Faith in mathematics:"
Faith has nothing to do with it.
It is important to understand that a calculation of "percent payback" yields a prediction which is approached as the number of trials grows large without bound. That last is a fancy way of saying "in the long run".
In the short run, the actual consequence of a session will only approximate the long term prediction. It may be higher. It may be lower.
A group of short-term experiments will yield a distribution around the long-term prediction. The width of that distribution is determined by the statistical variance of the long-term prediction.
Two different video poker games may have somewhat similar long-term paybacks, but will exhibit quite different variances. This is sometimes called "volatility". When playing on a limited bankroll, other things being more-or-less equal, it is better to play a low-volatility game. For instance. Full Pay Deuces Wild has a higher payback than does Full Pay Jacks-or-Better, but the deuces wild game has a much higher volatility. This means your bankroll will experience wilder swings.
Having said all that, what exactly is "long term"? The only meaningful answer is that, the longer you play, the closer your results will approach the probability computation of "expected payback".
It is certainly true that, in a contest between you and the casino, the casino is hands-down playing in the long term. You are not.
One final note: It is also important to understand that, as the number of trials increases, the payback can be expected to approach the theoretical prediction, but only in relative terms. The absolute difference between the theoretical prediction, and reality, may diverge.
This is illustrated by simple coin tossing. The theoretical prediction is that in the long term, heads will equal tails. If you actually try this (or program a computer to simulate it) you will find, as the number of trials increases, that the percentage difference between what you get, and "50-50", decreases, but the absolute difference increases! This surprises some people who are statistically naïve.
But think about it. If at some point in the proceedings heads leads tails by, say, 10, then it is improbable (less than even odds) that the tails will ever catch up. This can be shown by arguing that a new sequence can be thought of as starting with heads already 10 ahead. The theoretical expectation is 50-50 FROM THAT POINT in the proceedings.
Hope this helps.
- - Norma Posy
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--- In vpFREE@yahoogroups.com, "bobbartop" <bobbartop@...> wrote:
--- In vpFREE@yahoogroups.com, "bornloser1537" <bornloser1537@> wrote:
>
>
> In some sense, in my opinion at least, it is good news. I think that all results have to be normalized, so that you are always matching apples to apples.
>
> My "rate of loss" seems to be going done the more I play, meaning my loss per unit time is decreasing, even though my rate of coin-in is staying the same.
>
> In your example, I have increased my coin-in by a factor 10 and (I play 10 times longer), yet my loss only went up a factor 3.
>
> What am I doing wrong?
>
> I know that I am a recreational player. But, that is exactly why this sounds like good news to me.
>
> ..... bl
>
For all of us who have WinPoker, it might be awakening to do simulations of 3 or 4 million hands. I've done that a lot, with many different games. When I do "only" a million hands, the results are typically higher or lower by about 3/4ths of a percent of what it's "supposed" to be. When I do simulations of 3 million hands, it's generally a lot closer to that number, but still can be "off" a little bit.
Anyway, do you know how much 3 million hands is in reality? That's a lot of playing. Do the math. That's playing full time like a job, maybe for about 21 months. And expect to have occasional periods of 200,000 hands where no royal is hit. That will test anyone's faith in mathematics.
-BB