The Math Behind Casino Games

Gambling games are full of different possibilities and combinations. You don’t necessarily need to attend a maths course in order to grasp how casino games work, but you should at least be familiar with each game’s odds before deciding to wager.

While most casino games require luck, they are not all the same — some are more rewarding than others. In this article, we will focus on some of the most popular casino games in the world and try to explain the mathematical probabilities behind them.


The best chance to win in a casino lies in table games. Baccarat is one of the more popular games of this kind and you can even play bitcoin baccarat in many online casinos. You can bet on the player’s hand (player bet) or the hand of the dealer (banker bet), trying to guess which one of them will get closer to a total of nine. You can make a tie bet as well.

If you choose the player bet, you should be aware that the payoff is one to one and the house edge is 1.24%. The banker bet usually has a slightly lower house edge — it sits between 1.24% and 1.06%. Winning on the banker bet will reward you with 95% of your wager.

The tie bet is the riskiest of all, as the probability of a tie happening is less than 10%. However, if a casino customer guesses this bet correctly, an eight to one payout is rewarded.


Many consider blackjack the most rewarding casino game. When hearing the words ‘maths’ and ‘blackjack’, a lot of people immediately start thinking about card counting. While you can effectively win the blackjack game if you know how to count cards, that can be easily noticed, and you can get banned from the game. So, we will only talk about the mathematical probabilities of winning in blackjack.

The house edge in this game is only 1% in most casinos. As you probably already know, the goal of the game is to obtain a score of 21 or get closer to 21 than the dealer without exceeding that number.

Ideally, you would want to get 21 out of your first two cards — that is called the blackjack. The chances for this happening are approximately 4.82%. A natural blackjack (ace and a 10-point card) is even lower and comes to about 1.2%.

Since there are several cards which are worth 10 points, you will have the best chance of getting a 20 out of your first two cards — around 10.25%. Getting a 19 (6.03%) or an 18 (6.48%) is also considered a good initial hand.

Note that these percentages are in relation to the game of blackjack that’s played with only one deck of cards and that these percentages are lower when there are two decks involved.


There are three main versions of roulette which are commonly played in casinos — European, French, and American.

The American roulette is the least rewarding one as it contains an additional number — the double-zero. Because of that, the house edge for the American roulette is 5.26%. The European roulette has a house edge of 2.63%, while the French roulette has some additional rules that favour the player and is therefore the most rewarding version of the game with the house edge of 1.32%.

As far as the odds go for European, French, and American roulette, they are as following:

  • Straight up – 2.7% and 2.63%
  • Row and split – 5.4% and 5.26%
  • Street – 8.1% and 7.89%
  • Corner – 10.8% and 10.53%
  • Six line – 16.2% and 15.79%
  • Column and dozen bets – 32.4% and 31.58%
  • Odd, even, red, black, 1 through 18, and 19 through 36 – 48.6% and 46.37%

Slot Machines

Slot machines make for the majority of casino games and are extremely popular among gamblers of all ages. However, unlike other games we’ve mentioned so far, slot machines are all different from each other as each game can have its own set of rules.

Because of that, we can’t write about statistical probabilities of slot machines in general, since some are more rewarding than others and have different types of bets that players can make. Nevertheless, slot machines have something called the RTP (Return to Player) — we use that to measure how potentially rewarding a game of this kind can be.

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