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[Bayes]

Under Construction.

[Albalaha]

I wonder what would be the basis of predictions.
              It has to be a logical approach, if it is your own innovation.

[Bayes]

if it is your own innovation.

Not really, the formula itself is over 200 years old, although my use of it might be considered innovative (or controversial).

I decided to cut short the probability/stats tutorial because I'm working on my own blog/web site which will have the same info, plus some software and stats relating to roulette and systems.

[greenguy]

...I decided to cut short the probability/stats tutorial because I'm working on my own blog/web site which will have the same info....

I predicted that. 

[VLS]

I'm working on my own blog/web site which will have the same info, plus some software and stats relating to roulette and systems.

Don't forget to announce it around + adding it to your signature [smiley]welcome/handshake.gif[/smiley]

Coming from you, the community knows it's quality

[Bayes]

Thanks Vic, I will certainly do that. 

[Blood Angel]

Don't forget to announce it around + adding it to your signature [smiley]welcome/handshake.gif[/smiley]

Coming from you, the community knows it's quality

This!

[Bayes]

[math]p(A_i|n_i) = \frac{n_i+1}{n+m}[/math]

where

[math]p(A_i|n_i)[/math]

means "the probability that the next event will be in category i, given that n such events have occurred.

[math]n_i [/math]

is the number of times each category was observed.

[math]m[/math]

is  the number of categories, and

[math]n [/math]

is the total number of observations.

When nothing has been observed,
n_i = 0, and n = 0, so to use an example from roulette, there are 37 "categories" (numbers that could hit) so m = 37 and the probability of say the #13 hitting is

[math]P(13|0) = \frac{0+1}{0+37} = \frac{1}{37}[/math]

which is what you would expect. And obviously it would be the same for any other number. But when you have some data, the probabilities change. For example, if you have observed 50 spins and #13 has hit 3 times, the probability that it will hit on the next spin is:

[math]P(13|3) = \frac{3+1}{50+37} = \frac{4}{87} = 0.046 [/math]

It's important that the categories are mutually exclusive and exhaustive, i.e., that only one event can occur and that one of the events must occur. For example, the categories red and even are not mutually exclusive because the event could be red and even, and the events red and black, although mutually exclusive, are not exhaustive because the event zero has not been included.

If the event doesn't make any difference in terms of payoffs, it can be ignored. e.g. the tie bet in baccarat, so there would be just two categories in this case: P & B.

An important assumption for this formula is that nothing regarding the cause of the events is known about. Of course, in casino games we do know in a sense what causes the outcomes, but not in any detailed way. So most of the time in roulette we don't know why the ball falls into a particular number, because the train of events leading up to that outcome is too complex, although in principle it could be known, given enough information regarding the "initial conditions" (ball speed, wheel characteristics, ball type, environmental conditions, etc).

So if we do have some evidence that the wheel is biased, say, then we ought to take this into account, but we cannot use the above formula because it will give misleading results (the full machinery of Bayesian statistics is required, which is much more complex). So this formula only applies when we have data in terms of the frequencies of the events, nothing more - as far as we're concerned, the events are "random" and all we have are the frequency counts.

If you haven't realised yet, the formula is basically a trending system. It always gives those events which are "hotter" a higher probability. Obviously, this is controversial in regard to casino games, which are designed to have a fixed probability at all times. But are we justified in going along with this? even if we are, even if it's reasonable to conclude that casino games are deliberately set up to be as "fair" as possible (meaning no bias), variance is undeniable. So even if "in the long run" probabilities do converge to that predicted by the standard theory, the conventional probability formulas are of no help. What's needed is a way of tracking the short-term fluctuations (biases, if you prefer).

In the long run, the formula does predict what the other formulas say will happen in the long term. For example, if after 1000 spins you have 31 zeros, 496 reds, and 477 blacks, m = 3, n = 1000, n_i = 477, so the probability of the next spin being black is:

[math]P(black|477) = \frac{477+1}{1000+3} = \frac{478}{1003} = 0.477[/math]

which is not far off what it "should" be.

For some more background reading, see:

https://archive.org/stream/theprinciplesof00jevoiala#page/256/mode/2up

In particular I like the passage on page 260:

[attachimg=2]

There is a more mathematical account of the formula here:

http://en.wikipedia.org/wiki/Rule_of_succession

[BEAT-THE-WHEEL]

[quote author=Bayes 
   even if we are, even if it's reasonable to conclude that casino games are deliberately set up to be as "fair" as possible (meaning no bias), variance is undeniable. So even if "in the long run" probabilities do converge to that predicted by the standard theory, the conventional probability formulas are of no help. What's needed is a way of tracking the short-term fluctuations (biases, if you prefer).

In the long run, the formula does predict what the other formulas say will happen in the long term. For example, if after 1000 spins you have 31 zeros, 496 reds, and 477 blacks, m = 3, n = 1000, n_i = 477, so the probability of the next spin being black is:

which is not far off what it "should" be.
[/quote]


Hi Bayes,
My rusty and math-flunking brain can't understand the formula.[smiley]aes/cry.png[/smiley]

But I think u mean, as the standard "should" be, is, at last, they will "equilibrium, minus the pesky green", and our method,whatever it is,  should take advantages of these 'known' fact?

[Bayes]

Hi BEAT-THE-WHEEL,

But I think u mean, as the standard "should" be, is, at last, they will "equilibrium, minus the pesky green", and our method,whatever it is,  should take advantages of these 'known' fact?

No, that's completely wrong.  I was just making the point that the formula will, in the long run, reflect the long term results as given by the standard formula for the probability of red/black, which is 18/37.

The formula says to bet on the event which has the highest probability, which is usually the event which is the "hottest".

The procedure is this:

1. Identify your events. They must be mutually exclusive and exhaustive, meaning that only one of the events can occur and one must occur. So all the roulette standard roulette bets, streets, dozens, numbers, but also compound EC bets, for example, in baccarat there are 8 different permutations in 3 hands:

BBB
BBP
BPB
BPP
PBB
PBP
PPB
PPP

In any 3 hands, only one of these can occur and one must occur.

2. Get some data and use the formula to calculate the probability of each event. The event with the highest probability is your bet. That's it.

In practice, it's better to define some "event windows" for example, short term, medium term, longer term over which to calculate the probabilities. e.g. suppose you were betting single numbers, you could look at the last 25, 50, and 75 spins on a rolling basis. On each spin, calculate the probabilities for all numbers within these spin frames. Usually you will get some of the same numbers in each frame which have the highest probabilities. As you get more spins, numbers will drop out of the frames and be replace by new "hot" numbers.

Needless to say, there is a lot of tracking and sorting to be done, so this method isn't really suitable for B & M play; you'll need a spreadsheet, software tracker or bot. I'll post a detailed example later.

[Sputnik]

Are you saying its better to follow the flow then betting against it?

Cheers

[Bayes]

Sputnik,

Basically, yes. The formula (Laplace's Rule of Succession) is validation for those who like to play trends. 

But it's not easy to create a good trending system because you can get caught by the "whip-saw" effect, which is why I think it's better to work with rolling frames which target different histories. Events which are dominant in the short term can fade away in the middle or long-term, and conversely, events can be dominant long-term but not particularly so in the short term, so this technique aims to keep you locked on to all "hot" events, whether they are occurring in the short, medium, or long-term.

You might remember I posted this formula on betforum.cc, just before it disappeared. I had a couple of emails from members saying they were getting good results using it, which prompted me to investigate it more thoroughly.

[ybot]

So,  how does prediction formula work?

[bettyhernandez]

Yes, how it works