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Adjusting the House Advantage
to Maximize Profitability


arlier we said that casinos can increase the Expected Hold on their live games by hiring proficient dealers and by making sure that players are treated hospitably. Another way that casinos can increase the Expected Hold on their live games is by making rule changes that increase the House Advantage. However, casinos that increase their House Advantage run the risk of fewer players and fewer wagers. This can happen when players realize that the cost of playing has just increased, because their bets are at a new and greater disadvantage.

Indeed, a casino that increases its House Advantage could be compared to a department store that increases the price of its products. The store that increases prices will achieve greater earnings on the products it sells. However, the store is likely to sell fewer products, as customers hunt elsewhere for better deals. Similarly, the casino that raises its House Advantage will achieve greater earnings on the bets that players make, but is likely to get fewer bets. Greater earnings on each bet means that a casino's Expected Hold will increase, but fewer bets mean that a casino's Drop will decline.

Thus, an increase in the House Advantage should result in a greater Expected Hold for a casino, but a smaller Drop, while a decrease in the House Advantage should produce a smaller Expected Hold, but a larger Drop. Casinos that change their House Advantage do so in an attempt to achieve the best balance between the Drop and Expected Hold to maximize profitability.

An example of this occurs in the game of craps. Here casinos commonly adjust the House Advantage by changing the amount of odds they allow players on pass line bets and come bets. (Increasing the allowable odds on pass line bets and come bets decreases the House Advantage for craps, and vice versa. See below.)



House Advantage on line/come bets with:

             SINGLE ODDS . . . 0.8% on the total bet 
             DOUBLE ODDS . . 0.6% on the total bet 
             TRIPLE ODDS . . . 0.5% on the total bet 
             5 TIMES ODDS. . . 0.3% on the total bet 
             10 TIMES ODDS . . 0.2% on the total bet

In looking at this table, one might wonder how crap games can make enough money to be profitable. After all, a casino's edge on pass line bets and come bets is very small -- less than 1 percent with single odds, and one-fifth of a percent with 10 times odds.

However, the overall House Advantage in craps is much greater than suggested by the numbers in this table. This is because many players do not take the full, allowable odds on their line and come bets, and some players do not take any odds at all. Moreover, at the same time players make low percentage line/come bets with odds, they also make bets that afford the casino a much greater House Advantage: place bets, field bets, and prop bets. These high percentage bets considerably increase a casino's overall edge in craps.

Yet this is not to imply that pass line odds and come bet odds are insignificant. Clearly, the odds that casinos allow crap players do play an important role in a casino's total edge, which will be reflected in a casino's Expected Hold.


To understand how changes in the House Advantage affect the profitability of crap games, let's take a hypothetical example. Assume that a casino has single odds on its crap games, and that single odds have produced: (a) a long-term Hold (i.e., Expected Hold) of 19%, and (b) an average Drop of $63,000 per day.

Now suppose that, in an attempt to attract more players and increase profits, the casino decides to offer players double odds. And suppose that, in time, the Drop for the dice pit increases from the previous $63,000 daily average to a $75,000 average (as additional players are lured to the casino by the new, more liberal, double odds). However, the department's Hold percentage falls from the previous 19% to 17% (since double odds have reduced the House Advantage).

[Note: These figures are hypothetical. How much the Drop and the Expected Hold will change from a casino modifying its odds will vary from casino to casino. Casinos that attempt to increase their profits by adjusting the House Advantage must conduct their own experiments and can expect to achieve different results.]

To decide whether it was a wise decision to change to double odds, the casino must do the following: It must compute the profitability of winning 17% of a $75,000 Drop with double odds, versus the profitability of winning what it was before with single odds (19% of a $63,000 Drop). The following formula, already introduced in Chapter 2, makes this calculation easy:.

Expected Win = Drop x Expected Hold


Expected Win with Single Odds

Expected Win = $63,000 per day x .19

                       = $11,970 per day


Expected Win with Double Odds

Expected Win = $75,000 per day x .17

                       = $12,750 per day


In our hypothetical case, changing from single odds to double odds increased the dice pit's Expected Win from a daily average of $11,970 to an average of $12,750. Therefore, the casino's decision to go to double odds was a profitable one. (Of course, our hypothetical example was a simple one. When making profitability calculations of this sort, casinos must also account for such things as seasonal changes, promotions, the economic climate, etc.)

Now suppose that this casino -- noting how much its profits have increased by changing to double odds -- decides to liberalize even further by offering players 10 times odds. And suppose that after a time with 10 times odds, the dice pit's long-term Hold falls to 13%, while its Drop increases to $95,000 per day. To determine the profitability of 10 times odds, the casino again performs the same Expected Win calculation.


Expected Win with 10 Times Odds

Expected Win = $95,000 per day x .13

                       = $12,350 per day


We see that changing to 10 times odds produced an Expected Win of $12,350 per day for the casino, down from the $12,750 per day achieved with double odds. Do these results mean that our hypothetical casino should switch back to double odds? Perhaps, but the casino needs to consider another important point: a promotion like 10 times odds will not only increase the Drop in the dice pit, but will increase the Drop in other gaming departments as well.

This is because not every player attracted to a casino by the lure of 10 times odds will spend all of his or her time playing craps. Inevitably, some of these players, after playing craps for a time, will move about to gamble at other casino games. Therefore, a casino needs to seriously consider the positive effect that enticing players with liberal odds can have, not just on the craps department, but on the entire casino operation.



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