Calculating the Odds in Casino Games

If you’re good at math, you often can detect when the casino payout odds are lower than true odds (see the section “Factoring in the odds” earlier in this chapter). With dice, for example, you have 36 different combinations, and the odds are 35-to-1 for each combination. But with other games, the odds can be impossible to calculate. Take slots, for example: The thousands of possible reel combinations and ever-changing progressive jackpots make it difficult for anyone to calculate the odds of winning.

One of the most confusing aspects of odds is the difference between for and to. For example, in video poker a flush pays 6 for 1, which means your win of six coins includes your original wager. So your actual profit is only five coins. However, if the bet pays 6 to 1, your odds are better. Your profit is six and your total return is seven (your win plus your original wager). This small detail may seem like a silly case of semantics, but it can make a big difference in your payout.

This section ties together the joint concepts of payout odds and true odds that will get you on the road to understanding the house edge (or advantage). Armed with a full understanding of that key statistic, you’ll be able to discriminate between good and bad bets in a casino.

Identifying payoff odds

In almost all cases, the payoffs favor the house, and you lose in the long run. However, some unusual situations arise that give astute gamblers an edge.

Zero expectation

A zero expectation bet has no edge — for the house or the player. This balance means that both sides can break even in the long run. For example, if you remove the two extra green numbers (0 and 00) from the roulette wheel, the game now becomes a zero expectation game because it has 36 numbers, 18 red and 18 black. Any bet on red or black would be a zero expectation bet. In other words, when you bet on one color, your chances for winning and losing are equal, just like flipping a coin.

Negative expectation

However, casinos aren’t interested in offering zero expectation games. In order to make a profit, they need to add in those two extra green numbers to change the odds in roulette. Now, when you bet red or black, your odds of winning are rather than . So your even money bet moves from a zero expectation to a negative expectation.

Whenever you’re the underdog (such as in roulette), your wager has a negative expectation, and you can expect to lose money. It may not happen right then. You may defy the bad odds for a while and win, but over time you will lose.

Most bets carry a negative expectation because the house doesn’t give true odds for the payouts (as is the case for roulette). Craps provides another good example. Say you bet that the dice will total seven on the next throw. If you win, you are paid 4 to 1. However, the true odds for this occurrence happening are 5 to 1 ( ).

That difference may not sound like a major change, but the house edge on that bet is a whopping 16.67 percent! And a negative expectation bet for you is a positive for the casino. (The casino makes an average of $16.67 on every $100 bet in the previous craps example.)

Positive expectation

In a positive expectation bet, the tables are turned on the house so the players have the advantage. Most people can’t believe casinos actually allow a positive expectation for the gambler, but surprisingly, some are out there. One example is in tournaments, where, in many situations, the casino pays out more money than it takes in.

Getting an edge on the house edge

It’s a fact: In most casino games, the house has the edge. But you can get an edge over the casino in two ways:

Using match play coupons to double your fun. You can often find match play coupons in the free fun books distributed by many casinos. Rip these coupons out and tuck them underneath your bet. In most cases, they essentially double your wager without having to risk any more money.

Taking advantage of promotions. Promotions can be the best way to secure a positive expectation. Here are a couple of examples: We have played at several casinos where they changed the rules for a short period of time and paid out 2 to 1 on all blackjacks. This change tipped the odds enough so even basic-strategy players had nearly a 2 percent edge over the house.

Another great promotion was when the Pioneer Casino in Laughlin, Nevada, offered Double Jackpot Time on some slot machines. Twice an hour, for a short period of time (approximately 30 seconds), they generously doubled the payout on certain jackpots. Most people shrugged off this opportunity as just another marketing gimmick, but it was very lucrative. A friend of mine made six figures a year there playing only a few minutes every hour.

Finding out about these great deals isn’t easy. However, one helpful resource for casino promotions and coupons is the Las Vegas Advisor. Another tactic is signing up for casino e-newsletters to keep abreast of upcoming special events.

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