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100X ODDS

Las Vegas has it. Tunica has it. And now Biloxi and Gulfport have it. It’s 100-times odds in craps, the newest casino marketing ploy to revitalize craps and draw gamblers to the tables.

The ploy seems to be working. Anxious gamblers are flocking to the crowded craps tables, and casino managers are drooling at the increased action and revenues the promotion is reaping. As one casino manager puts it, “100-times odds is doing for craps what single deck games did for blackjack–packing them in”!

The 100-times odds “war” started last year when Richard Schuetz was hired to bolster the under-performing Stratosphere Casino in Las Vegas. His strategy was simple–offer players the best odds in town. But before he could raise the odds to 20-times, the Horseshoe upstaged him and implemented 100-times odds, a first for Las Vegas. The Stratosphere responded by matching the 100-times odds multiple.

Meanwhile, in the extremely competitive Tunica, Mississippi market, the Horseshoe implemented 100-times odds on its craps tables and witnessed a rush of casino patronage. Sam’s Town countered with the first ever unlimited odds in craps, but eventually came back to Earth with 100-times odds. Not to be outdone, the Grand Casinos in Tunica, Biloxi, and Gulfport, Mississippi launched their “Players Know Best” program, which included 100-times odds in craps.

So what’s all the fuss about 100-times odds? It all comes down to arithmetic. Mathematically, with 100-times odds, the casino’s edge can be reduced to a piddling 0.02 percent; that’s an expected loss of only 2 cents per one hundred dollars of action on the pass line and odds. It makes you wonder how the casinos can survive with such a small edge; but before you start feeling sorry for them, let’s take a closer look at the benefits and pitfalls of multiple odds betting.

The odds bet in craps is unique among casino bets. It has some unique characteristics that you may be familiar with. Others may be new to you.

The odds bet is the only bet in the casino in which the casino has no edge over the player.
The player can not make only an odds bet. It must be made along with a pass line bet (or a come bet, don’t come or don’t pass line wager). For this article we’ll focus on the pass line wager.
The combination pass line plus odds wager has a lower casino edge than the pass line wager.
The casino’s edge steadily decreases as the odds multiple increases.
Even though the casino’s edge decreases with an increase in odds, your expected loss remains the same.
You have a higher probability of doubling your bankroll by betting 100-times odds instead of no odds.

The basics of the odds bet is as follows: Once a shooter establishes a point on the come-out roll, players have the option to make a secondary wager known as an odds bet on the point number. You won’t find the odds bet marked on the layout and the dealer will not tell you about it unless you ask. To make the odds bet, just place your chips on the layout directly behind your pass line bet.

If you placed an equivalent amount of chips on the odds bet as you wagered on the pass line, this is known as single odds. Most casinos offer double odds, which means you could double the amount wagered in odds vs. the amount on the pass line. Others offer higher multiples such as three, five, ten and twenty, up to the spectacular 100-times odds.

The odds bet wins or loses by the same rules as the pass line. If the shooter makes his point by rolling the point number before rolling a seven, then both the pass line and odds wager win. If the shooter tosses a seven before the point number, then both bets lose.

When the shooter makes his point number, the pass line bet wins even money. However, the payoff for the odds bet is always greater than even money, and differs from one point number to another as follows:

POINT NUMBER

ODDS BET PAYOFF

4 or 10

 2 to 1

5 or 9

 3 to 2

6 or 8

 6 to 5

Casinos have the edge over players by adjusting their payoff odds to be less than the odds of winning. This is the case for all casino bets except the odds bet. It is the only bet where the casino pays off at true mathematical odds, insuring no edge over the player.

The relationship of the casino’s edge on the combined pass line plus odds wager as a function of the odds multiple is shown in the table below. The bottom line is the more a player bets in odds, the lower the casino’s edge for the combined pass line plus odds bet.

CASINO’S EDGE
PASS LINE PLUS ODDS

odds multiple

casino’s edge (%)

0

1.414

1

0.848

2

0.606

3

0.471

5

0.326

10

0.184

20

0.099

100

0.021

Casinos promote the fact that the 100-times odds lowers the casino’s edge. Even though this is correct, what they don’t tell you is the players expected loss remains the same regardless of how much odds a player takes.

This might seem confusing, but keep in mind that the lower casino edge touted for the 100-times odds is true when you consider the total amount a player wagers on the pass line plus odds. The following example will clarify this point:

Player A bets $1 on the pass line for one hundred consecutive come-out rolls. Player B bets the same but also makes a $100 odds bet on every come-out point number. Which player has the lower expected loss?

Player A made a total of $100 in bets. His expected loss is $100 times the 1.4 percent casino edge (pass line), or $1.40.

Player B also bet a total of $100 on the pass line. But he also made a $100 odds bet on every point number, which will occur about 66 out of 100 come-out rolls. Therefore, the total amount Player B wagered on the pass line plus odds is $100 (pass line) plus an additional $6,666 (odds bet) for a grand total of $6,766. Player B’s expected loss is $6,766 times the casino edge of 0.021 percent (pass line plus 100-times odds), or $1.40, the same as Player A.

Get the point? When you make the 100-times odds bet along with your $1 pass line wager, you are putting a lot more money into action. So even though the casino’s edge is lower for the combined pass line plus odds, the casino’s expected take is the same. In essence, multiple odds forces a player to bet more, which, when multiplied by the lower casino edge, yields the same expected loss.

Having said all this, which of the following players have a lower expected loss?

Player A betting $5 on the pass line.

Player B betting $5 on the pass line and making a $10 odds bet.

Player C betting $5 on the pass line and making a $500 odds bet.

You are correct if you said the expected loss is the same for all three players. It is simply $5 times the 1.4 percent casino edge for the pass line, or 7 cents. You can ignore the amount of the odds bet and just focus on the amount wagered on the pass line because the odds bet has an expected loss of zero. It does not effect the negative expectation of the pass line over the long run.

Making a 100-times odds bet also forces players to have a lot of money riding on the table at one time. This could lead to disastrous consequences, should a short run of consecutive losses befall an undercapitalized player.

So what are the benefits of 100-times odds? Take a look at how these three players are betting. They all have about $100 in action, but one is a smarter player.

Player A bets $100 on the pass line and doesn’t make an odds bet.

Player B bets $50 on the pass line and makes a single odds bet of $50.

Player C bets $1 on the pass line and makes a $100 odds bet.

You are correct if you said Player C is the smartest player. Why? Because if you ignore the amount of the odds and calculate the expected loss for their pass line wager, Player C’s is much lower (about a penny and a half) than Player B (70 cents) or Player A ($1.40). Therefore, as a general rule, to benefit from multiple odds including 100-times odds, you should always take the amount of money you would normally bet on the pass line and odds and redistribute it so that you bet as small as possible on the pass line (ideally $1 which is available at the Horseshoe Casinos), and then bet the rest as odds. Certainly, high rollers, who normally bet a black chip ($100) on the pass line, have the most to gain with 100-times odds if they instead put a dollar on the pass line and then place that black chip on the odds.

But be careful. Even betting $1 on the pass line with $100 in odds, you still have $101 riding on the table, and when that seven is rolled, you will lose it all. If you don’t have the bankroll or the stomach to plop down $101 from the start, you may want to begin your betting at a lower multiple odds betting level (i.e. single, or double odds), gradually increasing the amount of your odds bet up to the 100-times odds limit only on consecutive wins.

One final caveat to consider. The larger the bankroll a player tries to double before going broke, the smaller the probability of success. The reason is that the casino’s edge will start to take its toll the longer you play. However, for the same given bankroll, your success of doubling it will increase, the lower you can reduce the casino’s edge. The table on the next page shows these points quite clearly. It summarizes the approximate probability of a crap player doubling his bankroll before going broke betting just on the pass line, pass line with double odds, and pass line with 100-times odds. The probabilities were graciously calculated by Stewart Ethier, a mathematics professor at the University of Utah, and a world expert on the mathematics of craps. To ensure a fair comparison, it assumes an average bet of 70 betting units per come-out roll in all three cases as follows: The player wagering on the pass line makes an average bet of 70 betting units on every come-out roll. The player betting on the pass line and taking double odds bets 30 betting units on the pass line and 60 betting units in double odds (the average bet per come-out roll is 30 plus two thirds of 60 or 70 betting units). The player betting pass line plus 100-times odds bets 1 betting unit on the pass line and then 100 betting units in odds (the average bet per come-out roll is 1 plus two thirds of 100 or about 70 betting units).

Take a look at what the probability is for a crap player trying to double a 5,000 betting unit bankroll before losing it all. Betting on just the pass line, he has a 12 percent probability of achieving his goal. If he reduces the casino’s edge by betting double odds, his probability of success increases to 36 percent. By reducing the edge still further by taking advantage of 100-times odds, his probability of doubling his bankroll before losing it increases to almost 50 percent! Glance at the last column in the table. A high roller with a 100,000 betting unit bankroll doesn’t stand much chance of doubling it by only betting on the pass line or pass line and double odds. But look what happens to his chances if he takes advantage of 100-times odds. He has a 43 percent probability of doubling his bankroll!

Clearly these calculated probabilities prove that the larger the number of betting units you try to double, the lower your probability of success. However, the lower you can reduce the casino’s edge in craps, the greater the chance of doubling your bankroll before losing it. To put it another way, another benefit of 100-times odds is that it greatly increases a players chance of achieving a specified win goal.

In any negative expectation game including craps, your best chance to beat the casino is to bet the entire bankroll in one fell swoop. But realistically, that’s not a fun way to bet for most casino players. On the other hand, if you take a large bankroll and divide it up into a series of small bets, your chance of going broke before doubling it is almost certain (unless you take advantage of 100-times odds as the probabilities in the table show).

So what is the optimum way to play craps? If you have the bankroll, by all means take advantage of the 100-times odds. If you don’t, bet as much on odds as your temperament permits or use the increased odds betting method. Set modest win goals of 20 to 40 percent of your session bankroll, and when you achieve this goal be ready to take the money and run. If you play longer to try to win more, the casino’s edge will start to take its toll and the probability of achieving your goal will diminish.

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