Tough(?) roulette question

A friend of mine was claiming a virtual roulette wheel didn't have fair odds because it was "getting stuck" on various numbers. I wanted to explain that this is perfectly normal, but was having trouble figuring out the odds correctly. (He had seen like 3 pairs and 2 triplets in a short amount of time.) I think the "stuck" question can be answered by answering what is the odds of seeing X different numbers, say 14, in Y tries, say 20.

Presumably this is something like 37/37*36/37*...*24/37*(14/37)^6*"possible ways to do it", but how many ways are possible? Certainly it is not "20 choose 14". Or is there a better way to think of the problem.

Thanks!

The "virtual" wheel is no more stuck than a physical wheel would be and certainly an electronic wheel has no parts that could stick at all. Three pairs and two triplets on a physical wheel have a certain probability, why assume that some erroneous seeding value is being used on the electronic wheel if its not all that rare on a physical wheel?

Quote: ThaddeusB

what is the odds of seeing X different numbers, say 14, in Y tries, say 20.

Presumably this is something like 37/37*36/37*...*24/37*(14/37)^6*"possible ways to do it", but how many ways are possible? Certainly it is not "20 choose 14". Or is there a better way to think of the problem.

Thanks!

https://wizardofvegas.com/forum/gambling/other-games/3274-roulette-math-question/
LINK HERE
I started a thread about this and weaselman answered how to set it up in a spreadsheet. The first few columns returned the correct probabilities but failed after that. I just never got back to that spreadsheet and weaselman for a solution.
Looking into it more I found that the probabilities for repeating numbers change according to what spin they are on so it is not just an easy combinational solution.

I downloaded the Wizards 1 million roulette spins and just created the probability distributions in Excel.

Here is for 20 spins: Hmmm. These are for American Wheel 38 slots... you may be looking for the Euro wheel. I do not think the probabilities are too much different.

So, exactly 14 unique numbers in 20 spins shows 13.43%
20.26% for 14 or less unique spins (more repeats)

I found the Euro distributions.
Here is the European Wheel. Not too much difference

One day I will clean up the file I have and post it for download in my Blog.
I have the distributions for spins (showing uniques and repeats) from 1 to 100, each spin and from 100-350 every 10 spins. I do not remember doing all those. Must of had a lot of free time one evening. I will work on cleaning up all the worksheets.

Re: FleaStiff - The point of the question is to show that these "weird" occurrences in fact are perfectly normal, not the opposite. Well actually the point was to figure out how to set up this probability question (other than Monte Carloing it) b/c it was puzzling me. The specific example provided was just a setup for clarity purposes.

guido111, thanks for pointing me in the right direction.