Top 10 Casino Game Probabilities

This is an updated and more in-depth version of an earlier post we wrote on the Top Ten Best Casino Game Odds

One of the things you’re most likely to encounter when you talk to either a professional or amateur gambler are often distorted and unreliable testaments about the ‘odds’ of any given casino game – for the most part, professionals have both a mathematical and an intuitive grasp of probabilities, regardless of what game their playing, but it can often be very confusing (and more than a little intimidating) when the issue is brought up in comparison to other games.  Clearly, some casino games give you a better chance of winning, either based on the format of the game or the strategies employed.

When talking about probabilities and ‘odds of winning’, it’s most useful to refer to the house edge, which is the difference between the true odds and the odds that the casino pays you when you win.  Essentially, it’s the amount the player loses relative to any bet made.  For instance, if the casino only paid you 95 cents every time you won instead of a dollar the House edge would be 2.5%.  This is how casinos make their money, and regardless of what casino you go to, there will always be a house edge that favors the casino over the player.  Learning which games have the lowest house edge, and how to subvert this handicap, is the goal of professional and amateur alike.


Three of the most popular games with the highest payout to house-edge percentage are Roulette, Let Em’ Ride, and Tri Card Poker, and are considered fixed games because the house-edge doesn’t change.

1.  European Roulette & 2. American Roulette
Since there is a difference between European and American Roulette (American Roulette having an extra slot), the house-edge and chances of winning vary according to the game.  The general formula used to calculate the house-edge follows.


3.  Tri Card Poker
This form of poker has a variable house-edge that ranges from 3.3% to 4.28%, and fluctuates according to the strategy employed.

4. Let Em’ Ride
Fans of this variation of 5 card stud will also be familiar with a reasonable house-edge coming in at 3.5% – the beauty of Let ‘Em Ride is the ability for a player to withdraw a percentage (usually 1/3) of their initial wager based on the flip.  Depending on the table, the house-edge can increase – for simplicity’s sake, the graph only shows Table 1

probability article - house edge

5.  Pai Gow
Known for its slow rate of play, and its incorporation of ‘pushes’ to keep the game moving, Pai Gow is a classic casino game with a relatively low risk which makes it popular both online and in real life.  Every player plays against the dealer, which also makes for a very social game that is fun and comparatively easy to learn – its strategy is also straightforward as well, and once you’re familiar with the hands, overcoming the house-edge is just a manner of patience.

probability article - house edge pai gow

6 & 7. Baccarat
We’ve given baccarat two spots on this list because of the two different ways one can play which render different odds.  Play as the “Player” and the house odds are 1.63%.  However, if you play as the “Banker”, the house odds are decreased even further to 1.17%.Considered one of the more ‘high class’ games in a casino’s repertoire, Baccarat is also one of the more vexing games when it comes to trying to beat the house-edge.  The majority of the game follows a principle of deciding whether or not to hit (H) or stand (S) – if the banker hits on a total of 5 or less, the chart below is used to indicate what move the player should draw.


If the player wins a bet on the banker, the pay is 19 to 20 (minus a 5% commission).  If the bet is won on the player, then the pay is 1 to 1, and winning bets on a tie have a return of 8 to 1.  The house-edge based on whether the win was on the banker, player, or a tie varies slightly according to whether or not the game is played with 8, 6, or a single deck.


8. Blackjack


As a card game that utilizes basic strategy, Blackjack is one of the cheapest card games you can play in a casino, and with a basic understanding of the game and the rules, most professional players can limit the house-edge to 0.5-1%.  The house gets its advantage by being the last player to act, which gives them a slight lead, so it’s important to rely on a basic strategy to indicate whether you should hit, stand, surrender, etc.  Shown is a standard strategy guide based on the flip of the dealer vs. player.

S = Stand
H = Hit
Dh = Double (if not allowed, then hit)
Ds = Double (if not allowed, then stand)
SP = Split

There are a number of other things to consider in any given game, including the number of decks being used, and what probability you have of busting (when you exceed a value of 21) based on your hand – as a general rule, the fewer decks used, the lower the house-edge.

probability-article---black jack decks

The gameplay of Blackjack, relying on the value of two cards, means that there are a number of possible outcomes, and each outcome has its own probability – below is a general Two Card Count table with the projected frequency of that outcome.


9. Craps
As a dice game, Craps requires just as much – if not more – strategy and planning, and a keen grasp of the probabilities of a given roll of two dice, with 7 and 11 being a win and 2, 3, and 12 being a crap out.  More than that, though, a professional Craps player must also be intimately acquainted with the different kinds of bets and their corresponding probabilities.  The house-edge in a Craps game ultimately depends on what type of bet is being made since every roll is independent of the previous roll.


Whether you’re a seasoned Craps player or just starting, you’ll quickly learn that the most assured and reliable method of winning is to rely on the Pass Line bet.  However, the ratio probability of win/loss is still stacked against you on a Pass Line wager (which is considered the safest bet) as the graph below illustrates.


The expected value of 32 straight (on average an hour of play) $5 pass line bets (with a house edge of 1.41%) is a loss of $2.26.  There are exactly 16 outcomes that create a player win and 16 outcomes that create a player loss. The winning probability of the pass line (49.3%) creates the difference in the overall winning (39.89%) and losing (46.16%) outcome percentages. Enchant your skills on the

Source: Craps House Edge Guide
10. Five Times Odds Craps
This version of Craps is similar to the classic but allows you to add extra wagers to pre-existing bets.  For example, if you make a Pass Line bet, you then have the option of laying another bet which the house has no advantage over.  Unlike some of their competitors, Silver Oak Casino permits a player to stack up their bets 5 times, which will pay out at their true odds.  In this way the house-edge is reduced (up to 0.2%), which makes it one of the lowest risk games available.