video poker problem

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bstillmatic

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Jul 20, 2019
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Hello math wizards,

I play a video poker game called full pay deuces wild. It's a positive return game if played correctly(which I do) at 100.76%. I've played 2,028,269 hands and I'm 25 deuces below expectation. You should be getting 4 deuces once every 4,909.1 hands on average. Let's just say expectation is 50 million hands. Is there a mathematical limit to have bad it can get? thanks.
 
Not sure what you mean by mathematical limit. Look up the distribution graph for your scenario. It will be some sort of bell curve, I guess. The graph should have the maximum at the math expectation value and go down as you move away from it the left and right. It doesn't suddenly stop at some limit. You are just less likely to get the outcome the farther away it is from the math expectation.
 
Tks lev888..I just read an article where it says the absolute number of deuces will never be theoretically where it should be, but the percentage will as the sample size grows.
 
See "Law of Large Numbers".
The language is bad.
The ACTUAL result MAY be the same as the THEORETICAL result, at times.
The ACTUAL result SHOULD not wander very far from the THEORETICAL result, but it may wander far enough to offend your sensibilities, at least for a short time.
The use of the word "never" is inappropriate.
Your process is memoryless. Past results say nothing of future results. p(getting worse than you can imagine) > 0
 
Is it possible to calculate exactly how far the actual result can wander from the theoretical result? For example using a mathematical formula one can say that after 4 million hands you should be no more than 50 deuces below expectation? Or is this impossible to determine b/c past results say nothing of future results? tks.
 
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Your selection process is memoryless. Your accumulation of results has a memory.

Your accumulation (observed frequencies) will result in counts that can be compared to theoretical probabilities. The expected deviation of one from the other should decrease with increasing sample size.

I would be surprised to hear that you could establish "no more than". You can establish a probability of "no more than", but that probability will not generally be zero. p(more than 50 below | 45 rounds) = 0 :) This is why I say, "not generally".
 
Have you read up on the Law of Large Numbers? That would make this easier to discuss!

"According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed."​

There are a lot of weasel-words there; nothing can be said with certainty, only that it gets more and more likely that results will be reasonably close to the expected as you repeat more times.

bstillmatic said:
Is it possible to calculate exactly how far the actual result can wander from the theoretical result? For example using a mathematical formula one can say that after 4 million hands you should be no more than 50 deuces below expectation? Or is this impossible to determine b/c past results say nothing of future results? tks.
Click to expand...
Note your words I marked above. You have asked two different things.

How far can the results be from theoretical results? All the way! It's possible to have no deuces at all!

How far should it be? That depends on what you mean by should. It is possible to calculate the probability of a particular deviation; or you could calculate how close you can expect it to be with a given probability (say, 95%, or 99.9999% of the time).

In answer to your original question, there is no limit, just a likelihood.
 
I didn't realize how important semantics are when it comes to math :) What's the correct wording to google how to calculate how close you can expect it to be with a given probability? Would it be this?
HOW TO CALCULATE STANDARD DEVIATION IN A STATISTICAL DATA SET
 
Correction: p(more than 50 below | 12 rounds) = 0

I don't do cards or gambling at all, so I sometimes forget the parameters.
 
hey tkhunny--forgive me..I'm a math noob what does this mean: p(more than 50 below l 12 rounds) = 0
 
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