Simple question about VARIANCE

[TheCentaur]

Probably an easy question for math guys but I was wondering...

If you had 1000 units and had the choice of betting this on roulette:

One unit on 1 number each spin for 1000 spins

One unit on 2 numbers each spin for 500 spins

One unit on 4 numbers each spin for 250 spins

Which strategy has less variance? I think that's the right term, maybe it's volatility. What I'm asking is which strategy will most often to be closest to the expected return, or is it all the same?

At first I thought it would be betting 4 numbers at a time, but then you would have less total spins.

Thanks

[daimoshokage]

STFU YOU FUKKING DUMBSHIT!!!

[TheCentaur]

After seeing that Daimo replied to my thread the odds that he made a helpful on topic reply +50000

[tatehill2000]

just curious as to your thought? is it that those 4 numbers? (or 1 number) will eventually come up and hit? to overcome the house edge?

tater

[TheCentaur]

just curious as to your thought? is it that those 4 numbers? (or 1 number) will eventually come up and hit? to overcome the house edge?

tater

no not trying to overcome house edge

just wondering if there is a difference in variance by putting 1000 units in action with the different strategies

[d2bets]

Not supported by any math, but my intuition says less spins = more variance.

[TheCentaur]

Not supported by any math, but my intuition says less spins = more variance.

I tend to agree with you

but the thing that is confusing me is:

If you divided your 1000 units by 37 you get 27.03

If you placed 27.03 on each number and the 0 (Euro Roulette) for 1 spin you would get a return of 946.05 + 27.03 with no variance

If you placed 27.03 on one number for 37 spins you would have a high variance even though there were more spins

[Kaabee]

I tend to agree with you

but the thing that is confusing me is:

If you divided your 1000 units by 37 you get 27.03

If you placed 27.03 on each number and the 0 (Euro Roulette) for 1 spin you would get a return of 946.05 + 27.03 with no variance

If you placed 27.03 on one number for 37 spins you would have a high variance even though there were more spins

well, if you place a bet on each number, your return is the same every time, so it's kind of impossible to deviate from the mean.

[TheCentaur]

well, if you place a bet on each number, your return is the same every time, so it's kind of impossible to deviate from the mean.

If all numbers with one spin has zero variance, would that mean that as you increase numbers per spin and reduce numbers of spins your variance decreases though?

If a gun was to my head and I had to bet 1000 units on roulette and get a return of at least 900 I would definitely bet an equal amount on all 37 places for one spin.

What if I only had 3 choices though like in post #1?

The theoretical return is the same for all but which is less of a gamble to get that return of at least $900?

[GP]

starting with 1000 units, all 3 of those scenarios will result in the same expected return of 945.95.

playing 1 + n numbers increases your likelihood to win, however it also guarantees n losses per spin.

[TheCentaur]

Ok I think I am using the wrong term. I think standard deviation is what I'm asking.

Which strategy has the lowest standard deviation?

Are you saying all 3 strategies have the same standard deviation GP?

[GP]

All strategies are going to have a binomial distribution. xbalto posted a nice answer below.

[xbalto]

1/38 chance of winning, 1000 bets: std. deviation = 182.23
2/38, 500 bets: sd= 179.75
4/38, 250 bets: sd = 174.69
(american roulette)

the variance of a single spin is proportional to p*(1-p), where p is the chance of winning. if you make B independent spins, the total variance is proportional to B*p*(1-p). Your three scenarios have B*p = constant, so variance changes as 1-p. spreading out over more bets reduces variance, but the smaller chance of winning raises it. as you noted, if you bet on every square your chance of winning is p = 1 so variance is 0.

[NYSportsGuy210]

I tend to agree with you

but the thing that is confusing me is:

If you divided your 1000 units by 37 you get 27.03

If you placed 27.03 on each number and the 0 (Euro Roulette) for 1 spin you would get a return of 946.05 + 27.03 with no variance

If you placed 27.03 on one number for 37 spins you would have a high variance even though there were more spins

How could this confuse you? If you put 27 units on ONE NUMBER and spin it 37 times the odds of you winning each spin is STILL ONLY 1 out of 37. If you put 27 units on EVERY POSSIBLE for one spin then the odds of you hitting are 1 or (100%) despite the fact that it's only one spin.

You fail to understand the concept of each spin being a mutually exclusive event. And no the number of spins doesn't reduce variance or standard deviation if the odds of hitting a number is ALWAYS gonna be 100%.....rofl.

[TheCentaur]

How could this confuse you? If you put 27 units on ONE NUMBER and spin it 37 times the odds of you winning each spin is STILL ONLY 1 out of 37. If you put 27 units on EVERY POSSIBLE for one spin then the odds of you hitting are 1 or (100%) despite the fact that it's only one spin.

That isn't what is confusing. WHat is confusing is d2bets and I agree that more spins would lower the standard deviation, but 1 spin with all the numbers bet has the lowest standard deviation possible, so it would seem moving closer to 1 spin would move closer to that standard deviation as well.

You fail to understand the concept of each spin being a mutually exclusive event. And no the number of spins doesn't reduce variance or standard deviation if the odds of hitting a number is ALWAYS gonna be 100%.....rofl.

NY I think you fail to understand what is being discussed in this thread. Each spin being mutually exclusive is a basic idea and has nothing to do with the topic. Perhaps I didn't explain it clearly. Variance and standard deviation can be altered by certain variables such as bet size or number of bets per spin while odds remain constant and results remain random.

For example betting all 1000 units dispersed evenly on all 37 numbers on one spin has 0 standard deviation. But betting the same unit size per number on 18 numbers on one spin, then betting 19 numbers on a second spin has a very high standard deviation. Increasing spins to 1000 and only betting one unit on one number each spin has a standard deviation in between the former 2 strategies. This isn't about changing the odds, it's about the best strategy in the original post for a low standard deviation with the bankroll remaining constant

[NYSportsGuy210]

That isn't what is confusing. WHat is confusing is d2bets and I agree that more spins would lower the standard deviation, but 1 spin with all the numbers bet has the lowest standard deviation possible, so it would seem moving closer to 1 spin would move closer to that standard deviation as well.


NY I think you fail to understand what is being discussed in this thread. Each spin being mutually exclusive is a basic idea and has nothing to do with the topic. Perhaps I didn't explain it clearly. Variance and standard deviation can be altered by certain variables such as bet size or number of bets per spin while odds remain constant and results remain random.

For example betting all 1000 units dispersed evenly on all 37 numbers on one spin has 0 standard deviation. But betting the same unit size per number on 18 numbers on one spin, then betting 19 numbers on a second spin has a very high standard deviation. Increasing spins to 1000 and only betting one unit on one number each spin has a standard deviation in between the former 2 strategies. This isn't about changing the odds, it's about the best strategy in the original post for a low standard deviation with the bankroll remaining constant

Nope if you bet less spins but more # are bet on per spin your std. deviation decreases. Why? Because your probability of hitting the winning # increases per spin even though you are taking less spins. Mutual exclusivity of each spin is a reason for this.

This xbalto guy above explains it nicely.

[TheCentaur]

right thanks xbalto