### Author Topic: @ Mike - Probability Question  (Read 388 times)

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#### Sputnik

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##### @ Mike - Probability Question
« on: March 07, 2018, 09:01:06 AM »

I have one question - assume the true odds in 1 in 8 in the long run.
You have eight patters and wait until one sleep and bet against it.

Now reality check about what happens during real life experience and what happens with computer code.
Both show that you can get twenty winning session before you bust and some times less or more.

So in real life when you enter a live wheel you might for the next coming eight hours have twenty winning sessions and one losing sessions - but we don't know the exact results as the future hold the secret.
But we know from computer simulation and real experience that you get variations in winning strikes and losing strikes. Sometimes eight winning strikes and two losing strikes and sometimes thirty winning strikes and one losing strike.

Assume now some one enter the live wheel and play once - hit and run - and the result is twenty winning strikes and one losing strike for the next eight hours - then the true odds should be 20 to 1 hitting a winning bet.
So if you look at this with lotto perspective so is that pretty good odds.

So i understand this happens during the short term and that the odds even out in the long run.
Now my question is that can you talk about true present odds not being the same as fix odds because of variance and fluctation during the short term.

Cheers

« Last Edit: March 07, 2018, 09:02:41 AM by Sputnik »

#### SugTips

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##### Re: @ Mike - Probability Question
« Reply #1 on: March 07, 2018, 09:25:55 AM »
Very Good Question. Thanks for asking it.

#### cht

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##### Re: @ Mike - Probability Question
« Reply #2 on: March 07, 2018, 10:41:44 AM »
The odds for the last 8 hrs may be 1:20.

It may also be 5:16 at the other extreme in the next 8 hrs and so on.

The long run rate is 1:7 +- variance.

So how do we know that when we are at the table the odds is 1:20 or 5:16 for the next 8 hrs ?

#### Mike

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##### Re: @ Mike - Probability Question
« Reply #3 on: March 07, 2018, 12:28:28 PM »
Sputnik,

I'm not quite sure what your question actually is, but as cht has already implied, you can only know what the "intermediate" probability is (as opposed to the "true" odds) AFTER the sequence of outcomes.

Of course you can bet by taking these intermediate probabilities into account, ie you can go with the flow, as it were, and actually that's the most rational way to bet, assuming you have no other information.

There's a long running debate among statisticians about what probability actually means, which is more philosophical than mathematical. Some say that probability is the long run relative frequency, but this doesn't help much with one-off events where you can't run lots of trials, and it can't say anything about the short term (as J.M. Keynes said : "in the long run we are all dead").

Then there is the probability-is-a-measure-of-belief interpretation, which is more flexible and is based on Bayes' rule. Using Bayes' rule it's easier to include prior information. An example would be if you suspect  a wheel may be biased, but based only on the past number history you have some doubts. However if you have some other data such as an observation that a pocket is worn, for example, you can include this in the calculation and the resulting probability will give you a more accurate assessment.

But if you only have past numbers and nothing else, Bayes' rule isn't much help, although I suppose you could incorporate other stats into the calculation.

Then there is something called Maximum Likelihood Estimation (MLE) which finds the most likely probability based on the data. In that case you take the "current" probability to be the actual probability, and you can update it as you get more data. Both of these approaches will track the trend, so you will always end up betting on the "hot" events or numbers.

https://www.quora.com/Intuitively-speaking-What-is-the-difference-between-Bayesian-Estimation-and-Maximum-Likelihood-Estimation

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#### Reyth

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##### Re: @ Mike - Probability Question
« Reply #4 on: March 08, 2018, 02:49:30 AM »
Thank you for this excellent post.  How do number of trials effect  the accuracy of these two comparisons (Bayes/MLE)?  This is certainly how I am approaching roulette.
« Last Edit: March 08, 2018, 03:32:41 AM by Reyth »

#### Mike

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##### Re: @ Mike - Probability Question
« Reply #5 on: March 08, 2018, 09:57:28 AM »
Reyth,

Good question. The honest answer is I don't know, but MLE is prone to "overfitting". Maybe you could write a little program to find out : get some spins and use both MLE and Bayesian updating, then compare the final probabilities generated from each with the theoretical probabilities. Bayesian updating is more complex to calculate, but as a framework it's very powerful and flexible, and as that article mentions, it includes MLE as a "special case", so there's really no compelling reason to go with MLE.

For more info on Bayes there's an excellent video here which assumes you know almost nothing, and there's a short article here on Bayes applied to sports betting.

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