It occurred to me also that many ante games have a forced bring in, and some only that. You'd be profitable in both of those games if you won only the hands you were forced to play. If there were 8 people, for instance, even with an ante and a bring in, you'd bring it in 1/8 times and win 7 antes plus whatever else was put in the pot.

If everyone else folded every time you were the forced bring-in, you'd be break even. You'd have some streaks dependent on your opening cards (sometimes you'd bring in more than your share, sometimes less) but long-run it'd be even. Otherwise you'd win.