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The Probability, Odds and Luck in relation to Gambling Games

The theory of probability is absolutely essential for the correct evaluation of individual wagers of various casino or gambling games. We will get familiarized with the definitions of gambling games, luck, investment, calculation of probability and we will also point out to some myths and common mistakes the players make when assessing probability.

What is a Gambling Game

A gambling game can be defined as a game of chance, when the payout ratio is lower than the true, mathematically calculated, odds. It is understandable. If a casino wants to make profit in the long run, it has to have some edge over the players.

How big the house edge will be, though, is a matter of the players themselves – their knowledge of the games, their rules and wagers (especially the true odds) and players' temper.

What is the Difference between Gambling and Investment?

You gamble when you play, even though you know about your disadvantage (= house advantage) but you hope to overcome it by your luck. On the other hand if you invest your money you suppose not only to get back what you have invested but also some interest on it.

The investment can be also defined as a surrender of the present value of the capital in favor of the future profits. Of course it does not mean that every investment will go well and bring you the profit or economic benefits, but there is a high probability of success.

This is the case of a casino, whereas a long term profit is guaranteed due to the house edge in almost every casino game. The house edge can be determined universally on the basis of the concept of expected value.


There are four basic definitions of probability. The most known is the classic one, which defines the probability as a fracture of the number of favorable events and all possible events that can occur.

Simple Example of the Classic Probability

What is the probability to roll six with a regular dice at one attempt? The count of favorable events is 1 (there is only one six) and there are 6 possible events (numbers 1–6). Then the probability is P = 1/6 = 0.1667. This digit form is required by the definition of the probability as it takes the values from 0 to 1, whereas 0 is the impossible event and 1 is the certain event.

Example of the Impossible Event

What is the probability to roll 7 with one dice? The count of favorable events is 0 (there are only numbers 1–6), therefore the probability is P = 0/6 = 0 and we call it the impossible event.

Example of the Certain Event

What is the probability to roll one of the number 1–6 with one dice at one attempt? Here we talk about the certain event, since there are no other numbers than 1–6 on the dice, P = 6/6 = 1.


The Odds is just another stipulation of the probability. Let us assume that P is the probability. Then the odds can be stipulated as follows: Odds = P / (1 – P) and the result is usually converted to the form „1 to …“.

Example of the Odds Calculation

If somebody asked you what is the chance (odds) to roll either side of a coin, you would probably answered 1:1 or 50:50 without hesitation. And you would be right, of course. How is this connected with our definition? The probability to roll either side of the coin is P = 1/2 = 0.5. The Odds is then 0.5 / (1 – 0.5) = 0.5 / 0.5 = 1:1 (or 50:50 if you like).


The luck can be defined as a specific random event, which happens according to our wishes and which we were not able to influence in any way. A player's luck might be another's bad luck.

Even when playing gambling games you can control your luck at least partially. If somebody always complains about his or her disfavor of Fortune, then he or she is likely a bad player. In some games, like Poker for instance, you can influence your luck directly – by your knowledge of the game, experience, determination and "reading" of your opponents.

If you play the games of chance, then it is vital to know the true odds. They will help you use advantageous wagers and avoid disadvantageous ones. Even though the house has edge in most cases, the knowledge or true odds will help you optimize your winning chances and/or eliminate unnecessary losses.

The next thing you can influence is the style of your play – a distribution of the risk. If you have e.g. 1,000 chips in the pocket, then it is fully up to you, whether you put all your capital in jeopardy or if you distribute it for let us say 100 chances. The expected result is the same, but the first option is highly risky.

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