In a martingale betting system, a player that bet against a fair coin will double its bet if he loses. Following this strategy, the first win would cover all the previous loss and get a profit the size of the initial bet. It doesn't work on the long run as the bet grow exponentially and can reach enormous size, outside of the player bankroll. Another way to see it's not profitable is to remark that every coin flip still has an expected value of exactly 0.

I was wondering about the existence of similar strategies in quantitative finance. However my intuition is that as they don't modify the pay-off, they are not really usefull (plus they require large amounts of cash). Basically, making money would be about playing with a coin biased in your favor (statistical arbitrage), not building intricate betting strategies.

Are there exemples of usefull strategies inspired from the martingale betting system ? (or conversely, other reasons why they are actively avoided)

  • $\begingroup$ You are right, these strategies are not useful for exactly the reasons you mention. Therefore they are not used by those who understand Probability. Instead quants like J. Simons find many trades with (small) positive expectation and combine them together. $\endgroup$ – Alex C Dec 10 '19 at 13:49

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