Latest casino articles

The Casino Games Math Easy

Thursday March 19th, 2026

It is recommended to look through basics of the gambling math so that you can understand what the site pages say. If you are good with Theory of Probability and Mathematical Statistics, if you are not scared by the terms "mathematical expectation" and "dispersion", then you can instantly go to the further sections of the site.

So, any gambling game is a random process. Ideally, the chances in dice, cards or roulette are equal. For example, let's take roulette. It has 37 figures from 0 to 36. It's quite a wide range of possible stakes (from one number to chance bets). Let's take a chance bet on colour. You place one chip on the red. The roulette has 18 red numbers, 18 black numbers and one green zero. Probability of falling of each of the numbers is equal, consequently, you place 37 chips and on the average you'll win 18 chips (pay-offs in chance bet is one to one) and lose 19. It turns out that placing 37 chips, you will finally end up losing one chip, in other words, the expected loss is one chip against 37 placed = 1/37.

It may be explained in other terms, you will have 36 bets back as pay-offs out of 37 bets, thus we can draw a conclusion that the average pay-off percentage in the roulette is - 36/37. This value 36/37 or approximately 97,3% shall be mathematical expectation (ME) of pay-offs in the roulette. 1/37=1-36/37=2,7% (approximately) - this value is referred to as the advantage of the casino. Most games have pay-off percentage less than one hundred, so the casino has an advantage. However, sometimes players may use the situation for their own benefit and make pay-offs exceed 100%, this is a case of player's advantage (0,1% player's advantage means that pay-offs amount to, 100,1%).

All of the above are just average number! It is clear that exactly 18 reds and blacks and one zero will hardly fall in 37 roulette spins. Indeed, practical results will probably differ from the average expected results. Diversion of the fact from the theory is known as dispersion. Dispersion is not just a general notion of dispersion but a quantitative measure as well as mean square deviation; we will not give their formulae, as they are not of much use. Dispersion varies depending on the game and even bets in one game. Just imagine, you place one chip on numbers or on odds. Mathematical expectation in roulette is the same for all bets - 97,3%, but dispersion is different. When staking on odds you will lose and win now and then, in 37 spins you will hardly lose or win more than 5-7 chips. But when placing a bet on numbers you may win in one of the first spins and you will win more than 30 chips. It can also be just the opposite - 37 spins with no "necessary" number and you are in the deep hole. Generally, dispersion allows a player to be a winner on a short term distance.

However the laws of the Theory of Probability state that the more we play the closer are our results to the mathematical expectation. If you stake on odds, after the first spin your chances to win is close to 50%, after 100 spins it's about 37% and after 1000 spins it is less than 20%. On the average after 1000 spins you will lose 1000*2,7%=27chips, but as you see, with some luck you can win it back. If you stake on numbers, then a chance to win after 1000 spins is higher and is about 30%, this is correct, as this type of bet is more dispersive and great fluctuations are possible, then you will have more chances to cross the barrier of 27 chips. You should not think that dispersion is only good. High dispersion means that you will win big as well as lose big. But in a long run of ten thousands games you will be maximally close to mathematical expectation and your chances to win will be about nil.

Thus, when speaking about dispersion, we shall remember about such parameter as "bankruptcy risk", i.e. to lose all your money at a particular point of your playing process. This is what the players call "risk management". You should know what bets you can afford with a certain bank so as not to dice away. It will be very upsetting, if you come with $100 and lose it all in plus game, playing with $10. At least you should estimate the probability of leaving without a win but with empty pocket.

On the whole, you don't have to be able to calculate mathematical expectation and dispersion, the experts had already done it before you and you can use the ready numbers. You should understand the main thing - the higher the mathematical expectation of a game is (lower advantage of the casino), the better it is for you. It will allow you to play as long as you want and will boost your chances to win. Ideally you should search for the games with the player's advantage, and then you can expect a win. Regarding the "plus" and "minus" games for a player, one simple truth should be borne in mind - dispersion. The higher it is, the more "thrash" you will experience in a game. Even in the game with the player's advantage, you will lose some sessions (because, as usual the advantage is not that big and the losses will not be rare). But as you proceed in playing, the closer you will be to getting what the game has in accordance with its mathematical expectation.

Play to win, not to lose!!!

← Casino Bonus Promotions To Choose From