RINAD wants a comparison between progression and flat betting, the rise of Alembert is the simplest to make calculations because we know that this progression wins 1/2 unit per spin played.

Imagine a method that earns 1% with the flat bet. Let's say it takes 100 units of capital to hold. After 100 x 100 spins (or 10 000 spins) there are 100 units won that allow you to double your capital. With the rising of Alembert will also have to take 100 terms (1 + 2 + 3 ... + 99 + 100) is in total 5050 units [(1 + 100) x 50]. The D'Alembert will win in 9,900 spins (10,000 - 100), 1/2 piece per spins played, or 4950 units + 100 units won thanks to this 1% advantage. That is a gain of 5,050 units. There is equality of benefits between the d'Alembert and flat betting !

Now imagine a method that wins 2% with the flat bet. Let's say it takes 100 units of capital to hold. After 100 x 100 spins there are 200 units gained which allow to triple its capital. With the rising of Alembert will also have to take 100 terms (1 + 2 + 3 ... + 99 + 100) is in total 5050 units [(1 + 100) x 50]. The D'Alembert will win in 9,800, 1/2 piece by spins played, 4,900 + 200 units won thanks to this 2% advantage. The intuitions on the progressions are here not so good because the d'Alembert is very far from having tripled its capital !!!

The conclusion (with these figures) also suggests that a progression can beat the flat bet with a 0% method but it is hypothetical in practice because of the variance that requires a huge capital. But in theory, where the flat bet pays nothing, the d'Alembert or another progression can do better.

A progression does not show in the examples that its main quality is to make more profit. At best, it allows you to withdraw earnings more often from your method. It should be added that a method with a positive expectation

has two qualities: to fight against variance with the least possible number of units and to make profit in flat bet. Add to that a complex progression is often complicated. But that does not prevent him from doing his theoretical research