Thread: Lets play Roulette!!

I am an avid gambler. Its not a problem for me. I enjoy it, i like betting on probabilities and roulette is my favourite game. Roulette is quite simply pure chance.

There is something about it that causes me distress though!
I sit at the table knowing my odds are 37 to 1 on a direct hit. I may look at the past results of the table and see that the number 24 has not been hit for about 40 spins, so i may bet heavily on that number.

Now the chance of 24 coming in has not changed over these 40 spins (or any amount of spins). But i also know that over the course of my betting spree that the stats for each hit should roughly even out, so i know that 24 not being hit is an anomaly and it will be smoothed out, therefore i bet heavily on it. WHY!! It drives me nuts, but i cant stop doing it, also it pays off quite often, but i know it shouldnt as my odds have not changed. This is a paradox inside my brain.

I recently read about bell 'error' curves when i was reading about average behaviour and i think it must be related. I am no mathematician though.
Id like to hear your thoughts on it, although i suspect the feeling of paradox is entirely psychological.

Originally Posted by harvestein

But i also know that over the course of my betting spree that the stats for each hit should roughly even out,...

Not over the course of your betting spree, but over the course of what is called (informally) the long run.

In the long run, each number should come up roughly the same number of times. What most gamblers fail to fully appreciate is how long the long run really is. For example, exactly the same phenomenon will be noticed in dice rolling. In the long run, each number will come up roughly the same number of times. The long run for a six-sided dice is, however, approximately six million rolls of the dice; which at one roll every five seconds would take about a year to complete.

For the UK National Lottery it is approximately 268,919 years. I could work out what it is for roulette, but suffice it to say it is much, much longer than your lifetime, so please do enjoy your game, just don't hold your breath waiting for the odds to even out.

i dont understand why it is not scalable though? I can see the graphs that show roughly even distribution of numbers over a thousand spins, never mind the amount of spins i can bet on in my life time!
If i toss a coin a hundred times it is roughly even? so what is the 'long run' for a coin toss?
I take it you mean when the difference in results gets down to very small fractions like heads=0.49999999999 or something.

My question isnt really about at what point they even out, i just want to know how it works. Like what are the odds of 24 not coming out for a thousand spins? What is the mechanism?

Originally Posted by harvestein

I can see the graphs that show roughly even distribution

That's your problem, right there. Define roughly even distribution? Different people will have different ideas about what constitutes even distribution, and they will have to make an assumption on this because life is too short to run a simulation until it gets to exactly even distribution.

Originally Posted by harvestein

so what is the 'long run' for a coin toss?

The question makes no sense as it stands; first, you have to define what it means to win. If a win is throwing a head, the long run is two tosses. If a win is three heads in a row the long run is eight tosses.

Originally Posted by harvestein

I take it you mean when the difference in results gets down to very small fractions like heads=0.49999999999 or something.

Or something. I actually mean much smaller than that. I ran computer simulations which were programmed to run until the difference between the most frequent number and the least frequent number was less than or = 0.00025% of the expected value.

Originally Posted by harvestein

Like what are the odds of 24 not coming out for a thousand spins?

Please don't refer to odds, they are merely the opposite of evens. The probability of 24 not coming up in a thousand throws at roulette, on a European roulette table is:.....

On a US roulette table the probability is:.....

But 1000 spins on a roulette table is at least 16 hours of play. Can you actually afford to play for 16 hours without winning on the hope that 24 is going to come up?

I re-wrote my dice rolling programme so that it would simulate a roulette table with 37 slots, so this is a european roulette table (there is an extra slot on US tables).

I started by setting it to simulate 1000 spins of the wheel. The statistics I got were as follows:

Max f(x) = 36
Min f(x) = 19
f(N) = 62.9

This means the number that came up most often came up 36 times; the number that came up least often came up 19 times. After 1000 spins each number should have come up approximately (1000/37) = 27 times. The function f(N) calculates the difference between the max number and the min number as a percentage of the expected figure, which in this case is 27. So, the lower f(N) is the closer we are to equality.

Yesterday I said (from memory) that for dice rolling I used 0.00025% as meaning equality, but that isn't correct. I actually used 0.025%

Let's see how many times we have to spin a roulette wheel to get a figure that low.

f(1 million) = 2.538
f(2 million) = 1.705
f(3 million) = 2.122
f(4 million) = 1.437
f(5 million) = 1.607
f(10 million) = 0.779
f(15 million) = 0.569
f(20 million) = 0.501
f(25 million) = 0.628
f(30 million) = 0.496
f(35 million) = 0.319
f(40 million) = 0.489
f(45 million) = 0.432
f(50 million) = 0.405
f(100 million) = 0.271

If you could spin a roulette wheel once per minute (which is not likely in real play) it would take over 190 years to spin it 100 million times. I tentatively suggest that this is longer than one session of play (or roulette table for that matter) is likely to last.

Cheers for that. The way you speak you seem to think that i know there is some kind of secret technique to it. I know there is none but the maths i found interesting!
Think ill just go back to blackjack.

Cheers for that. The way you speak you seem to think that i know there is some kind of secret technique to it. I know there is none but the maths i found interesting!
Think ill just go back to blackjack.

Cheers for that. The way you speak you seem to think that i know there is some kind of secret technique to it. I know there is none but the maths i found interesting!
Think ill just go back to blackjack.

I had to vote for option 3 in your poll. While for any amount of time leadin up to inifinty, it's possible (however unlikely) to miss a number, at infinity (which isn't exactly possible), the chance drops to 0.

Around 8 months ago me and my mate went to a casino in leicester square (London) As I was sitting down sipping my vodka martini (sad I know - lol) i looked over and said "32" and low and behold the number "32" came up - damn damn damn damn damn - if only i had put money down !!

Anyway........ I wasnt choosing lottery numbers (if only!) The truth is, on the roulette wheel there are 37 numbers, ranging from 0 to 36; each with an equal chance of coming up. If you choose a number you have 1 in 37 chance of being correct; so the odds are stacked against you. That doesnt necessarily mean that if you spin the wheel 37 times that your number (whether it is a variable or static) will come necessarily come up - some numbers may repeat but the longer you play, the chance of your "lucky number" not coming up at some point decreases with time. Although, nothing is impossible in this universe and the laws of entropy may dictate otherwise BUT it is my belief that I stand more of a chance of winning the national lottery than you do of your lucky number not coming up if you spin the wheel 100,000 times.

I have in my head already 100,000 / 37 as part of the maths to work out the odds. Anyone else care to help ?