Hmmm, at first glance I actually think you have that backwards.
Given that house edge exists, the longer you play and the more you bet, the more likely you are to lose. I've always argued that the smartest (although least entertaining to be sure) way to gamble in vegas would be to take ALL of your bankroll, bet it on a single hand of blackjack, and then walk away regardless of the outcome.
Strategically, that's right, though you wouldn't choose blackjack because blackjack has terrible odds if you're not allowed to split and double down (and since you're betting your whole bankroll, you can't do those things).
However, what I'm saying is also true. There's a difference between your expected loss and the probability of losing on any given trip. The probability of losing is easily changeable by the player. The way most players play, it's around 90%. With your strategy there, you can get it down to about 49% (betting banker on baccarat, you get paid 19 for 20 but you're more likely to win than lose). Anyone can make it lower than 1% simply by using the strategy of doubling your bet after every loss. But here's the thing......it has zero impact on your expected loss, which depends only on how much you bet times the house edge. And that's all the casino cares about.
If you make small bets, you'll be more likely to end up close to your expected loss. If you overbet your bankroll, you're likely to lose far more than your expected loss (like 20x more). You're also more likely to win big of course. And then people go home and think that they lost because the house always wins. No, 95% of their losses came because they overbet their bankroll and got unlucky.
Edit/short version: Your strategy is betting everyone on one hand is the best for minimizing expected loss if you are not counting cards. Expected loss is the only thing casinos care about, but players sometimes also care about the probability of ending up or down.
--
Congratulations to SuperNiceDog, Guru Winner, who was smart enough to pick
your 7 time champion, Link.