Strange post, Bayes. You say that classical maths does say that The Long Run is towards infinity and wonder why we claim that is what the maths says ? If, as you say , that it depends on context then that means that the classical view is untrue - and that the Long Run can actually be measured . Is this the accepted view of the maths community or your personal opinion ?
"Towards infinity" is just mathematician speak meaning that the empirical results will tend towards the theoretical probability as you take more trials. It's really talking about variance; there will be more variance over 10 spins than 20, more over 20 than 40, more over 40 than 80, and so on. Yes the long run can be measured and this certainly isn't my opinion; the formula I give in my article is derived from the law of large numbers, and anyone can check the results for themselves: don't take my word for it.
I was just pointing out that you can't consistently assert that statistics and probability only applies in the long run (meaning "infinity") and at the same time use statistics and probability as guide to betting when your play is over the short term. The formula I gave shows that you have to take into account both the probability of interest and the interval within which the probability will converge to, in order to make a meaningful "prediction". And that prediction will also be subject to uncertainty, which can also be quantified.
It's just not true that probability is useless as a guide to betting, nor does it mean that you're necessarily committing the gambler's fallacy if using it. In particular, it's useful for assessing the risk involved when applying money management or progressions.
Suppose someone visits a casino for the first time and has no idea of the roulette odds and probabilities. He has $100 and decides to bet $5 on number 17, thinking that he has a fair chance of getting a hit before his money runs out. So he can make 20 bets before this happens. His chances of winning are 42%. Now whether you call that a "fair" chance or not is beside the point, but it would be nice to have known the chances before betting, don't you think?
Most systems I see posted on forums, especially those using progressions, are far too optimistic. They don't take into account probabilities at all. Another example: a system was posted recently which suggested betting on streets with a D'Alembert progression (+1 on loss, -1 on a win). This progression was designed for the even chances. Knowing that, and also that it fails because eventually the stakes get too high when there's a strong imbalance, wouldn't it be more prudent, when using the progression on streets, to not increase the stake after every
loss, but after multiple losses? But how many?
This is where probability can help. Since the progression is for the even chances, what number of bets on a street will result in probability of 0.5 that you get at least one win? Using the binomial distribution, the answer is 8. So betting on a street, if you increase your stake by 1 after 8 lost bets, you are far less likely to hit a run from hell, because your staking plan is more appropriate for the bet.
I'm not saying this is necessarily what you should
do, that's up to your individual risk preferences, and maybe other factors. What I'm saying is that using probabilities gives you more options and enables you to take calculated
risks, otherwise you're just gambling.
Incidentally, did you have a look at UK 21’s site and if you did what was your impression ?
No I haven't looked at it. Do you have a link?