I had a mental breakthrough in another thread.
The key to understanding Mendelson and Argentino (and others) is to grasp that nothing about their gambling is actually about the money. Now as a lifelong gambler, I should have understood this immediately, but I am so divorced and insulated from the emotions of it, that I didn't see the obvious.
Their way of gambling is all about emotion.
Anyway, here's the gist.
First, let's compare regular losing gamblers to those employing "Singer's" systems. Singer's systems are designed to have one leave the casino with a profit 85% of the time. And then sometimes, one gets annihilated. Regular video poker players, on the other hand, lose the majority of their sessions. So if both budget the same amounts annually, what benefits does the use of "Singer's" systems provide?
Well, emotional well being, self-defining as a "winner," and perceiving oneself as having self control are, from a percentage of time perspective, enjoyed by Singer more than a regular gambler. If he plays just a handful of sessions each year, some with wins and a minority with massive losses, then the bulk of the time he walks away a "winner." He can maintain his self narrative of being a "winner" until those days when he gets martingale crushed. That self narrative includes perceiving self as having control, of being a winner, and of having the proverbial "money in the pocket."
If the individual playing like this derives a great deal of satisfaction, emotional reward, and self-perceptive boosts from the times he wins small amounts, then there is value. If the individual is able to shrug off the monster losses quickly, or goes all depressed, then quickly reorients and recovers, then the time spent weeping and gnashing teeth may be short. It could be brutal, but if the recovery is quick, then the person spends very little time in recovery mode without his self perception being damaged.
So someone who ties his self perception into results, but for whom the TIME spent in one mode or the other is important, benefits. And if the severity of the large occasional financial losses isn't matched by proportional emotional devastation, then that kind of person also benefits from the martingale approach.
It's all about emotion. The martingaler, to simplify this, spends 85% of his time in an emotionally positive state. That's compared to the regular losing player, who spends most of his/her time as a "loser."
One could make certain projections from this. The martingaler would avoid detailed overall records, as that infringes on the status as a "winner." There would probably be an amped-up sense of superiority. And, I suspect, if the martingaler has a devastating losing session, it would be important to "get back on the horse," so one of those 85% winning sessions could regenerate one's emotional mojo. In addition, "training people," using other's money, could be a substitute for actual playing and reinforcing one's self-definitions, especially after a devastating (financial) loss.