100x odds at craps: great deal or not?

One of the marketing ploys used by some casino managers is to implement 100-times odds in craps. They’ll usually promote it in billboards, TV and radio commercials, in the casinos, and in print and advertising promotions to their loyal customers. Apparently, 100-times odds seems to be bringing customers to their tables, and casino managers are drooling at the increased action and revenues this promotion is reaping. As one casino manager put it: "100-times odds is doing for craps what single-deck blackjack games did for blackjack — packing them in"!

Here’s a little history on how 100-times got started in Las Vegas and then spread to other gambling jurisdictions. The 100-times odds "war" started years ago when Robert Schuetz was hired to bolster the underperforming Stratosphere Casino in Las Vegas.

His strategy was simple: offer players the best odds in town, including increasing the odds in craps to a multiple of 20. Before he could launch his strategy, however, the downtown Horseshoe Casino upstaged him and implemented 100-times odds, a first for Las Vegas. The Stratosphere Casino responded by matching the 100- times odds multiple.

Meanwhile, in the extremely competitive Tunica, Mississippi market back then, the Horseshoe Casino implemented 100-times odds in craps and started to "pack ‘em in." Sam's Town Casino countered with the first ever “unlimited odds” in craps and then eventually changed to 100-times odds. Not to be out done, the now defunct Grand Casinos in Tunica, Biloxi and Gulfport, Mississippi launched their "Players Know Best" program, which included 100-times odds in craps.

So what’s the fuss about 100-times odds when a casino decides to offer it? That’s because mathematically the casino's edge can be reduced to a piddling 0.02% (that's an expected loss of only 2 cents per $100 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 feel sorry for them, let's take a closer look at the benefits and pitfalls of multiple odds betting.

The odds bet in craps is quite unique among casino bets. It has the following characteristics, some of which you may be familiar with, while others you will be after you read this article.

• The odds bet is the only bet in the casino in which the casino has no edge over the player.
• The player can’t 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 but for this article I will concentrate only 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 vs losing it betting 100-times odds vs 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. Other casinos offer higher multiples, such as three, five, ten, 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 or her point by rolling the point number before rolling a seven, then both the pass line and odds wager win.

If instead the shooter tosses a seven before the point number, then both bets lose.
When the shooter makes his or her point number, the pass line bet wins 1 to 1 or even money (e.g., you bet $5, you win $5). However, the payoff for the odds bet is always greater than 1 to 1 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 the true mathematical odds; therefore, they have 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: the more a player bets in odds, the lower is 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

Note:
To calculate the casinos edge for any combination of pass line plus odds multiple, you can use this handy equation where x equals the odds multiple.

Casino's Edge = 28/1980 + 1320x

For example, for double odds substitute 2 for x in the above equation and when you do the arithmetic on a calculator your answer will be .00606. Multiply your answer by 100 to convert to percent or 0.606%. For 100 times odds substitute 100 for x, multiply your answer by 100, and you'll get 0.021%. Suppose some enterprising casino offers 200-times odds. What's the casino's edge? (Answer at the end of article this article.)

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 player’s 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% casino edge (on 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, on average, 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% (for the 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 force 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% casino edge for 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. In other words, it does not affect 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 any 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.

If you said Player C is the smarter player, bravo! Why is Player C’s method of betting the best? Because if you ignore the amount of the odds and calculate the players 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 or whatever the table minimum happens to be) 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 if you found a casino that allowed a$1 minimum bet on pass line with $100 in odds, you still have $101 riding on the table, and when that dreading 7 is rolled, you will lose it all. If you don't have the bankroll or the stomach to plop down $101 from the get go, you may want to start your betting at a lower multiple-odds betting level (i.e. single, or double odds) then gradually increase the amount of your odds bet up to the 100-times odds limit only on consecutive wins.

One final caveat to consider. All casino games with a negative expectation have this characteristic: the larger the bankroll a player tries to double before going broke, the smaller is 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 craps 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 craps player trying to double a 5,000 betting- unit bankroll before losing it all. Betting on just the pass line, he has a 12% probability of achieving his goal. If he reduces the casino's edge by betting double odds, his probability of success increases to 36%. 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! Now 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 is 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 player’s 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 (except if 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 instead 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.



(Answer: The casino's edge for pass line with 200 times odds is 0.011%).

Note: The above analysis assumes that the shooter is a “random roller.” If you learn the technique of dice setting and control by throwing the dice in a precise manner, you can have the edge. For details on how to bet as a control shooter, consult Frank Scoblete’s book "I Am a Dice Controller."

Henry Tamburin, Ph.D. is the editor of the Blackjack Insider e-Newsletter (www.bjinsider.com) and host of smartgaming.com. Visit Henry's web site at www.smartgaming.com.

This article is provided by the Frank Scoblete Network. Melissa A. Kaplan is the network's managing editor. If you would like to use this article on your website, please contact Casino City Press, the exclusive web syndication outlet for the Frank Scoblete Network. To contact Frank, please e-mail him at fscobe@optonline.net.