If you want to know how far one point is from another, you use “distance” to measure that. 

Another example of a word used to describe a measurement is “volume.” You can buy milk by the quart or by the gallon, for example.

“Probability” isn’t just the mathematical study of likelihoods. It’s also the word we use to describe and measure how likely something is to happen.

Probability, by its nature, is measured differently from other kinds of measurements.

Most things we measure using arbitrary units. In the previous example, we use inches to measure distance and ounces to measure volume.

But in probability, we use a measurement that’s based on fractions. And the probability of an event happening is always just a fraction that’s less than or equal to 1.

If something has a probability of 1, it’s a sure thing. It will happen every time.

Here’s an example: If you have a jar with 20 marbles in it, and all those marbles are white, and you pick a marble from the jar without looking, the probability of picking a white marble is 1.

The probability of picking a black marble is 0. There aren’t any black marbles in the jar.

It gets more interesting when you put different colored marbles in the jar. If you put 10 white marbles and 10 blackjack marbles, you have a probability of 1/2 for getting a white marble at random. You also have a 1/2 probability of getting a black marble at random.

The formula for probability is simple, too. The probability of an event is the number of ways that event can happen compared to the total number of possible events.

In the marble example, you have 20 possible events (20 possible marbles you could pick at random). 10 of those are white. The probability of getting a white marble at random, then, is 10/20, which reduces to 1/2.

You can express that probability in multiple ways, too, not just as fractions.

The odds of something happening are just a comparison of the number of ways it can happen versus the number of ways it can’t happen. In the marble example, you have 10 white marbles versus 10 black marbles, so the odds are 10 to 10 of getting a white marble.

You can reduce that just like you would a fraction to get even odds – 1 to 1.

Let’s change the example, though. Now, let’s suppose you have a jar with 5 white marbles and 15 black marbles in it. Your odds of drawing a white marble are 15 to 5, which reduces to 3 to 1.

For every possible white result, you have three possible black results. Obviously, you’re likelier to get a black marble in this situation than you are to get a white marble.

One of the reasons that this is so useful is because odds are also used to describe how much a bet pays off. A lot of bets are even money bets. You bet $100, and if you win, you get $100. If you lose, you’re out $100.

But in some bets, you might win more money than you’re risking. For example, you might place a bet where you could win $200 and only risk $100.

When you play casino games, the casino always has a mathematical advantage. It’s easier or harder to measure depending on the game you’re playing and the rules.

The easiest example might be roulette. The math behind the house edge is relatively easy to calculate.

Let’s look at an even money bet, a bet that the ball will land on a red number.

You have 18 red numbers on a roulette wheel, 18 black numbers, and 2 green numbers. You have a total of 20 ways to lose and 18 ways to win.

The odds, therefore, of winning are 10 to 9. But the payout is 1 to 1.

Let’s say you place this bet 19 times in a row. You’ll win 9 times, and you’ll lose once on average, in the long run.

If you bet $100 every time, after completing those 19 bets, you’ll have won $900 and lost $1000. This results in a net loss of $100 over 19 bets. Your average loss per bet is $100/19, or $5.26.

Since $5.26 is 5.26% of $100, we say that the house edge for that roulette bet is 5.26%.