bet

Playing VP and slots on your computer...you never loose...

Larry Stone Mar-13-2021

100% guarantee!

if you play one million hands of video poker you're 100% guaranteed to get sore fingers!  and a headache too.

Derbycity123 Mar-13-2021

Math vs VP Machine

In math the chance of being above and below are the same but this is a VP machine. So you can only make mistakes that will increase the below and not the above. Luck as in more than 25 Royals or more than normal 4 of a kinds could put you above 97%. Depending on your play you could be 99.5 % accurate. This would move the whole bell curve down to 96.6%.

Mark Mar-13-2021

obviously it isn't guaranteed

I don't know how any sane person could possibly think a certain return is 'guaranteed' after a million (or any finite number) of hands.

If it were, you're essentially saying that if you'd played through 999,999 hands and you were 4000 credits away from being at 97% through 1M hands, that your next hand is guaranteed to be a royal.  Logically this makes no sense.

Jackie Mar-13-2021

I wonder why

nobody stated the obvious.

Your answer is the most correct but still you would have to play on one VP machine with that paytable exclusively, never leaving it until the million hands have been played. You would have to make note of your total coin entry for those hands along with total winnings to actualize how close you came to the 97%.
Changing VP machines to another with the same paytable or going to another casino with the same VP machine will severely screw up your rate of return.

You started with a bankroll to play that VP machine.
Those laminated cards that tell you the best way to play hands dealt helps you to lessen how much of your bankroll you will lose otherwise.  So Perfect Play only helps you to not lose as much of your bankroll versus regular pay and in no way effects the rate of return over a million plays.

The RNG does not effect the rate of return.
It is how the casino programs the amount of coins paid per hand that determines the rate of return.

Question of the Day - 13 March 2021

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