You can make the following reasoning when you see a martingale that will show you that it is a gambler's fallacy:
- A martingale is a strategy with low probability (let's say it is 0.001%) of busting
- If you have two strategies with the same probability of busting, you should choose the one which plays less times, because the less you interact with the adversarial edge, the better
- You can always play the vanilla strategy of betting all your money at 99.999%.
- Thus the vanilla strategy must be better than the martingale
A martingale is just a way to hide a bad way to play with a low probability of busting strategy
This again?
Your reasoning is faulty, leading you to an incorrect conclusion.
The part where you went wrong is "choose the one which plays less times, because the less you interact with the adversarial edge, the better". It's not the number of bets that determines your expected profit; it's the amount you risk. If you risk less, you expect to lose less. A carefully planned martingale progression can cause you to expect to risk less and so lose less than a single large bet. We've gone over this many times before both on the forum and in the on-site chat.
The correct conclusion is that any single large bet can be replaced by a series of smaller bets which achieve the same return as the large bet but with a better chance of success.Umm... you're right in the first part, but to the last paragraph I could add: given any fully specified Martingale (odds, betting size progression, ending conditions), I can construct an equivalent single bet strategy. The only reason to employ a Martingale over a single bet strategy is that the former seems easier to risk-manage intuitively for the human mind. (Which, btw, is a pretty good reason, and probably why so many bet Martingale)