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 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 three-hour sessions of video poker. I assumed each session consisted of 2,100 hands of video poker (700 hands per hour). 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. 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 the player will lose about 68.5% of the sessions and win 31.5% of the time. So, even when playing a full-pay jacks or better machine, the player can expect to lose two of three when playing for three 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 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 six of 10 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 one additional session out of 10 and still lose a significant majority. 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 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 sessions, but wind up winning $1.85 million over a lifetime?
One last point for those trying to use the information here as “proof” that the long run is really too long. I ran each machine for a mere 1,000 sessions or 3,000 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.
For more articles, check out my blog at gambatria.blogspot.com!