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