JeffBet by Matthew Gover |
Date of Publishing: 8 November 2022

5/5 - (5 votes)

Casino Game Mathematics Guide


Playing casino games can be a lot of fun because they provide excitement and the possibility of winning money. However, to take prudent risks, you need to understand some fundamental casino math. Nothing is more important in gambling than the odds you are betting on. An understanding of casino math will help you determine if the games you are playing are profitable.

The Link Between Math and Gambling

In gambling, mathematics plays a critical role. Perhaps the most pervasive mathematical concept you’ll encounter is probability, or the odds of a certain event occurring. Many gamblers don’t give much thought to the intricate mathematical systems underlying the games they play. While some casino games rely solely on a player’s good fortune, there are games where an understanding of strategy and math will contribute to the player’s chances of winning.

Mathematical Gambling Strategy 

Professional gamblers typically weigh the probability of each round or bet they place. Such analysis would include noting the odds of winning, the expected win value, the volatility index, and length of play to determine how much to wager. These metrics provide a quantifiable depiction of risk and inform the gambler whether or not a wager is worthwhile. In some games such as poker, deciding whether the game is plus EV (expected value) is an essential part of the decision-making process.

Before Gerolamo Cardano in the 16th century, no one had attempted to put a number on chance. This sparked a new era of inquiry. He authored one of the earliest guides to gambling, where he explored the idea of a “sample space” of likely outcomes. There are 36 possible outcomes when using two dice, but only one of them will yield two sixes. Some believe this was the beginning of a new branch of mathematics, the theory of probability, which became the foundation for strategic gambling.

How has it changed as time has passed? Mathematical analysis of gambling outcomes is now available in the form of gambling strategies. This allows punters to reduce their exposure to risk in any form of the gambling enterprise, be it a live game of poker or even roulette. That, of course, is a simplified explanation.

Casino House Edge and Return Percentage

The house edge is a mathematical advantage the casino has over the player in all casino games.

Each casino game has its house edge, and in many cases, individual bets have their house edge as well (as in roulette). A bet’s house edge is the percentage you lose to the casino while placing that bet.

The house edge cannot be completely removed, but it can be reduced by careful play. This is accomplished by establishing game rules that favour the house, as in blackjack or by paying slightly less than the genuine game odds. 

The house gains an advantage when a player goes “bust” at blackjack. Since the dealer’s turn comes last, they may sweep the table without even taking a risk of busting.

If you want to play the best game possible, you can look up the return-to-player percentage for each game offered by an online casino. The game of blackjack does have the lowest house edge.

Games are generally discussed in terms of their “Return to Player,” or RTP, rather than their “House Edge,” which is the percentage of money won by the house over the long run. RTP is most often associated with slot machines, but it is also available for other games like cards and tables.

However, the “return to player” (RTP) is more commonly employed to determine the typical payout of a game.


House Edge and RTP go Together

The house advantage and RTP are two sides of the same coin. By deducting the RTP from 100%, which represents the entire amount of stakes returned, it is simple to determine the average house edge or casino profit.

Take the slot machine game Starburst, for instance, which has a potential RTP of 96.06%. Since 100-96.06 = 3.97, the house advantage is 3.97%.

Theoretical vs Actual RTP

The theoretical RTP is the rate of RTP that has been published, although this outcome is not guaranteed. It is certainly feasible to spend £100 on slots and win nothing, just as it is feasible to spend £0.50 and win enormous jackpots.

It only depends on your luck during that playing session in pure chance games. While you can employ techniques to increase your chances of winning at “skilled games” such as blackjack.

Therefore, you can rely on the published RTP to be accurate, even if the actual and theoretical RTP may alter as you play based on how you play the game. RTPs for casino games are independently examined by gaming auditors like iTech Labs and eCOGRA. To ensure that the RTP is as promised, these businesses utilise software regulated by the appropriate gambling licenses for their region.

Video Poker Math Facts

Following a basic strategy is not the only way to get better at video poker. Players should remember that they also need to analyse the various draws they may encounter during gameplay.

Both the classic game of poker and its video variant heavily rely on mathematics. Mathematics should be an important consideration for all players, especially when it comes to probability and how it relates to poker. When it comes to probability, dealing with particular cards is always a part of formulating strategy and pertains to arithmetic so that a player may determine their chances of winning. Additionally, knowing the mathematics of video poker can aid players in maintaining emotional stability and mental focus.

The 52 cards in a poker deck are split up into four suits and exactly thirteen ranks. As a result, your chances of receiving an Ace as your first card is equal to 7.7%, or 13 to 1. In contrast, the chances of getting a spade from the four suits as the initial card are 25%, or 4 to 1.

Because each card changes the way the rest of the deck looks after it is dealt with, understanding the maths behind this game is arguably more important than it is in any other casino classic. For instance, there will only be three more Aces in the remaining deck of 51 cards when a player gets an Ace as their initial card. This simply means that the chances of receiving another Ace card are 3 in 51, or 5.9%, which is substantially lower than the possibilities at the beginning, before the first Ace being delivered. If you bet not knowing these odds, you are very much relying on luck only. Additionally in poker, a lot of people continue with the hand in the hope that they will hit the card they need. If you have a 5% chance of hitting that card this should determine how much you are prepared to call.

Blackjack Math Facts

The likelihood of getting a blackjack is the number of ways we have to draw two cards from the deck to reach 21.

We need an Ace and a 10 to make 21 with just two cards. In addition, the deck has 16 tens and 4 aces (between face cards and 10 value cards).

Since there are the same 4 aces in 52 cards and 8 in 104 cards, each figure or number keeps the same proportion when playing with many decks. However, the likelihood of obtaining a specific outcome varies slightly since removing a card from a deck of 104 cards has a smaller impact than one from a deck of 52 cards. As a result, each game with various decks has a unique probabilistic study.

In a game with only one deck of cards, it is easier to calculate the dealer’s and the player’s odds and probabilities of winning blackjack, even if these calculations are dependent on the hands of both parties. Accordingly, the player has a 4.8% chance of receiving a blackjack.

The percentages for a “No Bust,” “Standing,” and “Decision” hand are 26.5%, 30%, and 38.7%, correspondingly. The dealer’s final blackjack hand odds are 4.82% for a natural 21, and 17.58% to 28.36%  for a hand between 20 and 16. In a one-shoe game, the player’s odds of busting are 100% for a total of 21 and reduce to 0% for hands < 11.

Slot machines math facts

For many players, the concept of payout percentages and slot game RTPs is one of the most perplexing aspects of playing online slots. Every slot machine game you see online has been created so that players can receive a share of the bets they make. Knowing these numbers allows you to identify a slot machine that will provide you with better winning rewards over time.

Also, players can calculate their chances of winning the bonus games in some slots by counting the number of Scatter or Bonus symbols on each reel.

The average number of spins needed before bonus games are activated will surprise you. When you get this knowledge, you can use it to play with a strategy that will allow you to maximise bonus rounds.

Casino Game Mathematics FAQs

An RTP is a game’s return to player percentage. This is the percentage of every bet that can be returned to the player.
House edge is what’s left of every bet after the RTP is removed. It’s the percentage of a player’s bet that’s in favour of the casino.
Mathematics is the basis of all casino game strategies. Every strategy monitors the probability of a player getting a favourable outcome based on calculated actions.
Casino game math doesn't guarantee winnings, but it might help improve winning chances.
A game’s volatility depends on how likely a player is to go on long losing streak. Blackjack, for example, is a game with a very low house edge, and it would be quite unlikely to lose time and time again, providing you know what you are doing.

About the Author

Author: Matthew Gover.

After graduating, Matthew began working as an English teacher abroad, initially in Spain and then Vietnam before finally coming back to the UK to settle. Matthew has always had a love for writing and an even bigger love for the igaming industry... Read More

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