Vegas gambling guide: Understanding the odds

Gambling is the reason Las Vegas (in its modern incarnation) exists. It is the industry that fuels the local economy, paves the roads and gives the city its identity. To visitors and tourists, gambling may be a game. To those who derive their livelihood from gambling, however, it is serious business.

There is an extraordinary and interesting dichotomy in the ways gambling is perceived. To the tourist and the recreational gambler, gambling is all about luck. To those in the business, gambling is about mathematics. To the visitor, gambling is a few hours a day, while to the casinos, gambling is 24 hours a day, every day. The gambler hopes to walk away with a fortune, but the casinos know that in the long run that fortune will belong to the house. To visitors, gambling is recreation combined with risk and chance. To the casinos, gambling is business combined with near-certainty.

The casino takes no risk in the games themselves. In almost all cases, in the long run the house will always win. The games, the odds and the payoffs are all carefully designed to ensure this outcome.

If casinos did engage in fair bets, like when you flip a coin with a friend, they would win about half the bets and lose about half the bets. In other words, the casino (and you), on average, would break even, or at least come close to breaking even. While this arrangement would be more equitable, it would not, as a rule, generate enough money for the casino to pay its mortgage, much less foot the bill for the dancing waters, erupting volcanoes, lounge shows, $10 buffets and free drinks.

House Advantages

Baccarat: 1.17% on bank bets, 1.36% on player bets

Blackjack: 0.5%-5.9% for most games

Craps: 1.4% to almost 17%, depending on the bet

Keno: 20%-35%

Roulette (with double zeros): 5.26%-7.89%, depending on the bet

Slots: 2%-25% (average 4%-14%)

Video Poker: 0.2%-12% (average 4%-8%)

Wheel of Fortune: 11%-24%

To ensure sufficient income to meet their obligations and show a profit, casinos establish rules and payoffs for each game to give the house an advantage. While the house advantage is not strictly fair, it is what makes bargain rates on guest rooms, meals and entertainment possible.

There are three basic ways in which the house establishes its advantage:

The rules of the game are tailored to the house's advantage

In blackjack, for instance, the dealer by rule always plays his own hand last. If any player busts (attains a point total over 21), the dealer wins by default before having to play out his hand.

The house pays off at less than the actual odds

Imagine a carnival wheel with 10 numbers. When the wheel is spun, each number has an equal chance of coming up. If you bet a dollar on number 6, there is a 1-in-10 chance that you will win and a 9-in-10 chance that you will lose. Gamblers express odds by comparing the likelihood of losing to the likelihood of winning. In this case, nine chances to lose and one to win, or 9–1. If the game paid off at the correct odds, you would get $9 every time you won (plus the dollar you bet). Each time you lost you would lose a dollar.

Let's say you start with $10 and do not win until your 10th try, betting your last dollar. If the game paid off at the correct odds, you would break even. Starting with $10, you would lose a dollar on each of your first nine attempts. In other words, you would be down $9. Betting your one remaining dollar, you win. At 9–1, you would receive $9 and get to keep the dollar you bet. You would have exactly the $10 you started with.

As we have seen, there is no way for a casino to play you even-up and still pay the bills. If, therefore, a casino owner decided to install a wheel with 10 numbers, he would decrease the payoff. Instead of paying at the correct odds (9–1), he might pay at 8–1. If you won on your last bet and got paid at 8–1 (instead of 9–1), you would have lost $1 overall. Starting with $10, you lose your first nine bets (so you are out $9) and on your last winning bet you receive $8 and get to keep the dollar you bet. Having played 10 times at the 8-to-1 payoff, you have $9 left, for a total loss of $1. Thus the house's advantage in this game is 10% (one-tenth).

The house advantage for actual casino games ranges from less than 1% for certain betting situations in blackjack to 35% on keno. Although 1% doesn't sound like much of an advantage, it will get you if you play long enough. Plus, for the house it adds up.

Because of variations in game rules, the house advantage for a particular game in one casino may be greater than the house advantage for the same game in another casino. In most Las Vegas casinos, for instance, the house has a 5.26% advantage in roulette. At European casinos, however, because of the elimination of 00 (double zero) on certain roulette wheels, the house advantage is pared down to about 2.7%.

The rule variations in blackjack swing the house advantage from almost zero in single-deck games (surrender, doubling on any number of cards, dealer stands on soft 17, etc.) to more than 6% in multiple-deck games with draconian rules, such as a recent wrinkle at blackjack, where a natural 21 pays off at 6–5 rather than the age-old 3–2. Quite a few mathematicians have taken a crack at computing the house's advantage in blackjack. Some suggest that the player can gain an advantage over the house by keeping track of cards played. Others claim that without counting cards, a player utilizing a decision guide known as "basic strategy" can play the house nearly even. The reality for 95% of all blackjack players, however, is a house advantage of ­between 0.5% and 5.9%, depending on rule variations and the number of decks used.

Getting to the meat of the matter: blackjack and some video poker played competently, baccarat, and certain bets in craps minimize the house advantage and give the player the best opportunity to win. Keno and wheel of fortune are outright sucker games. Slots and roulette are only marginally better.

How the house advantage works in practice causes much misunderstanding. In most roulette bets, for example, the house holds a 5.26% advantage. If you place a dollar on black each time the wheel is spun, the house advantage predicts that, on average, you will lose 5.26 cents per dollar bet. Now, in actual play you will either lose one whole dollar or win one whole dollar, so it's not like somebody is making small change or keeping track of fractional losses. The longer you play, however, the greater the likelihood that the percentage of your losses will approximate the house advantage. If you played for a couple of hours and bet $1,000, your expected loss would be about $53.

All right, you think, that doesn't sound too bad. Plus, you're thinking: I would never bet as much as $1,000. Oh, yeah? If you approach the table with $200 and make 20 consecutive $10 bets, it is not very likely that you will lose every bet. When you take money from your winning bets and wager it, you are adding to your original stake. This is known as "action" in gambling parlance, and it is very different from bankroll. Money that you win is just as much yours as the stake with which you began. When you choose to risk your winnings by making additional bets, you are giving the house a crack at a much larger amount than your original $200. If you start with $200, win some and lose some, and keep playing your winnings in addition to your original stake until you have lost everything, you will have given the house (on average) about $3,800 worth of action. You may want to believe you lost only $200, but every penny of that $3,800 was yours.

The house takes a commission

In all casino poker games and in certain betting situations in table games, the house will collect a commission on a player's winnings. Sometimes the house combines its various advantages. In baccarat, for instance, rules favor the house; payoffs are less than the true odds; and in certain betting situations, the house also collects a commission on the player's winnings.

--Bob Sehlinger is the author of the Unofficial Guide to Las Vegas 2014.


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