Brimming with Confidence

            Expert Strategy has always been about the long run.  Occasionally, someone has come along and tried to knock it by stating that 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 that if you were to play blackjack for 1 hour that 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 that if you were to play one night a week for the next 20 years, and keep tabs of your results, you'll begin to notice that 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'll notice that it gets closer and closer.  After several years, you'll find that 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 that 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.  What this is telling us is that if 1000 people were to also play blackjack for one night a week for 20 years that we should see a clear pattern.  If our math tells us that there is a 95% probability that after 1 year the Player should be within 2% of our theoretical amount, it should mean that 950 of these Players after 1 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 that there is a 99% probability that 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 that there is a 99% probability that 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 throughout the year and over the 20 years, you will 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 1.  With video poker it might take 2-3 years.  But, you will notice over time that 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.

            But, again, what does this do for you?  That's simple.  Over time your payback will begin to approach the theoretical payback for the game you are playing given the strategy you are using.  There is only ONE strategy that maximizes this theoretical payback.  Any alterations from Expert Strategy will result in a lower theoretical payback.  On any given night, this might work to your advantage.  But over time, your true payback will begin to approach the theoretical payback associated with YOUR strategy.  By very definition, this means less money in your wallet.