This is a difficult question to answer because it depends on a number of variables, mainly how much do you want to win relative to your bankroll, but also with how much risk are you willing to take. It should also be pointed out that a more realistic way to phrase the question would be “What Games give you the least chance of losing”, as in the long run, no matter what, eventually the player will lose as no game has a payout of over 100%. Every game has what is known as a “house edge” which is the amount on average for each $1 wagered the casino will make in profit. But every game has a different probability of the players winning, so which games in the casino have the best odds?
If we make the assumption that you will sit at the table with a bank roll of $100 and play for a stake of $1 per game, and never change stake size, then the casino game with the best odds is “Vegas Strip” BlackJack to perfect strategy. There is a large number of different varieties of Blackjack and they have different payouts but Vegas Strip (If played perfectly) has a house edge of just 0.28%. It is quite rare to find a casino with these rules though (being able to split and double multiple times is the main player advantage) and an edge of 0.4% is more common, but 0.28% is possible.
The next best would be “Jacks or Better” Video Poker which has a house edge of 0.46% again IF played to a perfect strategy. It must be pointed out here though that the edge must seem higher when you are playing as a huge amount of the payout, some 4%, is the Jackpot for getting a Royal Flush. A bet of just $1.25 pays out a massive $4000 on one hand. Without this Jackpot (which you are unlikely to get over 100 deals) the house edge would often appear to be nearer 5%.
This game has a very low house edge at just 1.06% and is also a very very simple game to play. You can not go wrong and there is no strategy, you just pick “Player” or “Banker” and then let the cards decide if you won or not. Banker is the better of those two options by the way. This game due to its simplicity is favoured by many “High Rollers” of the Casino World.
The next best option in a casino for a player is not a card game but one that uses dice, and the game is known as “Craps”. Much like Blackjack the payout will be determined by decisions the player makes as the game progresses and also the bet types he chooses to make. The optimal bet a player can make is to bet on the “Don’t Pass/Don’t Come” line, which will mean on average he shall lose 1.36%.
This game should have a quick mention in that its payout is a possible 1.5% house edge, and it is found in several online casinos but not many land based ones. This is because it is not favoured by players due to the (relative) complexity and it is not favoured by casinos due to the large number of cards involved and the slow turnover of the game (resulting in less profits).
Now this is arguably the most popular and certainly the iconic casino game and yet remarkably it has a fairly high house edge of 2.7% if it is a European wheel with a single zero but 5.4% if it is an American wheel with two! The reason Roulette is so popular is partly because it is so quick and simple and partly as you can very easily win many multiples of your initial stake (unlike BlackJack for example which would only x2 your money, picking a correct number would x36) but mostly because it appears to be beatable with skill. It is very visual, black and red, or easy to spot “patterns” in the numbers. But of course this is a fallacy, anybody with a PHD in mathematics and code breaking from Cambridge University would have just as much chance of making a profit as a monkey randomly throwing his chips on the table. Sit there for 100 spins betting one a time and after the 100 is up chances are you would each have 97 chips left.
A modern addition to Casinos both land based and online is “Video Slots”, these are almost like computer games with many bonus features involved often involving pseudo skill to win higher value amounts. They are designed in a range of themes and styles to suit every taste, with very often a link to popular culture be it recent movie releases or memories of childhood cartoons. The payouts vary from game to game and there is no real mathematical way to formulate it it is set by the programmers at the outset of the games run, but it is safe to assume the average is around 10%. You can check the individual casinos to see which games have the highest paying slot game as it varies from place to place. Overall Video Slots are one of the most lucrative games for the Casinos by quite some way. BUT… If you want to win at the Casino, if you want to actually walk away with more money than you can think what to do with, Video Slots is the game for you because of the variance involved. The Jackpots are huge, and any $1 spin can win 1000s of times this amount, so this is your best chance of winning at the Casino!