There are various misunderstandings about progressions, what they are used for and what is the logic behind them.
Many people relate the use of negative progressions
(up as you lose) with gambler's fallacy (GF).
They think than one increases his bet because one believes that a win is due.
It is not exactly like that. I think I can explain mathematically why negative progressions can offer an advantage.
Let's take the Even Chances. Let's say we bet on Red.
Our aim is that our won bets are higher in value than our lost bets. This way with less wins we can recoup more losses and reach a profit.
BEFORE each spin, we have 50% of winning.
Let's say we lose the first spin, in which we bet 1 unit.
Now (AFTER the spin) the probability of losing the 1st spin is 100% and winning the 1st spin is 0% (since we already know the result).
For the 2nd spin the probabilities are 50%-50%.
Now what we have?
We have a "sure loose" spin, on which we bet 1 unit.
And we have a 50% win spin. It is reasonable to bet more on a 50% win spin than a 0% win spin, if you want on average to have wins of higher value than loses. It is reasonable to bet higher when your probabilities are higher.
This is the main logic behind every negative progression. It is not based on GF. It is based on trying to bet more on a 50% win spin than a 100% lost spin. The negative progression player, uses the knowledge of the past lost spins, to calculate how much to bet on the next spin.
And no, It does not work always, because there is no certainty when the win will come.
Yes, very aggressive progressions will lead to doom, because of bankroll depletion and table limits. But these are practical problems, not problems with the "higher average win" rationale of the negative progressions.
The true weak point of the negative progressions is quite the opposite than most people think. It is the fact that they often begin with only 1 unit and if we win on the first spin, we win the minimum amount. This defies the concept of "higher value wins". This could be solved by starting with a higher amount and decreasing the amount after a win. Because AFTER a win we have bet X amount on a 100% win probability spin, so on the next spin with only 50% win probability we should bet less. But if we increase the initial bet the practical problems of bankroll depletion and table limits, become more pressing.Conclusion
Although based on sound logic, negative progressions often fail due to the following reasons:
- They start with minimum bets, that lower the average win value in case of win on the 1st spin
- Bet increases are practically limited by our bankroll and casino betting limits.