There can be a great deal of debate about which games should be on a beatable list based on all the ways that exist for winning at any game. However, the list that follows comprises games that are beatable by skill-based decision-making only. That leaves out special situations (e.g., tournament play) and physical techniques (e.g., roulette prediction and dice control), which are discussed further below.
The five beatable games that you can play in a casino are blackjack, video poker, poker, sports betting, and race betting.
Blackjack and video poker are rare among casino games, in that you can get an edge despite playing directly against the house. This can't be done in other banking games, such as craps, roulette, baccarat, Three Card Poker, Let It Ride, etc.
Blackjack is beatable through card counting and various shuffle-tracking techniques. To win at video poker, you must be able to identify schedules that return greater than 100%, then be able to play them properly to achieve close to the optimum return.
In poker, sports betting, and race betting, you're playing more against the public than against the house.
In poker, the "public" is defined as the players at your table. If your skill level is higher than the collective skill level of the other players by a big enough margin to overcome the rake, then you'll win money in the long run. Winning at sports betting requires handicapping skills and/or shopping for lines that are better than the market average. You make the bets with a sports book, but you're ultimately competing with the sports-betting public at large. It's similar for horse-race betting, though more difficult because of the large amount taken out of the pari-mutuel pools (20% range). Winning at horse racing requires handicapping skills, and often, access to information that's not available to the general public.
Those are the beatable games. There are also several situations that render virtually every game potentially beatable. They include, but are not limited to, coupons, comps, promotions, progressive jackpots, equity overlays, and as referenced above, tournaments and physical techniques, the latter of which includes cheating.
For a leg up on the game that spawned this question, be sure to read Bob Dancer's excellent video poker articles, which are posted here every Tuesday.
