The mathematical explanations of casino winnings

It is not entirely unusual to consider gambling as a means to eke out a living. With hard economic times yet to come, jobs are getting harder to get by the day. If you seriously want to make an income via gambling, then this article is for you.

The idea of getting rich quick in itself has helped casinos, and their stakeholders earn copious amounts in revenue each year. Many people get into betting with hopes of winning but don’t realize that the math and probability give the casino a foot forward. Cases of winning without actually losing are quite rare.

Let’s first understand where and how math is used in gambling.

Where Math is used in gambling

Math is basically the base of gambling. It is practically used everywhere. The most common thing related to math that you will hear in betting is the likelihood that a particular thing will occur. This is what we call probability. Probability in math is a way of measuring how likely it is to have an event happen or not.

To understand probability, you need to know that it is always a number between 0 and 1. An event that will never occur has a probability of 0 while that that will always happen has a probability of 1.

To calculate this, you divide the number of ways an event can happen by the total number of events possible.

Here is one example:

When you flip a coin, two probable events are likely to happen. It either lands on heads or tails. Say you want to know the probability of it falling on heads. The likelihood of this ½ as there is the only way for it to do so. This can also be indicated as 50%, 0.5 or 1 to 1.

There are also odds in gambling. Odds and probability are almost similar, but odds also indicate how much a player can spend and win in the event he/she wins the bet.

For example, if you are given 6:1 odds on a match, you will win 6* of your stake if you win the bet. If you are given 3:1 you’ll win 3* of your investment.

As a gambler, you can use this to make better decisions when you bet. Say casino A offers the 6* odd whereas casino B offers the 3*. It is saner to gamble with casino A because the probability of winning remains the same.

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Converting Odds to Indirect Probabilities

Converting the odds mentioned above is one exciting part of this topic.

There is one rule to remember in the conversion of odds into indirect probabilities;

Implied Probability of an Outcome=Total Payout / Stake​

Where Stake= Amount gambled

To get the indirect probability of a result, you take the expected financial return on your bet and divide that amount by the amount wagered (Stake).

It is essential to note that the odds keep changing with time as the bets come in. This also means that the bookmaker’s (person that accepts and pays off bets) probability approximations also change from time to time. The odds also given by different bookmakers are also not always accurate as you will note that they vary remarkably.

To make gambling a profitable venture, you need to consider when the odds show a chance of winning and not only backing the winners. You can accurately say that team A will win a match against team B, but it wouldn’t make much sense to stake $100 for a payout of $60. Hope that brings us on the same page. Gambling becomes more fulfilling when you view it as an investment rather than a time-passing activity.

Here is a more straightforward explanation of the difference between probability and odds.

Probability is the ratio of the number of times an event occurs to the number of times trials are run. Odds are the ratio of the number of times an event does not happen to the number of times an event occurs.

House Advantage

So you may ask, why does the casino mostly, if not always, win? What they don’t tell you is that casino math gives them an edge over you. Every single time you play at the casino, the statistical probability gives you them an advantage over you. This tends to vary in every game is meant to make sure that the casino doesn’t lose money to a player. After all, why else would they be in business?

The casino’s advantage in a game of Blackjack might only be 0.5%, but that is only if you’re outstanding. Some types of slot machines have a 35% advantage over a player, and other games fall therein between. Slot machine odds are the worst. When using the maximum coin play, you have a one in 5,000 to a one on 34 million chance of winning the top prize.

Sometimes people do win, and some win vast amounts of money. So this does not entirely mean that winning is impossible. One thing that is beyond reasonable doubt though is that the more you play, the more the odds work against you. The more time you spend in a casino, the higher your chance of going home with a slimmer wallet.

Further, the odds displayed never match the real probability of the event occurring or not occurring. The bookmaker always adds a profit margin to the odds. This means that the payout won by the player is still less than the amount they would have won if the odds matched the real probabilities.

To achieve this, the bookmaker has to accurately estimate the actual probability of an event so as to set the odds on display in a way that benefits them regardless of the outcome.

Since the math is simply not your friend, it is your best financial interest not to walk into that casino. However, for the bold ones who still want to try out their luck, it’d be best if you quit while you’re still ahead. That sequence of won games in your head is all but imagination.


A gambling chance is worth pursuing if the probability assessed for the outcome of an event is higher than the probability given by the bookmaker. The odds on display also don’t match the true probability of the occurrence of an event or not. If the odds had reflected the real chances, then the payoffs would’ve been much higher. The casino always wins because the bookmaker includes profit margins.

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