SOOPOO
SOOPOO
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September 30th, 2011 at 12:59:48 PM permalink
Quote: MathExtremist

What if I said that there's a roulette wheel in Nevada right now where the number 00 came up 9 times in the past 200 spins. Yes or no: is the wheel biased?



Maybe. But not likely.
MathExtremist
MathExtremist
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September 30th, 2011 at 1:24:27 PM permalink
"Maybe" wasn't one of the choices, though. According to statman, he has tables of statistics which detect bias over the course of 200 spins. I want to know what his tables say about the scenario where 00 comes up 9 times in 200 spins. Is that wheel biased or not?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
DJTeddyBear
DJTeddyBear
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September 30th, 2011 at 1:54:19 PM permalink
Well, not exactly 9 times out of 200, but any single number, 5 times in a row, will win the progressive jackpot for my Poker For Roulette side bet. (I figured it was time to slip in a shameless plug...)
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁 Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition. 🤗
guido111
guido111
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September 30th, 2011 at 2:08:51 PM permalink
Quote: MathExtremist

I want to know what his tables say about the scenario where 00 comes up 9 times in 200 spins. Is that wheel biased or not?


From statmans tables it shows a 0.81660 probability.
So I do not think that would show a bias.
My sim shows 0.8358
But you already showed that his formula is about a particular number and not just any number.

ME, just give statman a quick PM and I am sure he would email to you his Excel worksheet and Kindle file of tables as he did for me.

I am in the middle of a large math and music project and just do not have the time, at this time, to pursue this matter.

I am always interested in unique math solutions to interesting math problems, that is the only reason I became involved.

Enjoy
MathExtremist
MathExtremist
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September 30th, 2011 at 2:13:12 PM permalink
Quote: guido111

From statmans tables it shows a 0.81660 probability.
So I do not think that would show a bias.
My sim shows 0.8358
But you already showed that his formula is about a particular number and not just any number.


I'm interested in what is statman's interpretation of that number (whether it's 0.81 or 0.83) and what it means to his understanding of whether the wheel is biased.


Quote: guido111

I am in the middle of a large math and music project and just do not have the time, at this time, to pursue this matter.


To completely hijack the thread, that sounds really cool. Are you doing something with algorithmic composition?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
guido111
guido111
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September 30th, 2011 at 2:45:51 PM permalink
Quote: MathExtremist

I'm interested in what is statman's interpretation of that number (whether it's 0.81 or 0.83) and what it means to his understanding of whether the wheel is biased.

To completely hijack the thread, that sounds really cool. Are you doing something with algorithmic composition?


Statman uses a 150 spin and 9 times hit as an example in his document that does not show a biased wheel but he really does not get into what would be a wheel bias as far as I understand.

He continues with "We would have to see 11 or 12 on the same number to call it unusual."
0.36028 = 9 hits
0.05660 = 11 hits
0.01806 = 12 hits

FYI: I do musical score arrangements and have done some interesting algorithmic compositions in the past but not currently.
It is fun stuff with the quality of today's digital keyboards.
MathExtremist
MathExtremist
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September 30th, 2011 at 3:05:32 PM permalink
Quote: guido111

Statman uses a 150 spin and 9 times hit as an example in his document that does not show a biased wheel but he really does not get into what would be a wheel bias as far as I understand.

He continues with "We would have to see 11 or 12 on the same number to call it unusual."
0.36028 = 9 hits
0.05660 = 11 hits
0.01806 = 12 hits



So let's make it unusual: suppose you observe a roulette wheel for 150 spins and see the 00 show up 15 times. Now what? Does he conclude that the wheel is biased? Does he conclude that the likelihood of 00 appearing on the next spin is greater than 1/38?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
DJTeddyBear
DJTeddyBear
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September 30th, 2011 at 3:28:04 PM permalink
I'm not sure if it's been mentioned, so I'll mention it:

If there is a wheel bias, for example because the slots are not all the same size, more likely than not, the error is caused by a misplaced single divider. As such, on that wheel, there would be a bias for a number, as well as a bias against the neighbor.

Additionally, if there is a wheel bias because its out of balance, then it will be biased for range(s) of numbers and/or biased against range(s) of numbers.

I doubt that his formulas account for either of these types of multiple biases.
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁 Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition. 🤗
MathExtremist
MathExtremist
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September 30th, 2011 at 4:57:17 PM permalink
No formula based on a simple counting of past outcomes takes into account any aspect of the physical instrumentalities behind a bias -- wheel shape, dirt, poor maintenance, dealer interaction, etc. If you really want to detect a bias, you won't just count past numbers and expect that to show you anything about the wheel. Here's a potential table of information that would be much more likely to "work", as it were:

Dealer ID | Wheel direction | Wheel RPM | p(theta between 0 and 45 degrees) | p(theta between 45 and 90 degrees) | ...

where theta is the angle between the spot on the wheel when the ball was released and where it lands. On a fair wheel, fairly dealt by a croupier, each probability will be 1/8 (give or take for the rounding issues). If you find one that's significantly greater than 1/8, there's a reasonable chance of a bias, and there's also a credible physical cause. It's not one that you'd ever detect by counting outcomes because theta isn't computed based on the actual outcome -- just the distance between the outcome and the release point.

Granted, you still need to be able to make bets after the ball drop, but you still can in most casinos. So, for example, if you have a dealer who tends to hit the octant between 135 and 180 the most when the wheel is spinning at a given speed, and you see the wheel spinning at that speed, wait for the ball to release and then put your money on those 5 numbers. Consider this a relative, table-lookup version of Eudaemonic Pie.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
statman
statman
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October 1st, 2011 at 4:08:57 AM permalink
MATERIAL REMOVED

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.
A fool is someone whose pencil wears out before its eraser does. - Marilyn Vos Savant

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