Probability, Odds, and Luck in Casino Games

Casino Game

A casino game, also called game of hazard, is defined as a game of chance, whose primary trademark is that the ratio of winnings is lower than what the expected value would be, which is calculated using actual mathematical probability equations. This characteristic shouldn't come as a surprise; if there was no profit in it for the casino, it would never offer these games. They have to have an advantage, which is referred to as the house edge. How big the house edge will be depends not only on the particular type of game, but also on the player himself - his knowledge of the game, his bets and his temper. 

What is the difference between gambling and investment?

Gambling is when a player engages in a game with significant house edge, in hopes of beating the game by chance alone. An investment, on the other hand, is when a player not only expects to get his bet back, but actually profit from the game in the long run. The formal definition of an investment is the sacrifice of the current value of capital for the sake of future profits. This isn't to say that all investments will yield profits. The key, however, is that the probability of a particular investment being profitable is considerably high. Casinos don't have to worry about making money - all of their offered games exhibit such high house edges that the expected value of them is always positive in the long run.

The concept of expected value (EV) can also be applied in real life. When considering a business investment, for instance, a potential investor will always calculate the EV and compare it with the risk associated with the endeavor. Another real life example where EV is used is the compilation of a stock portfolio.

Probability

There are four basic definitions of probability. The most often applied one is the classical definition, which says: "Probability is the ratio of the number of cases favorable to it, to the number of all cases possible, when all cases have an equal likelihood of occurring in a random experiment." Consider the following simple example:

What is the probability of a 6 coming up on a roll of a die. The number of favorable cases is 1 (the die has only one 6), the total number of possible cases is 6 (the numbers 1-6). The probability P therefore equals 1/6 = 0.1667. The definition of probability stipulates that the value of a particular probability will always be between the numbers 0 and 1, with 0 being impossible and 1 certain. 

Now consider this example of an impossible event:

What is the probability that a 7 will come up on a roll of a die? The number of favorable cases is 0, because the number 7 is not included on a die. P therefore equals 0/6 = 0.

Certain event:

What is the probability that a number from 1-6 will come up on a roll of a die? P = 6/6 = 1.

When assessing probabilities one needs to refrain from rushing to conclusions. Be sure to check out our article on myths and misconceptions in gambling, where we address many fallacious conclusions. Also check out our article on mathematical ratios and the calculation of the house edge.

Odds

Odds is quite frankly just a synonym for probability. As mentioned earlier we use the letter P to represent the probability of an event occurring. Odds can be expressed as follows: P/(1-P) and the result is commonly expressed in the form: "one-to-x".

Example of the calculation of odds:

If somebody asked you what the odds are that tails will come up on a coin toss, you would probably instinctively answer 1:1, or fifty-fifty. You would be right. How does this look mathematically, though? The probability of tails is P = 1/2 = 0.5. The odds of tails therefore are 0.5 / (1-0.5) = 0.5 / 0.5 = 1:1 (or 50:50 for that matter).

Luck

Luck is technically defined as a favorable outcome of a random event that occurs on which we had no influence. If one player is lucky, the other one is usually unlucky. For games of hazard, the old saying "you make your own good fortune" is true as well. Those that constantly use bad luck as an excuse tend not to be very good players. Some games, such as poker for instance, you can directly influence your fortune through good knowledge of the game, skills, correctly assessing your opponent and determination. Casino games that depend on chance require good knowledge of the bet ratios, which will enable you to use advantageous bets and avoid the disadvantageous ones. Even though the house always has the edge, this knowledge will help you optimize your strategy and minimize your losses.

The final thing you can influence is your style of play. If you have 1000 chips in your pocket, it is only up to you if you want to invest your whole capital at once or if you want to spread your wager into 100 bets for 10 chips each. The house edge remains the same, but the first way of gambling is way riskier.