Smart Craps By Henry Tamburin

When it comes to playing craps, time is money

This is a controversial article because it presents quite a different point-of-view on how to determine the best bets in craps. The results may surprise you.

If someone were to ask you to select which of the following four bets is the best, which one would you pick?

Most players would pick bet number 1, the $5 pass line bet, because "it has the lowest casino edge" when compared to the other three bets. Technically, this is correct. But this analysis only compares the casino's edge of one bet to that of another. What we haven't considered is the amount of the bet, or the number of times a player bets.

First, let’s focus on the casino edge. It’s an important (but not the only) criteria to determine which is the better bet. Unfortunately, most players have only a vague understanding of what the casino edge means, and how the casino creates it for the different bets on the crap layout.

Casinos don't depend on luck to generate the income they need to show a profit. To ensure themselves a steady income, they must have a mathematical advantage over every crap player at all times. They create their advantage—or "edge"—in two different ways, and each has the same result.

Take a bet on the pass line, for example. For every 1,000 bets a player makes, 493 will win and 507 lose. In other words, the rules for the pass line favor the casino winning more bets than the player. If you bet a dollar every time, you would win $493 and lose $507, for a net loss of $14. Thus, for every $1,000 worth of bets you make on the pass line, the casino stands to win $14 (or 1.4 percent of the amount of money wagered).

The casino creates its advantage on other crap bets a little differently. For example, a bet on Any Seven is a one-roll bet that the dice will show a 7. If you win, the casino will pay you $4 in winnings (4 to 1 payoff). That seems like a substantial payoff, but it’s not, because the true odds of winning the bet are 5 to 1. If the casinos were to pay at 5 to 1 odds, they wouldn't make a penny profit on this bet. But being the smart business people they are, they pay off a winning bet at 4 to 1 rather than 5 to 1 odds. By simply short-changing players one chip when they win, the casinos have discretely created their edge.

The casino edge is usually written as a percentage. In the above example, the casino's edge on the Any Seven bet is 16.7 percent. This means a player can expect to lose 16.7 percent of all the money wagered on Any Seven. It doesn't matter whether your bets win or lose, only that you bet. If you make a total of 25 one-dollar bets on Any Seven during the course of play, the casino will expect to win from you about $4.00 for your action (16.7 percent times $25). Most likely, you will win or lose a lot more than $4, but the more money you bet, the closer your losses will come to the statistical 16.7 percent casino edge. The casinos bank on this fact every day.

Table 1 ranks all the crap bets according to their casino edges. The pass/come/don't pass/don't come bets with odds clearly have the lowest casino edges. On the other end of the ranking are the proposition bets, which command the highest casino edges—with the bet on any Seven, having the highest. In fact, the casino edge on any Seven is 833-times higher than a pass/come bet with 100-odds. That's a very large spread in casino edge for different bets within the same game.

TABLE 1

"Casinos don't depend on luck to generate the income they need to show a profit. To ensure themselves a steady income, day-in and day-out, they must have a mathematical advantage over every crap player at all times."

Let's return to the question I posed at the beginning of this article: Which of the four bets is best?

By multiplying the amount of the bet by its corresponding casino edge from Table 1, you can calculate the cost to make each bet.

By factoring the amount of the wager with the casino edge, you come to the conclusion that the $1 bet on the field is a cheaper bet. Although that's true for a single bet, most crap players don't make one bet then quit. In fact, most players make many bets before they quit a playing session, and the number of bets varies from player to player, depending upon the length of the playing session. To keep it simple, we'll assume a one-hour playing time, which is average for most players.

During that one hour of play, a player will make a number of bets; some will win and some will lose. The key point is that the number of decisions per hour for all bets is not the same. Think about it. When you make a field bet, you are betting on every throw of the dice, which means the number of decisions per hour will be relatively high compared to a bet on the pass line, where many throws do not result in a decision.

The fourth column of Table 2 summarizes the number of rolls it takes for a decision for every bet in craps. The information was obtained from the new book, Casino Operation Management, by Jim Kilby and Jim Fox. For example, it takes 5.7 rolls on average for a decision on the 4 and 10 buy bet versus only one roll for most proposition bets. (If you are wondering why a place bet on the 6 and 8 has a slightly higher number of rolls per decision than a bet on the similar big 6 and 8, it's because the place bets are off—or "not working"—on the come out roll, and this fact was considered in the calculation of the number of rolls per decision).

It's easy to convert the number of rolls per decision to the number of decisions per unit time (in our case, one hour). All you need to know is how many times the dice will roll per hour. This varies depending on the number of players. Kilby and Fox report the following average dice tosses per hour, from a 1990 study conducted in an Atlantic City casino:

We'll take an average of the above, and assume 160 dice rolls per hour.

The number of decisions per hour for each crap bet is listed in the fifth column of Table 2. Glancing down that column, you'll find that the number of decisions that occur per hour for all crap bets varies from a low of 28 for the 4 and 10 buy bet, to a high of 160 decisions per hour for several of the one-roll crap bets.

We now have the information we need to put it all together and calculate what it costs per hour to make every bet on the crap layout. The "cost per hour" is just what its name implies. It's what the casinos expect to earn—or what it costs you per hour to bet. The equation to calculate the cost per hour is: amount of the wager times casino edge times number of decisions per hour.

Notice the equation includes all three factors that are important when you bet—the amount of your wager, the casino edge, and the number of times your bet wins or loses (decisions) per hour.

TABLE 2

What's surprising when you scan the ranking of the bets in Table 2 is that several "bad bets" all of a sudden become better bets because they have a relatively lower cost per hour.

For example, even though the 6 and 8 hardway and big 6 and 8 bets have a high casino edge, their cost per hour is relatively low because you are betting a small amount of money ($1) on a bet which has a relatively low number of decisions per hour (48). Remember, it's the combination of bet size, casino edge and number of decisions per hour that determine the ranking in Table 2.

Take a look at the hourly cost of some of the proposition bets, which include the hardways, any craps, any seven, and bets on the 2,3,12 and 11. If you are prone to making these bets, you should confine your betting to the hardway 6 and 8 because the hourly cost is lower.

If you like to bet the field, do so in a casino that pays triple (not double) on the 12. Your hourly costs will be cut in half from $8.90 to $4.45, a significant savings in what it will cost you to make this bet.

A lot of crap shooters like to bet on the numbers. If you look at the hourly costs for making place bets versus buy bets, you can clearly see the place bets cost less per hour than the corresponding buy bets (remember we are comparing $6 place bets with $21 buy bets).

Glancing at the cost-per-hour figures also allows you to answer the question posed at the beginning of this article.

Surprisingly, the place bet on the 6 has the lowest hourly costs compared to the other three bets. In fact, the 6 and 8 place bet has the lowest hourly cost of all crap bets, reinforcing the fact that this is one of the best bets for crap players.

Keep in mind that the cost-per-hour calculations and rankings in Table 2 are based on a specific bet size. If you bet only $1 on the pass line, for example, your cost per hour would be one-fifth the figure in Table 2 (66 cents vs. $3.31). Likewise, if you decide to bet $5 in the field instead of $1, your hourly costs would jump from $4.45 to $22.25.

What about the odds bet, which is noticeably missing from Table 2? Because it lowers the casino's edge for these bets (see Table 1), shouldn't it reduce the cost per hour for the pass/come/don't pass/don't come wagers?

"As a general rule, you will always lower you hourly costs by betting the minimum amount on the pass line and putting the rest of your wager on the odds."

Well, let's see.

Table 2 tells us that the $5 pass line bettor's hourly cost is about $3. Suppose you wager doubles odds. The casino's edge for the combined pass line plus double odds is reduced from 1.41 percent to 0.61 percent, and the number of decisions per hour stays the same. But—and it's a big but—instead of making only $5 bets on the pass line, you'll be shelling out another $10 on the odds bet every time a point number is thrown (about two-thirds of the time).

Your average bet will be about $11.67 per decision. If you multiply $11.67 times the 0.061 percent casino edge times the 47 decisions per hour, you arrive at the same $3 hourly cost. Even though the casino's edge decreases when you bet odds, your average bet size increases. The net result is that the hourly costs are the same with or without odds.

Here is one tip, however, on how you can cut your hourly costs by making the odds bet. Suppose Player A bets $10 on the pass line and Player B bets $5 on the pass line, but also takes $5 in single odds. Both players have the same amount of money riding on the outcome. Players B's hourly costs, however, will be lower ($3.31) than Player A's ($6.67). The reason? Player B has bet less on the pass line where the casino has the edge. The net result is Player B's hourly cost will be less than Player A’s. Therefore, as a general rule, you will always lower you hourly costs by betting the minimum amount on the pass line and putting the rest of your wager on the odds.

You can calculate the hourly costs for any size bet by multiplying the costs per hour listed in Table 2 by the ratio of your bet size to the bet size listed in column 2. For example, if you normally bet $25 on the pass line, your hourly costs will be $25/$5 times $3.31, or $16.55. Likewise, if you play 2 hours instead of one, your costs per hour will be double the amount listed in Table 2.

So, why do I say, "time is money" when you play craps?

Simple. Since the casino has the edge on every crap bet, the more you bet or the longer you play or the faster the action, the more it is going to cost you to play in the long run. Your goal is to keep your costs to play to the minimum, which you can do by referring to Table 2. It's the smart way to play craps.

Henry Tamburin is the author of 5 best-selling books including his latest, Henry Tamburin on Casino Gambling-The Best of The Best. He is also featured in three instructional videos. For a free catalog call 1-888-353-3234 or visit http://www.smartgaming.com.