The mathematics of gambling may seem like a complicated topic (and sometimes it is) but most people can the basics of how a casino makes money relatively quickly. After all, everyone knows that casinos are in the business of making big money really quickly. How else do you think The Pioneer Club in Vegas could afford a giant neon cowboy? Hint: it’s not because they were in the business of writing checks. Odds Versus Probability The first thing you have to know to be effective in the casino is what the differences between odds and probability are. It’s a pretty simple concept to grasp, overall, but you’d be surprised at how many people forget it when they’re at the table. When it comes to odds, essentially it’s the amount of money staked by two betting parties. For example, if the casino has odds of five-to-one then that means the casino is betting five times the amount of money that you are. In a fair event, such as a roll of a single die, this would mean that if the die landed on your number, they would pay out five times the amount you put down and, if you lost, you would have to pay only what you put down. This is because the odds of five-to-one are essentially based on their five chances compared to your one chance, or six different possible results overall of which you’re likely to win one out of every six. When betting on a game like football, the odds can be very confusing to come up with (there are a lot of stats to consider!) but still essentially the same when it comes down to how they structure them. The higher the probability of your team winning, the lower the odds because it’s a fairly safe bet. On the other hand, probabilities are the ratio of times an event won’t occur to the amount of times it will occur. For example, a coin flip has a one-to-two probability ratio because the coin has a one chance out of two possibilities to land on a certain side. In other games, like blackjack, the probabilities are much harder to calculate. For instance, if you have a hand containing a king and a two, you know that the probability for getting a 10 when you hit is smaller, but still significant. But if you had been playing for a while and know that all of the tens and face cards are now out of the deck then you can be certain that you won’t bust since the ratio of cards equaling ten to cards in the deck is 0-to-the number of cards in the deck. House Edge This brings us to what the house edge is. As I said before, the house doesn’t make money by playing fair. It makes money by giving itself an advantage, however small it may seem. This is calculated by taking the difference between the probability and the odds. For example, if you bet on red at the roulette table you have an eighteen-in-thirty-eight probability of winning. If the casino odds (or payout) for the spin is twenty-to-thirty-eight then that means the house edge on that particular bet is 5.26%. On average a roulette bet gives the house an edge of about 2.7% to 5.25%. This may not sound like a lot but if the overall house edge is around 3.5% and a million dollars is played at one table over the course of the night, the house makes a profit of $35,000. That’s in one night! On one table! To really understand why this is (or at least why it’s extremely profitable) suppose the casino payout for a single roll of one die was 5:1 or completely fair odds. Suppose you bet a dollar for each of six rolls and you lost five, that’s five dollars down. If you bet a dollar the sixth time and won you’d receive your five dollars back. So the casino would break even with a person who was only lucky 17% of the time. That’s not very good business. How House Rules Can Change the Game Blackjack is notorious for having a very low house edge for skilled players (only about a half percent) so the casino stacks the deck (pun intended) in their favor. One of the house rules for blackjack is that if a player at the dealer turns over their cards last. This may not seem significant until you realize that if a player at the table busts before the dealer turns over their cards, the dealer doesn’t have to turn over their cards. While the dealer’s bust percentage is anywhere between 17%-42%, a player’s bust rate is anywhere between 31% to 92% (obviously the high end is if you make a bad decision and hit on a 20),which is a significantly higher probability than hitting a blackjack in your first two cards (about 8%). So, not only is the dealer’s bust rate lower, if a player at the table busts then that drops to 0% and the house wins. Legislation can also change the game quite a bit. In certain cities there are protections for card counters, preventing casinos from throwing them out regardless of their wins. In Las Vegas, specifically, there is no law against this, making card counting in Vegas a risky proposition and protecting the casinos’ investments. Now you know about how exactly casinos make money and why it is good to make wise choices of what games to play and what to look for when you’re in a casino. Now go out there and make some money!