Cornix
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Martingale isnt going to improve the win rate, or the number of consecutive wins or losses. It just ensures that the eventual winner offsets the earlier losses, and in its simplest form with fixed R:R puts you ahead by the size of the original bet.
The primary factor which influences the probability of a streak of a given length occurring is win rate. If you have a high win rate, then you'll get longer streaks, if you have a low win rate you'll get shorter streaks of winnners. Thats the situation if the win rate is due to a genuine edge, or artificially achieved by altering R:R to engineer a higher win rate.
As you point out, there's no real correlation between streak length and expectancy.
Indeed, I expressed it wrong, meant averaging down combined with increased size of every entry, rather than martingale in a classic gambling sense of the term.