Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

Determining your advantage can be easy, just a simple calculation or very difficult. It depends on the game.

Let's do one thing at a time. I can determine your advantage in the example of 44 or 48.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

48/1000 is +72.8% of the total wagged.

We have to know the real long term advantage

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

I am assuming that you are being paid 35 to 1 on a number straight up.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

36 to 1

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

If the probability is 1 / 37 then the odds are 36 to 1. If you are paid 36 to 1 then the house has no percentage.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

We know we win 35, we are paid 35+1(the one we placed).

*Last edited by ybot (2012-12-31 02:26:24)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

So you are paid 35 to 1. The one you bet does not count.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

Yes, we know the basics.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

Okay, for your 48 out of a 1000 model, provided that is a true estimate of the mean.

The expectation is

E = (952)(-1) + (48)(35) = 728

which means you earn 72 cents on every dollar wagered. A very lucrative deal since a Vegas wheel only earns 5.26 cents on every dollar.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

But, it happened (in this example) in the first 1000 trials. The next 1000 trials it might hit 40 30 or 50, we don´t know it yet.

The real edge isn´t 72.8%, the sample is very short to have a conclusion

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

That is what I told you. But 1000 trials is a lot larger than 30 trials. We can say that the sample ( the thousand trials ) mean is pretty close to the true mean. From what you have given it is the best estimate I can do.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

ybot wrote:

Hi

About french european roulette

the chance to hit es 1/37supose we are looking for 3 standard deviation events

43 hits in 1000 trials is 3 st dev(we played 1 number)

1)what does reaching 3 st dev mean?

2)what is the difference in strentgh of hitting 76/2000, 170/5000 or 319/10000(they are all +3sd)

3)what´s the difference in PLAYING the 1000 2000 or whatever or watch some data where we you find 1 number with 3 st dev?

4)it is the same to reach 3 st dev for 1 number or 2 numbers(neighbors)?

5)having collectede data, you pick 4 numbers(isolated, not neighbors)) that their sum reaches 3 st dev. What is the difference with item 3) or if we actually play every spin?I hope you undestood my questions

I believe they are hard to answer

Best regards

We might start again.

What does 48/1000 tell?

What are the predictions for the play of this number?

What are the chances to repeat 48/1000? (from 44 to 50/1000)

We finished 3 pages with no conclusions.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

Hi;

We finished 3 pages with no conclusions.

That is not correct. We covered the expected value of the experiment ( 48 / 1000 ), we used the central limit theorem to state that the wheel probably has an average close to ( 48 / 1000 ) and I explained the standard deviation.

I told you your expected profit with the data you gave me, 72 cents on the dollar.

We might start again.

What does 48/1000 tell?

Like any empirical experiment it can only provide evidence. Statistics you can say is designed to make mathematical sense out of data like yours.

What would you like to do next?

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

How could inferencial statistics help to know I want?

Can you forward a roulette example where you use the correlation, the regression, the least square method and the student distribution?

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

Hi;

I am not following you here. What can I do a regression to? I have one piece of data, 48 / 1000.

Using that I guess that the mean is quite close to that and there is some mathematics to support that. To really nail the mean down you will need more experimental evidence, like another couple of runs, the more the better.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

As I lack of strong math knoledge I´m trying to undestand the event I withness

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

Hi;

Do you have the results of more runs?

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

I have tons of data

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

That is the point! You have tons and I have nothing but one example. I do not think I can get much more out of one example.

What is it you want to do?

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

Ok. I want to find out the actual mean of numbers that we have small samples.

Supose the ratio is 1/34 for the first 1000 trials, 1/35 for the 2nd 1000 trials, 1/33 at the 3rd 1000 and 1/33 at the 4th 1000 trials.

I guess we would be able to know the actual mean when we have 20k.

But the quest is to infer it sooner.

What are the math tool that you use?

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

How much sooner?

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

Soon, with the error %.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

To do better than what was done before requires more samples.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ybot****Member**- Registered: 2012-12-29
- Posts: 49

Coming back

Let's more events.

You recieve a roulette sample. You scan it and find the best choice you should have played.

For example, it was playing 12 numbers after some signal. This play has got +3.4 standard deviations in the first 400 trials

We make 4 more 400-trial-samples. We have got +1.4sd on each of the 4 samples playing what we found succesful in the first sample.

Supose we take the first sample(+3.4sd) as a prior probability and the 4 new samples as posterior probability.

How do you calculate backwards probability using Bayes rules?

And, what do all this test mean to determine a chance of random?

Warm regards

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,630

ybot wrote:

I have tons of data

Sherlock Holmes wrote:

Data! Data! Data!' he cried impatiently. 'I can't make bricks without clay.

I would like to help but without any data I am helpless.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline