Mathematical Facts About Gambling You Need to Know

Royal Flush of Hearts With a Math Equation Background

Casinos and other gambling establishments use math against you every time you gamble. But smart gamblers know how to turn the tables and use other mathematical principles to help them win. If you want to start doing so to become a better gambler, here are five things you need to know.

The first two sections are the most important, because once you understand the information, it’s going to change everything you know about gambling.

From there, you can use math to lower your losses. And if you become a true student, you might even be able to start winning instead of losing.

What Expected Value Means

You’ve probably heard of the house edge in gambling. If you haven’t, the house edge is the percentage advantage that the casino or other gambling establishment has over you when you place wagers.

While the house edge is important, it’s just a piece of what’s really important when you gamble. The most important thing you need to understand is expected value. Expected value is a mathematical concept that tells you exactly how much you can expect to lose on any wager you place.

It’s fairly simple to determine the expected value of a wager if you know the house edge. But many gamblers struggle with understanding exactly what it means and how it works.

When you make most wagers, you either win or lose your entire wager. As you make more wagers, you usually lose a few more than you win. This is where the house edge and expected value comes in. The more wagers you make, the closer your actual results come to equaling your expected results.

Multiple Hands of Casino Blackjack

It’s not important to understand exactly why this happens, but you do need to accept that it’s a mathematical fact. The way you determine the expected value of any wager is to multiply the amount you’re wagering with the house edge. Here are a few examples of determining the expected value.

If you’re betting $100 a hand on a blackjack game with a 1% house edge, your expected value is -1. The reason why it’s negative is because the house edge is against you.

You’re wagering $40 a hand on the player bet at a baccarat table. This wager has a 1.24% house edge. $40 times 1.24% is an expected value of -0.496, which can rounded up to -50 cents. The only way to have a positive expected value is to place wagers where you have an edge over the house.

Positive and Negative Expectation Options

In the first section, you learned why most gamblers lose money. They make negative expectation wagers, and the long-term math comes into play, creating a long-term loss. You can create a few opportunities to place wagers with a positive expectation.

Even if you’re not able to make positive expectation bets all of the time, you still need to try to do it as often as possible to offset your losses.

You can find a few positive expectation plays beyond the ones I list here, but they’re rare and/or extremely difficult. Here are the three main areas where you have a chance to gamble with positive expectation.

The first opportunity is playing blackjack. You have to learn how to count cards, but many players are able to do it.

The second opportunity is poker. You can practice your strategy and skills enough to learn how to play with an edge.

The third opportunity is gambling on sporting events. You have to learn how to handicap games and find profitable betting lines.

Bet Sizing Considerations

Now that you know what expected value is, and what negative and positive expected value means, you should understand that gamblers are expected to lose money. You might get lucky and win for a short period of time, but eventually, the edge is going to catch up with you.

This information is important because it allows you to use math to determine the best bet size every time you gamble.

If you’re gambling in a negative expectation situation, the best bet size is 0. In other words, if you’re playing against an edge, you should not place a wager.

Sportsbook Betting Window

The next best bet size in this situation is the smallest bet you can make. This can involve the table minimum bet in a land-based casino or choosing to play at the lowest stakes poker table. You can also make the minimum bet on a sporting event or place bets at an online gambling establishment that offers lower minimum bets.

On the other hand, if you’re making bets in positive expectation situations, you want to bet as much as you can afford without risking going broke.

The first step is determining if you’re making a positive or negative expectation wager. Once this is determined, the next step is either betting the lowest possible amount or determining the maximum you can bet while keeping enough money in reserve to continue making more positive expectation wagers.

Bankroll or Budget?

Do you know the difference between a gambling bankroll and a gambling budget? I’ve read dozens of articles and books that claim every gambler needs to have a gambling bankroll. But the truth is that most gamblers don’t need a bankroll, they just need a budget.

A gambling budget is a set amount of money for a particular trip to a casino or other gambling establishment, or a set amount of money for a set amount of time. You could have a $600 budget for your Saturday casino outing, or a $1,200 budget for gambling in March.

A casino bankroll is an account or separate pool of money that you only use for gambling. When you lose, the money comes out of your bankroll, and when you win, the money goes back into your bankroll. A gambling bankroll is meant to stay in place forever, while a budget is a short-term thing.

If you’re serious about gambling and are working toward playing as an advantage gambler, you need to start using a bankroll. It’s not only a good way to keep your gambling funds separate from the rest of your money, but it’s also a good tool to help you track your profits and losses.

However, if you’re not an advantage gambler, there’s no need to have a bankroll. If you don’t know how to be a profitable gambler, your bankroll is going to continually go down and you’re going to have to add money to it or stop gambling.

In this case, you’re better off with a budget. Set aside money you can afford to lose and use this money for your gambling budget. You can set a new gambling budget for every gambling outing.

Entertainment or Advantage Play?

In the last two sections, you learned that if you aren’t an advantage gambler, you should always make the smallest wager possible and you don’t need to have a bankroll. This is where most gamblers spend their entire gambling careers. They never learn how to gamble with an advantage.

If you just want to gamble for entertainment, this is your choice. Sometimes, you’re going to win, but most of the time, you’re going to lose. When you gamble for entertainment, the main thing you need to focus on is not losing too much money.

Closeup of a Poker Hand and Chips

But you have another option. You can concentrate on finding gambling opportunities that offer positive expectation. Learn how to count cards or handicap sporting events or play poker for real money. If you can learn to play with an advantage, everything changes.

Instead of budgeting how much money you can afford to lose, you figure out how to maximize your return. This should be the goal of every gambler, and you can do it if you know how.

Start looking at the advantage gambling options to identify one that you want to try. Then, learn as much as you can., and start practicing. Keep learning and practicing until you’re an advantage gambler.


Expected value and expectation are the most important mathematical concepts that every gambler needs to learn. Once you understand how these things work it helps you in every area.

If you can figure out how to make more wagers with positive expectation you can limit your losses or possibly win more than you lose. Even if you can’t find enough positive expectation situations, you can use this information to determine how much you should wager.

It also helps you determine if you need to use a gambling bankroll or a gambling budget. Negative expectation gamblers need a budget, and advantage gamblers need a bankroll.