This might be a bi-modal bias due to alternating use of large and small ball by the croupier.

>if there is a wheel bias because its out of balance,

This would be detectable by octet analysis.

Best bet: don't waste time trying to prove either of these very rare events.

Quote:statmanIn his paper, Murphy gives a circular chart showing unusually high frequencies for the the numbers 0, 25, and 29, however he doesn't say exactly what those frequencies were. That kind of information would be useful to me. Even with a perfectly true wheel it is possible to look back at the record and say you could have made money by betting on such-and-such a number, however with a perfectly true wheel there is no way of knowing in advance what that number would be. In order to make money consistently on a number, that number has to have a probability of coming up greater than 1/35.

MathExtemist says that your computations will be precise if you are working only with integers. That is true if they remain as integers, however the majority of mathematical environments have a limit on the size of an integer and if exceeds that maximum the variable will be converted to a floating point number and only the first fifteen or so digits will be retained. The rest will become zeros. The Python programming language has a large integer data type that will preserve all digits regardless of the size of the number. The computer algebra systems (CAS) also will do this. The top ones are Maple and Mathematica. These are pricey, but there are also some free ones. For details see the "Comparison of Computer Algebra Systems" topic in Wikipedia. The CAS's also will preserve the precision of rational and irrational numbers. If the square root of 2 is entered or is arrived at in the course of a calculation it will be kept as "sqrt(2)" in all further calculations. Sqrt(2) is accurate to an infinite number of decimal places. When the calculation is finished the CAS will approximate it to a number of decimal places specified by the user, which can be in the thousands. I recommend calculating an alternating series using a CAS lest some of the positive and negative terms cancel and produce garbage digits in the answer.

I don't know why I keep reading this junk.

Wait a sec...Quote:FleaStiff>If there is a wheel bias because the slots are not all the same size

This might be a bi-modal bias due to alternating use of large and small ball by the croupier.

>if there is a wheel bias because its out of balance,

This would be detectable by octet analysis.

Best bet: don't waste time trying to prove either of these very rare events.

Are you saying that a bias is a rare event, or that if there is a bias, it would be different than what I described?

If it's the latter, please elaborate, because the two types I described are all I can imagine.

Quote:statmanIn his paper, Murphy gives a circular chart showing unusually high frequencies for the the numbers 0, 25, and 29, however he doesn't say exactly what those frequencies were.

Yes he does. Re-read the article -- it's on the first page, bottom of the 2nd column.

Quote:MathExtemist says that your computations will be precise if you are working only with integers. That is true if they remain as integers, however the majority of mathematical environments have a limit on the size of an integer and if exceeds that maximum the variable will be converted to a floating point number and only the first fifteen or so digits will be retained. The rest will become zeros. [snip] I recommend calculating an alternating series using a CAS lest some of the positive and negative terms cancel and produce garbage digits in the answer.

You misquote me. I said "exact", not "precise". Exact has one meaning; precision is a relative measurement. Double-precision floating point representation is plenty precise to handle the sort of calculations we're talking about. The few results from you that I've seen, however, are incorrect by fully 1% or more. That cannot be explained by rounding error, but it is neatly explained by the fact that you used the wrong formula. See this post for the difference between "one specific number appearing N times in 38 sessions of M spins" vs "any of 38 numbers appearing N times in one session of M spins".

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.

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.

sucker bought it and then complained that he only bought that piece of shit because he trusted this forum.

THIEF

Good name in man and woman, dear my lord,

Is the immediate jewel of their souls.

Who steals my purse steals trash; 'tis something, nothing;

'Twas mine, 'tis his, and has been slave to thousands;

But he that filches from me my good name

Robs me of that which not enriches him,

And makes me poor indeed.

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.

Here are three pieces of advice.

First, check your work via simulation. You have a fair wheel simulator, use it. You won't get close to 19.75%.

Second, re-read the Wizard's article on this problem. You've gotten things wrong.

Third, in view of the above, check your ego. Miscalculations and overwrought proclamations do not qualify you as one who can credibly lecture the members of this particular forum.