3 Ways You Can Benefit from Gambling Math

Two People Playing Casino Slot Machine, Math Problem on Chalkboard
Over the years I’ve shared advice about gambling with hundreds of thousands of people through my writing and in person. I’ve also spent time teaching freshmen level math in college. One thing I run into over and over is most people don’t like math and aren’t interested in learning much about it.

The problem with this is if you want to be a successful gambler you have to understand and use math. This doesn’t mean you have to have a degree in math or love it, but you have to be able to use it to reduce the house edge as much as possible, especially if you’re doing real money gambling.

It doesn’t matter how much you know about math, or how much you like it, because you can start using it right away with the three tips I cover below. Once you start using these three things, hopefully you can continue learning more about how math works in gambling and continue improving your results.

1 – Strategy Cards

Some gambling activities involve strategy, while others are designed in a way that it doesn’t matter how you play. The games that let you use strategy to alter the house edge run from complicated to easy. The best strategy when you play baccarat is to always bet on the banker hand. The best strategy when you play craps is to always bet on the don’t pass line and back it with full odds. These are easy strategies.

On the other end of the strategy list are games like video poker, blackjack, and poker. Poker, consisting of games like Texas holdem and Omaha, involve many layers of strategy that can’t be contained in a single book. But games like video poker and blackjack have strategies that can be contained on a single card or chart.

In blackjack, every combination of your cards and the dealer’s up card has a single best strategic way to play. The only way to keep the blackjack house edge as low as possible is to make the best play on every hand.

Here’s an example of a blackjack strategy play.

When you receive a pair of eights, the best strategy is to split them. This is because two eights form a hard total of 16, which is the worst possible total.

When you split the eights, any two, three, nine, ten, jack, queen, king, or ace you receive on one of the eights creates a much better hand.

This particular hand is pretty easy to understand. It’s easy to see why splitting eights is the best play. But many hands are more difficult to understand. The way to learn the best play in every situation is to determine every possible outcome for every possible card you can draw.

Blackjack Strategy Chart, Ace of Diamonds Card

This is time consuming, but there’s good news. People have already used computer programs to handle all of the difficult mathematical work and created strategy cards and charts you can use. You don’t have to know the math behind the strategy; you just need to take advantage of someone else’s work and use the strategy card.

The same thing is true for video poker. Each starting hand, when compared to the pay table and the mathematical possibilities, has a single best way to play. The good news is that just like blackjack strategy cards, someone has already run all of the mathematical possibilities, and put them on a single card or chart.

In both blackjack and video poker, you need to play games with good rules or find machines with good pay tables. The rules and pay tables change the house edge, but when you find good games the way to keep the house edge as low as possible is to use strategy cards or strategy charts.

2 – The House Edge

I mentioned the house edge in the last section. The house edge, usually stated as a percentage, is the amount the casino keeps from all of your wagers on average in the long run. Games with a higher house edge take your money faster than ones with a low house edge. Low house edge games also give you a better chance to win any particular playing session.

People Gathered Around Casino Blackjack Table, Icon with Money Speech Bubble

So how do you know the house edge for individual casino games?

It takes quite a bit of mathematical work to determine the house edge for casino games. But just like the strategy cards I mentioned in the last section, someone else has already done the hard work. You can find a list of casino games with the house edge already figured out.

All you have to do is go down the list and find games with a low house edge and avoid playing games with a high house edge.

The games with the best house edge in most casinos are blackjack games with good rules, video poker machines with good pay tables, and baccarat. The worst games in most casinos are the slot machines and table games other than blackjack.

3 – Reduced Vig

Sports betting is one of the most popular forms of gambling. Billions of dollars are wagered with sportsbooks around the world every year, and billions more are wagered with bookies, in office pools, and between friends and co-workers as well.

While many bettors feel safer placing their wagers with sportsbooks, the ones betting off book benefit in a mathematical way. When you bet at a sportsbook you pay a small fee. You can’t bet $75 to win $75 like you can when you bet with a friend or someone else you know.

Instead, you have to risk $82.50 for the chance to win $75 when you bet at the sportsbook. If you win your bet you receive your $82.50 back and get $75 in winnings. But when you lose, you lose $82.50.

The sportsbook prefers to have an equal handle on each side of a game, so when they take your bet on the home team they hope to take a bet of equal size on the road team.

What actually happens is they end up with more money on one side of a game than the other, but over time and thousands of games the money they take on both sides of games evens out.

This is how sportsbooks make money.

Here’s what happens when they have the same amount bet on each side of a game. Using your bet of $82.50 to win $75, they take the same sized bet on the other side. One bettor wins the bet and gets their $82.50 back and receives a win of $75. The $75 win comes from the bettor on the losing side. This leaves $7.50 in profit for the sportsbook.

Crowd at Sportsbook, Money Falling Down

When the sportsbook has an equal handle on both sides of a game they lock in a guaranteed profit. The extra amount you have to wager beyond what you can win is called the vig.

If you bet on 100 games and win 50 of them, if you don’t have to pay the vig you break even. But because of the vig, if you win half your bets you still lose money.

Here’s how the vig hurts you.

If you make 100 bets risking $82.50 to win $75 and win 50 bets, here’s how the numbers work out. Your total cost to make 100 wagers is $8,250. When you win you get back $157.50, which is your bet of $82.50 plus a $75 win. The 50 games you win times $157.50 is $7,875.

The total amount wagered of $8,250 minus your return of $7,875 is $375.00. This means that you lose $375 when you win half the games you bet on. This is an average of $3.75 a game.

Notice that $3.75 is exactly half the vig. When you place bets with vig and win 50% of the time your average loss is half the vig.

Compare this to placing all of your bets without vig. You make 100 bets of $75 to win $75. The total cost of placing 100 bets is $7,500. The 50 times you win you get back $150. This is a total return of $7,500 on the 50 games you win. In other words, you break even.

Here’s what all of this means.

You don’t have to know anything about math to use it to your advantage in sports betting. Placing bets with vig costs you every time you do it. The way to avoid this cost is to place as many bets as possible without the vig.

If you bet a large number of games, you might not always be able to find other people to place bets with on all of your games. When you have to place bets with a sportsbook, look for ones offering reduced vig wagers. Some books regularly offer smaller vig, and others run specials from time to time. Every time you can place bets with no vig and reduced vig you save money.


You don’t have to be a mathematician to benefit from math while you gamble. You don’t even need to like math. You simply need to use the work that others have already done. Use strategy cards, understand the house edge, and make as many bets as possible with reduced vig.