Expert Strategy has always been about the long run. Occasionally, someone has come along and tried to knock it by stating the long run is so far out there that striving for it is a fool’s errand.
Obviously, I disagree.
If it truly took a lifetime of playing, I might agree. But this is simply not the case. I can’t tell you exactly how long it takes to get to the long run. First of all, the results depend greatly on the specifics of each game. Second, the math simply doesn’t work like this.
Technically, the long run never officially arrives. But, strangely enough, it doesn’t take all that long to get close to it. This seems like a paradox, but it isn’t. In probability, there is something called a confidence interval.
I avoid getting into deep math concepts in my column and prefer to put these things in laymen’s terms. A confidence interval is given as a percent. We might say if you were to play blackjack for 1 hour you have a 95% chance of getting within 5% of the theoretical payback (just to be clear, I just made the specific numbers up).
What does this mean? The payback of blackjack is about 99.5% (depending on shoe size and specific rules). This means if you were to play one night a week for the next 20 years, and keep tabs of your results, you’d begin to notice your overall results keep getting closer and closer to 99.5%.
In any given week, it might get further away, but if you were to plot out each month (or 3 months), you’d notice it gets closer and closer. After several years, you’d find the overall results are almost assuredly between 99.4% and 99.6%.
Blackjack is a very low volatility game. It is hard to win or lose a lot (relative to your wager) over a few hours. There is no big hand to turn your night around. It is a lot like flipping a coin.
There is a great big math calculation that can state the probability your results will be within a certain percent of that 99.5% based on the number of hours you have played. This is our confidence interval. If 1,000 people were to also play blackjack for one night a week for 20 years we should see a clear pattern.
If our math tells us there is a 95% probability that after one year the player should be within 2% of our theoretical amount, it should mean 950 of these players after one year will be between 97.5% and 101.5%.
After 20 years, we would actually have 20,000 samples to look at; 19,000 of these samples should show a payback of between 97.5% and 101.5%. But the math can go further. It might be able to tell us there is a 99% probability the payback will be between 95.5% and 103.5%.
So, now we would be able to expect that 19,900 of our 20,000 samples will be between this amount. Or, the calculation might tell us that over a 5-year period there is a 99% probability the player will be between 98.5% and 100.5%.
What does any of this do for you, the player? These calculations give us some idea of what we can expect over time. Video poker is far more volatile than blackjack. As a result, the numbers will not look nearly as “tight.”
If you played video poker one night a week for 20 years, the range for a 95% confidence interval is going to be much bigger than it is for blackjack. It might be 4 or 5% away from the theoretical payback instead of only 1-2%. But the concept is still the same.
And, it will not be a range of 20-25%. On any given night, your payback might be 80%, but if you were to track your payback over 20 years, you would see a similar pattern to the one I described for blackjack.
Jacks or better video poker also has a 99.5% payback. But, with blackjack, you’ll probably be within 2 points of that at the end of year one. With video poker it might take 2-3 years. But, you will notice over time the cumulative payback is slowly moving closer to 99.5%. It will go up one week. It will go down one week. But, little by little, you’ll notice it getting closer and closer.
Over time your payback will begin to approach the theoretical payback for the game you are playing given the strategy you are using. On any given night, this might work to your advantage. But over time, your true payback will begin to approach the theoretical associated with your strategy. This means less money in your wallet.
Speaking of “less money,” the postal service raised their rates this past week. For a couple of years, I have been offering our best video poker books (Winning Strategies for Video Poker, Video Poker: America’s National Game of Chance and Expert Video Poker for Las Vegas) to GamingToday readers for $5 per book. With the postal increase, I just can’t keep the prices at this level anymore. The prices will be increasing at the end of the month (January) to $7/book or all three for $20. They retail for $15.95, $19.95 and $9.95 respectively. But, for the next two weeks or so, you can still get them for $5/book. Send a check or money order to: Gambatria, P.O. Box 36474, Las Vegas, NV 89133.
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Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Email: [email protected].