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Casino Probability Guide

casino probabilityKnown as the backbone of casino game mathematics, probability is chance of something happening. Since casino games rely on odds, casino probability is basically the odds of an event happening in a game. Probability is usually represented in a fraction or a decimal format between 0 and 1, or as a percent between 0% and 100%. Generally, when representing casino probability of games, it’s in the percentage format.

Now don’t be intimidated by all the numbers and mathematical concepts. Mostly, Kiwi players don’t have to calculate casino probability themselves. But, it’s an interesting concept that’s useful to understand. It will give you an edge when it comes to learning and picking casino games to play.

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What you’ll find in this guide:

How do Casino Use Probability?

So, going back to basic probability, 0 means that the event never happens and alternatively 1 means that it always happens. In a mathematically ideal world, for example, in a coin toss there are zero chances of a coin landing on no sides a 1 chance of landing on either heads or tails, and a ½ chance of landing on heads. Another factor involved in understanding probability; you need to know about sample space. Simply put, a sample space is all the possible outcomes. Some sample space probability examples are:

  • When tossing a coin, there are two outcomes and therefore the sample space is {Heads, Tails}.
  • Rolling a six-sided dice, there are six outcomes. So therefore, the sample space is {1, 2, 3, 4, 5, 6}.
  • When playing American roulette, there are 38 outcomes on the roulette wheel when it’s spun. Therefore, the sample space is 1 to 36 along with the 0 and double-0.
  • There are 52-ways a single card can be dealt to a player. The sample space is made up of the set of cards from Ace to King, looking at both rank and suit.

Casinos use probability to create games that allow players to both win and lose. However, they are slightly tweaked to make sure that the house – or the casino – wins more often than it loses. There are quite a few equations used to ensure that this happens. But don’t think that if you figure out their equation it will give you an advantage. This is because human interaction has an influence on the results too.

Expression of Probability: Fractions, Decimals & Percentages

When working with probabilities, they are by their nature fractions. However, you can use multiple ways to express the probability. Probabilities, or odds, are expressed by the number of ways it can’t happen vs. the number of ways it can happen. Using the coin toss as an example, probability can be expressed in the following way:

  • The chances of it landing on heads or tails is 1/1 in fractions, 1.0 in decimals, and 100% in percentage.
  • Landing on the heads side has ½ chance in fractions, 0.5 in decimals, and 50% in percentage. The same goes for the tails side.
  • There’s no probability of it not landing on any side. Therefore, it’s 0 in fractions, 0 in decimals, and 0% in percentage.

Probability Examples: Best Probability Casino Games

Looking at casino probability, it’s used for the purposes of figuring out a player’s chances of a win occurring. This is also translated to asking “what are the odds of a game?”. Based off this casino probability, the game comes highly recommended or not. Let’s take a look at the odds of some popular casino games probability examples. They tend to be the same as the odds at a land-based casino.


Because of the way the game is played, blackjack casino probability is very interesting. In this game, it’s almost as if the deck of cards has a memory. This is why people who have learnt to count cards get an advantage over those who haven’t. They can keep track of every time a card is dealt and the resultant odds change. A probability example for blackjack is: you’re playing a single deck game and you notice that all four Aces have been dealt. So, what the probability of you getting a blackjack? Since it takes an Ace and a 10 to make a blackjack and there are no Aces left in the deck, the probability is at 0%.

Card Game

Casino probability for card games are based on the qualities of a card. A standard deck of cards has 52 cards. Therefore, the probability of getting a single card is 1/52. To get the casino probability of getting a specific suit, then it’s ¼ because there are four suits – diamonds, clubs, hearts, and spades. For a specific rank, it’s 1/13.


There are two variations to roulette that Kiwi players will find in a casino – American roulette and French roulette. And both of them have different odds for winning. Because the American wheel has an additional double-zero pocket, it increases the probability to 1/38. Whereas the French wheel doesn’t have the double-zero and therefore, the probability is at 1/37.

Pokies & Video Poker

Pokies aren’t the greatest games in terms of casino probability. There’s no way of knowing what the odds and payout are. The pay table is designed to show you what the payoff is which the various reel symbols. But you don’t have to worry about this as this information can be found online when searching for reviews of that specific game.

On the other hand, video poker doubles the probability that you’ll find with a standard deck of cards. NZ players know both the combination of cards that payoff and the casino probability of getting each combo. Probability can be used in video poker to work out calculate the house edge and the payback percentage for the game.


Calculating Expected Return

Learning how to calculate expected return is a great skill to have. It’s basically learning how to work out how much a bet is worth. If the bet is worth more than what you’re risking, you expect a positive return. Alternatively, if the risk is more then it’s a negative expectation bet. The abbreviations +EV and -EV are often used. To calculate expected return:

  • Take the casino probability of losing and multiply it by the amount you’ll lose.
  • Then, take the probability of winning and multiply it by the amount you’ll win.
  • Then take those two values and subtract the one from the other to get the expected return.

A probability example to see how this works:

  • You’re playing American roulette and bet NZ$100 on a number. Win and you get NZD3500; lose and you lose NZ$100. As we know the casino probability of winning on this roulette wheel is 1/38 and losing is 37/38.
  • So, 1/38 x NZ$3500 = NZD92.11 and 37/38 x -NZ$100 = NZ$97.37
  • NZ$92.11 – NZ$97.37 = NZD5.26. Therefore, this means that you can expect to lose NZ$5.26 or the -EV is NZD5.26.

Learn more about these casino probability games:

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