Quote:statman3. DorothyGale, who despite what she thinks of me, seems to be a competent C or C++ programmer.

You are in NO position to judge my skills and compliments from you aren't worth the electrons they're written with ... you couldn't program yourself out of a wet paper bag ... you couldn't even be bothered to double check your own results ... that program took me the better of 4 minutes to write and 90 seconds to execute ... by the way, it's a C program.

Quote:Here is what I think is some worthwhile reading from William Feller of Princeton University

This is just a brief discussion of inclusion/exclusion, which appears in countless books ...

Edit. Once again Statman deleted his post after my reply ... what a guy ...

--Ms. D.

Great work.

Quote:statman

The Pr that at least one of the numbers 0 through 37 will not be hit by the 200th spin can be expressed

as 1 - (1 - (37/38)^200)^38. This evaluates to 0.16793785. The Wizard gets 0.1698457.

Actually, that's not the probability that "at least one of the numbers will not be hit by the 200th spin". Here's how to break it down:

A. (37/38)^200 = probability that one specific number is absent for 200 spins

B. 1 - A = probability that A doesn't happen, i.e. the probability that one specific number appears at least once in 200 spins.

C. B^38 = probability that B (not-A) happens 38 times in a row, i.e. the probability that one specific number appears at least once in 200 spins 38 different times (38 sessions of 200 spins).

D. 1 - C = probability that C doesn't happen, i.e. the probability that one specific number does not appear at least once in 200 spins 38 different times.

The probability that "one specific number does not appear at least once every 200 spins for 38 sets of spins"

is not the same as the probability that

"at least one number does not appear over 200 spins".

So statman had perhaps the right answer to the wrong question. Regardless, neither question is relevant to the reliable detection of a biased wheel over 200 spins. You can't tell anything with one datapoint.

I think he had no idea who his audience was ...Quote:boymimboThis is a prime example of why I love this site. Someone called statman comes on and claims he's found something that hasn't been found in 150 years, provides the program. Buzzpaff flags, MathExtremists debunks, DorothyGale finds the bug in the program, debunks, and this guy deletes all of his posts.

Great work.

BTW, Guido was the 111! He made it all happen by requesting the data.

And MathE actually told him the solution early on, the multinomial distribution ... I actually looked that one up (I forgot about it) after M.E. said it ... bingo ... then he suggested summing over the partitions of M not containing N ... Yikes ... but it's the perfect solution. Ramanujan, where are you?

--Ms. D.

Quote:DorothyGaleI think he had no idea who his audience was ...

BTW, Guido was the 111! He made it all happen by requesting the data.

And MathE actually told him the solution early on, the multinomial distribution ... I actually looked that one up (I forgot about it) after M.E. said it ... bingo ... then he suggested summing over the partitions of M not containing N ... Yikes ... but it's the perfect solution. Ramanujan, where are you?

--Ms. D.

I am sure Statman learned something of lasting value.

I even sent him my Excel worksheet with the Wizards formula already set out.

So in the beginning it was the "Ask the Wizard" article and his excellent reply.

I remember when I tried to first duplicate the Wizard's answer, I came up with what MathEx described and exactly what the Wiz mentioned not to do in his article.

To do what Statman wants to do in a spreadsheet takes many hours, even with some VBA.

Would be faster to have a program run it.

But then, as ME pointed out, the results really do not have any true value in finding biased roulette wheels, other than saying I did the math correctly.

Some of it eventually may reappear on the web site of the

Rancocas Valley Journal of Applied Mathematics

Please flag this page so that it may be deleted.

Many thanks to those who have been helpful.

Of course you shouldn't claim anyone else had wrong results, because they weren't ... your results were wrong ... period. No round off error, no cancellation error, no double-precision error, no Autocad , no Maple, no compute algebra system -- just wrong. Your methods are wrong ... your results are wrong ... what a bunch of nonsense to try and blame it on something else when the blame is squarely on your lack of mathematical and programming skill ... accurate to 3 decimals is wrong ... not to mention how wrong your idea is from the start ... your conception that bias can be detected and exploited by your "method" is wrong ...Quote:statmanI'm sorry Shack didn't participate in this discussion - he could have been a great help. I went to him first. I think guido111 established that my tables are accurate at least to three significant figures, which is all you need for tests such as this.

I'm not claiming that anyone's results are wrong, but one thing you have to be on the watch for in experimental mathematics is rounding error and cancellation error. In using a spreadsheet or a compiler you will be computing with hardware double-precision floating point math. Single-precision hardware floating point math is used by vector drawing programs such as Autocad.

You will notice that in Shack's answer to the roulette no-hit problem he uses an alternating series. That is a situation where you have to be especially careful. The safest thing to do in such a case is to add the positive and negative terms separately and then compare them. Then you can tell how many places in your answer are good. Another way to avoid these demons is to use a a computer algebra system with exact math. I have been using Derive for twenty years. I still use it, but I also use Maple, which has good programming capabilities. Answers often come up in the form of a rational number: an integer of hundreds of digits divided by another integer of hundreds of digits, but it is exact.

I did post tables of simulated games with 00 rigged to have a strong favorable bias. One set was for 1,000 spins and the other was for 200 spins. In both cases the tables found the biased number three times out of four and did not return any false positives. Rude responses caused me to delete this material and everything else and it will not be back. Remember what Jesus said about pearls in the sermon on the mount? I think the tables have been shown both to be useful and to be accurate enough to remain on the bookshelves. Perhaps I shall be able to improve them. Perhaps someone will be able to verify them more precisely.

Then you have the nerve to lecture us on methodology as if you have a clue ... and then you have the cowardice to delete all of your faulty logic and talking down to experts from the site ... a little humility, somewhere, would get you started in the right direction ...

Rude responses caused you to delete? Really? They reached through the screen and pushed the delete button? No, you chose to delete ... it was your choice ... you made the decision fully and on your own ... no one here caused you to do anything ... take some responsibility for your actions, come on, be an adult ...

I'm quoting you in full from now on ...

You are a piece of work ...

--Ms. D.