Okay, but I was fishing around with the idea of seeing whether the Martingale strategy might actually be viable (albeit prone to occasional significant drawdown) if you had equal risk reward, but greater than 50% win rate.

In the above scenario we could apply expected value theory and show a projected long term return.

Example

a system with equal net risk/reward = 1
winrate 55%
maximum affordable consecutive losses : 4 (on the 5th loss you cut your losses and start again)

Without Martingale we have 55 win - 45 loss = net +10 after 100 positions, therefore each position has an expected value of +10/100 = 0.1

With Martingale an absolute loss (5 consecutive losses) is worth -31 and has a likelihood of 0.45^5 =~0.0185
a non-absolute loss therefore has a likelihood of 1 - ~0.0185 = ~0.9815 and is worth 1
The net win - loss is then (0.9815 x 1) - (0.0185 x 31) = 0.41 for each position based on expected value theory.

0.41 > 0.1

This number is improved with a higher max loss count as you might expect.