Doesn't the Reverend Bayes Theorem state that the Probability at the start is the same as at the end ?
I agree with Palestis that no realistic gambler seeks to win EVERY bet but seeks only to win sufficient to show a profit.
This is a controversial issue, that I believe deserves more serious discussion. Because winning
consistently may depend on it.
We can easily compute the probability of winning at least one bet in a predetermined series of bets.
That's what many system players do whether they know it or not.
They wait for a trigger and then they start betting a predetermined series of bets with a specific target in their sight.
Since a series of bets aims only at winning one bet, normally the betting cycle (trigger plus bets), ends right there, and it only restarts after a new trigger appears. For example the probability to hit one EC in a series of 3 predetermined bets is 87.5%. Whether you hit it in the 1st, or 2nd or 3rd bet doesn't matter. What is certain is that you have an 87.5% chance to hit it in one of 3 bets. Once you hit it, it is very risky to continue for more wins. Because that 87.5% no longer applies.
Now the question is if the 87.5% still applies in the 3rd bet after the first 2 bets failed.
I'm am not sure about that, but what I am certain about is the fact that is higher that 50%.
That's what my long time tests over the years have proven.
Betting only the 3rd bet in a 3 bets series, after the first 2 failed in my presence, has won many more times than it lost, even if the probability supposedly is 50%. Not only I have tested it with EC's but with dozens, columns, 3 quads, 2 DS's and many other combinations of groups.
And in all cases, betting the later stages of a series (provided the earlier stages lost virtually of course), won far more frequently than lost.
And the simple reason to avoid betting the earlier stages of a series is to save money, and use them in bets that have higher winning certainty.
Could it be that by purposely waiting to lose the early stages, in a way we ride out a variance that is possibly present? Where betting from the beginning, we may be penalized by a variance?
I have used Ellison's system in the past. It's ok, but it's nothing special if played as described.
However waiting to lose virtually all bets after a trigger, when the second trigger appeared the results changed dramatically. There were a lot more wins in a new trigger after the first failed.
And I don't remember seeing 3 triggers lose in a row. Which means after 2 failed back to back triggers, you better bet heavy in the 3rd. The waiting time is worth its weight in gold.