One way to think about it is that there are really three games: game A (a slight loser), and games which I'll call BL (losing) and BW (winning). If you win a couple rounds of BW, the casino changes you to playing BL for a round. But if you don't play BL and instead go play A for a round, then when you come back to the table you'll be back to game BW. So you use game A, a slight loser, to avoid BL, a bad loser.

Playing only A is a slightly losing strategy. Playing a mix of BW and BL is a losing strategy, because BL is so harsh. But if you play BW mixed with A, you combine big wins with small losses, and therefore come out ahead.

This doesn't work in roulette because, no matter what color you play, it's a slight loser. Black and red are both examples of game A, so no matter how you mix them you're just playing AAAAAAAA.

Another concrete example is to define BL and BW as any point at which a game B has a negative or positive expectation. A real-life example of using the A, BL, BW strategy were the MIT blackjack teams of the 80's and 90's.

They had a spotter at each table that would count cards and wait until the odds were in the player's favor before calling in the big money player. Assuming that the bets placed by the spotter are negligible, the the big money player could choose from the following games:

   A : Do nothing. E[x] = 0  (break-even)
   BL: Play blackjack when the deck favors the casino, E[x] < 0
   BW: Play blackjack when the deck favors the player, E[x] > 0

Obviously playing blackjack has negative expectation in the long run, and we could choose another casino game with very-close-to even odds for game A (like Baccarat), rather than doing nothing.

With European roulette, you'll win 47.30% of the time. With American roulette, you'll win 44.74% of the time.

The same odds as always choosing black or red.