Roulette wheel physics and probability

[dimes]

TL;DR Summary

How does the speed of the wheel and size of the ball affect the variance of results in roulette?

Hi all,

I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon.

However I have been proven wrong many times, and I have seen some unbelievable results where the ball can land in A 10-15 times in a row. Now that brings me to the question of why?

The ball is manually flicked by a dealer, so there is force and velocity. The wheel is also spun by the dealer - sometimes fast and sometimes slow. The dealer can also choose to use a small or big ball.

Now if the ball lands in A 10 times in a row, is the dealer doing something specific to get the ball to land there? That is, have they fallen into some routine or pattern? How many spins will it take to show the dealer has fallen into such a pattern? 10 spins? 20 spins? 30 spins?

This brings me to the real question: in which scenario would more variance be created? By variance I mean the ball landing in A and B relatively equally, as opposed to it landing in one half 10 times in a row.

1. Wheel is spun slow and the ball is heavy
2. Wheel is spun fast and the ball is heavy
3. Wheel is spun slow and the ball is light
4. Wheel is spun fast and the ball is light

My thinking is that if the wheel was NOT moving at all, it would be easier to train a dealer to hit A or B intentionally. The difficulty of this gets harder once the wheel is spun, and then of course the difficulty gets increasingly harder as the wheel is spun even faster.

I'm keen to hear people's thoughts on this, and please feel free to correct any assumptions I have made.

PS. And yes, I know the casino odds, but here I am only interested in the physics of the roulette wheel and what difference the various factors can make.

 

[anuttarasammyak]

I do not know the intentional technique of dealer at all. I expect all the four cases make no difference on the results with no intentional dealer.

 

[PeroK]

In general, you are being fooled by randomness. Ten A's in a row will happen with probability 1/1024. So, you are bound to see that eventually. In fact, about once in every 4000 spins. And similarly for 10 Bs in a row.

I doubt physics comes into it as long as there is a sufficient variation in the process. A robot could possibly take the randomness out of it. That said, once everything is in motion, the result may be somewhat predictable.

 

[jedishrfu]

Phys.org had an article on the physics:

https://phys.org/news/2016-08-isaac-newton-casino-roulette.html

Claude Shannon and Ed Thorpe took on the wheel with a shoe

https://www.winton.com/news/ed-thorp-claude-shannon-and-the-worlds-first-wearable-computer

https://www.cs.virginia.edu/~evans/thorp.pdf

I recall some grad student also developed a shoe-based computing device to predict where and when the ball would drop.

https://www.forbes.com/sites/starts...to-beat-the-odds-at-roulette/?sh=3b7b5d383c39

https://untamedscience.com/blog/mat...oulette-can-science-beat-the-wheel-after-all/

 

[PeroK]

I didn't realise you could place a bet after the wheel had started spinning. Then physics does come into it!

It's interesting how these articles always claim that a coin toss or dice roll isn't random. Then assume that you can start your calculations after the toss or roll. That misses the point that the process involves a human element. And it's not clear that human actions are completely subject to the laws of Newtonian physics.

 

[jedishrfu]

Card counting at blackjack was a good example. Originally they used only one deck of cards until they realized it was easy to card count and game the odds. Later the casinos adopted 8 deck boots that increased the odds in their favor.

There's even a convention on the latest gizmos and strategies:

https://www.techopedia.com/gambling/blog/the-card-counting-shoes

 

[Agent Smith]

TL;DR Summary: How does the speed of the wheel and size of the ball affect the variance of results in roulette?

1. Wheel is spun slow and the ball is heavy
2. Wheel is spun fast and the ball is heavy
3. Wheel is spun slow and the ball is light
4. Wheel is spun fast and the ball is light

Nice! What you refer to as variance looks to be how well empirical probability (when you actually play the game) tracks theoretical probability (your division of the roulette wheel into A and B is part of an attempt to predict the outcome of a spin). If the wheel is truly random in behavior, you should see equal number of "hits" on the A side and the B side. You've conveniently divided the wheel into 2 halves, it's just like flipping a coin with 2 possibilities, a head or a tail.

The idea then seems to be to maximize probabilistic behavior for the wheel-ball system, which is to say reduce predictability (cheating and rigging, etc.). I'd go with option 4: A fast spinning wheel is harder to track visually and a light ball maybe sensitive to even a small draft of air. Allowing for things outside the wheel-ball system to affect the outcome should make it extremely difficult to predict the slot the ball lands on.

 

[jedishrfu]

You might be interested in this report on Ed Thorpe and Claude Shannon's wearable computer for predicting roulette wheel action.

https://www.cs.virginia.edu/~evans/thorp.pdf