## Tuesday, August 16, 2011

### The Payback Mirage

The battle between the short-term and the long-term, where gambling is concerned, is an epic struggle and so totally misunderstood by most.  Why is this a problem?  Because it is critical to understand what to expect when you’re playing.  If you don’t, you may begin to believe that something is wrong about what you are doing and this can lead you to deviate from proper play.  When you do that, you may help yourself in the short-term, but this will eventually give way to damage done in the long run.

To try and prove this point, I ran some video poker simulations.  I played 100,000 3-hour sessions of video poker.  I assumed each session consisted of 2100 hands of video poker (700 hands per hours).  I started with a full-pay jacks or better game.  What did I find?

Well, in total, 210 million hands of video poker were played.  At the end of all these hands, the payback was essentially exactly where we would expect it to be – 99.52%.  If the simulation used max-coin quarters, the result would be a loss of about 1.26 million dollars.  Of course, based on 210 million hands, it would also take 34 years of 24 hour/day play to get to this point.  Quite frankly, this is MORE than a lifetime of play.

When we look at some short term results, we find that the Player will lose about 68.5% of the session and win 31.5% of the time.  So, even when playing a full-pay jacks or better machines, the Player can expect to lose 2 out of 3 times when playing for 3 hours.  Even though the edge is less than 0.5% for the house, the Player will walk away a loser far more often than a winner.

So, is it any wonder that I advocate playing games with a 100% payback or better.  To prove this point, I created a fictitious machine whereby the payouts are the same as full-pay, EXCEPT the Four of a Kind pays 30 instead of only 25.  The simulation showed that after 210 million hands, the overall payback was 100.70%, which is what we would expect.  So, this game is a bit more positive than full-pay is negative.  Thus, the results of our sessions should probably be flip-flopped from our full-pay version, right?

Not exactly.   We find that even with the payback of 100.7%, the Player will STILL lose 58% of his sessions!  That’s right.  The Player will still lose nearly 6 out of 10 sessions while playing a game that is significantly in his favor.   Despite this 1.2% turnaround (from 0.5% negative to 0.7% positive), the Player will wind up winning only an additional 1 session out of 10 and still lose a significant majority of his sessions.  How can this be?

These results occur because when playing video poker, our wins will, on average be larger than our losses.  Of course, even this is a bit deceiving.  What really happens is that every so often we have a HUGE victory, while our losses tend to be more moderate.   In sessions where we hit a Royal Flush, our winnings will be far larger than virtually ANY loss we would ever have.  As a result, we lose more sessions than we win, but those big winning nights tip the scale back in our favor.  When we play a 99.5% game, it only is enough to bring it back closer to even.  If we play a game with a payback of OVER 100%, those big wins are enough to turn the game positive in the long run, even if in the short run we are losing more than winning – in terms of sessions, not dollars.

As I said earlier, it is critical to understand how this all works.  Otherwise, it is way too easy to simply give up on playing the right strategy if you feel you are losing too often.  While we all play in ‘sessions’, in the end, all that matters is how we are doing over the long run.  In the second example (the 100.7% game), would you really be upset to lose 58% of your session, but  wind up winning 1.85 million dollars over a lifetime?

One last point for those of you who would try to use the information here as ‘proof’ that the long run is really too long.  I ran each machine for a mere 1000 sessions or 3000 hours of play.  This could be 3-5 years of play for a local in Las Vegas.  While there is a bit more deviation from the long term expectations, on the whole the numbers still prove my point.  The overall paybacks for the games were 99.26% and 100.49% respectively.  The win frequencies for a session were 70.8% and 58.7%, respectively.  So, even over a much shorter period than multiple lifetimes, we will begin to see a pattern develop whereby the Player loses more sessions than he wins, but can still end up a winner in the long run.