Best games to Play at the Casino
Since the question asks about "casino games" and not, specifically, table games, I'll add that there exist video poker machines in Vegas with positive expected value. (I'm not sure how to translate this into "odds" like the question asks, to be honest.)
Specifically, if you could make a single $100 bet on a game of "full pay deuces wild" video poker and execute perfect play, the expected value of that bet would be $100.76. See the pay table which generates this outcome and the detailed strategy at .
This positive expected value comes in part from a highly improbable event, a "natural royal flush", which pays pretty well ($400 on a 50-cent bet). The payout isn't so high as to be life-changing, which also means that the least probable event actually does happen every now and then - I've spent maybe two hours of my life playing this game with a friend and last summer we did get a natural royal flush.
I've seen these "100.76% return" machines in Vegas at Sam's Town (50-cent and $1.25 games) and at the Palms (not sure about the denomination - the area was mobbed with folks who were in it for the long haul). You can get a detailed, user-compiled, possibly outdated list of Vegas casinos with positive expected value games at .
There are other games with positive-expected-value pay tables such as the "100.17% return" "10/7 double bonus" game and the "100.07% return" "10/6 double double bonus" game.
It's pretty easy to understand why a positive expected value is still not a great deal:
1) You're at the casino to buy entertainment, not money, and despite your question, you don't really want to be playing the game with the best odds. (Otherwise by now you would have decided that the only way to win is not to play.) If you don't enjoy the math behind video poker, it's not very fun to win or lose $1 at a time grinding away like a gold farmer, and you're better off risking it all on a high-variance table game. Who cares about bankroll preservation? Go wild!
If you're afraid of betting don't pass and laying full odds at craps (house edge typically below 0.5%) at least go for the banker bet in baccarat (1.06% house edge) or play a few hands of blackjack (analyzed in other answers).
2) Risk of ruin is inherent to a finite bankroll: in order to have a 99.9% chance of not losing all your money at full pay deuces wild video poker, you need about 10, 000 betting units, or over $5000 at a 50-cent machine. The math has been done for you at .
The risk improves if you're a member of a casino loyalty program which gives cash back, typically 0.25% of your total bets for this kind of video poker machines.
Expectation says that before you hit a $400 natural royal flush, you'll have to cycle more than $22, 500 (45, 000 betting units) through the machine.
3) Making error-free plays costs time: with an infinite bankroll but finite time, you're still only making $1-$10/hr, and there is a theoretical upper bound on your expected winnings.
If you could play 1, 000 hands per hour with perfect play in a $1.25 game (the best denomination I've heard of) with 100.76% return, you would be making $9.50/hr. If you play perfectly but an order of magnitude more slowly you make 95 cents per hour.
Even if you got someone to give you an unlimited bankroll, you still don't have infinite time. The typical American has an expected lifespan of about 700, 000 hours, and even if one such person could spend every single hour of that playing full-pay deuces wild video poker perfectly with an infinite bankroll at 1000 hands/hour, they would only have $6.65 million to show for it.
So $6 million is a rough theoretical upper bound for the expected value of a human life as determined by full-pay deuces wild in Las Vegas.
One plus is that you get to hang out with the fascinating community - mostly elderly locals - who play the game for fun on the weekends, often for hours at a time. Makes total sense for them: the upside isn't nearly as good as the lottery, but the odds are a whole lot better.