by Henry Tamburin
This is a controversial article because it is going to present a different view on how to determine what are the best bets on the crap layout. For example, if someone were to ask you to select which of the four bets is the best bet, which one would you, pick?
- $5 bet on the pass line.
- $1 bet on the Field
- $6 Place bet on the 6
- $1 bet on Any Craps
Most players would pick bet number 1, the $5 pass line bet because “it has the lowest casino edge” compared to making bet number 2, 3 or 4. Before we go on with our analyses let’s make sure you understand what the casinos edge is really all about and why it has its shortcomings.
We all know that casinos can’t depend upon luck to generate the income they need to pay their expenses and have a few bucks left over as profit in profit for their shareholders. To ensure themselves a steady income they must have a mathematical advantage over every crap shooter at all times. How do they create their advantage in the game of craps? They do it in two different ways but with the same result.
Take a bet on the pass line for example. Based on the rules for winning a pass line bet, for every 1,000 bets a player makes, he will win 493 on average and lose 507. In other words the rules favor the casino winning more bets than the player. How much more? If you bet a buck 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% simply because the rules favor the casino winning more times than the player.
The casino creates its advantage on other crap bets a little differently. Take the bet on any seven whihc is a one-roll bet that the dice will show a 7. If you win that bet the casino will pay you $4 in winnings (4 to 1 payoff). That’s very nice that they give you $4 for only a dollar bet, but unfortunately it isn’t quite enough. You see the number 7 can be rolled in 6 different dice combinations out of a possible 36 combinations. You can only roll the number 7 with a pair of dice when the following numbers show: 1,6; 2,5; 3,4; and the opposites 6,1; 5,2 and 4,3. Any other dice combination – like 3,6 or 2,1 – will yield a non-7 number. There are in fact 30 combinations that yield a non-7 therefore the odds that a 7 will appear are 30 to 6 or by rounding 5 to 1. That is the true mathematical odds against rolling the dice and having a 7 show.
If the casino were to pay players at the same odds, namely 5 to 1, they wouldn’t make a penny profit on this bet. But being the smart business people that they are, they pay off a winning bet not at 5 to 1 odds but rather at 4 to 1 odds. By simply short changing the player one chip when he wins, the casinos have discretely created their edge on this bet. Frank Scoblete says it best: “when you lose a bet it’s lost; but when you win a bet you have a silent partner – the casino – who keeps a part of your winnings.”
Let’s be sure you also understand what the casino’s edge means in dollars and cents. The casino’s edge or advantage is usually written as a percentage. In the above example the casino’s edge on the any seven bet is 16.7% which means a player can expect to lose 16.7% of all the money bet on any seven. It doesn’t matter whether your bets win or lose in the calculation of how much the casino’s expect to win from you. All that’s required is that you bet and what the casino will earn day in and day out is 16.7% of what 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 for your action (16.7% times $25). Now most likely you will win or maybe lose a lot more than $4 but the more money you bet the closer your losses will come to the statistical 16.7% loss rate. The casinos bank on this fact day in and day out.
Table 1 ranks all the crap bets according to the casino’s edge. The pass/come/don’t pass/don’t come bets with odds clearly have the lowest casino’s edge compared to the other bets.
Table 1 – Ranking of Crap Bets by Casino’s Edge
|Bet||Casino’s Edge (%)|
|pass/come/don’t pass/don’t come with 100-times odds||0.02|
|pass/come/don’t pass/don’t come with 20-times odds||0.10|
|pass/come/don’t pass/don’t come with 10-times odds||0.18|
|pass/come/don’t pass/don’t come with 5-times odds||0.33|
|pass/come/don’t pass/don’t come with triple odds||0.47|
|pass/come/don’t pass/don’t come with double odds||0.61|
|pass/come/don’t pass/don’t come with single odds||0.85|
|pass/come/don’t pass/don’t come||1.41|
|place 6 and 8||1.52|
|lay 4 and 10||2.44|
|field (paying 2x on 2 and 3x on 12)||2.78|
|lay 5 and 9||3.23|
|lay 6 and 8||4.00|
|place 5 and 9||4.00|
|buy 4 and 10||4.76|
|field (paying 2x on 2 and 12)||5.55|
|place 4 and 10||6.67|
|hard 6 and 8||9.09|
|big 6 and 8||9.09|
|hard 4 and 10||11.11|
But does comparing the worth of one bet to another solely based on the casino’s edge tell the whole story? Not really, because the number of times a bet wins or loses per unit of time has not been factored into the equation.
Think about it for a minute. Is the number of times you win or lose a pass line bet per hour the same or different then say a field bet? How about a bet on any craps or the place bet on the 6? In fact they are not the same. Which is why a meaningful comparison of the worth of different craps bets should be based on their “cost per hour” and not solely on their “casino’s edge”.
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 make a bet. The equation to calculate the cost per hour is simply the amount of the bet times casino’s edge times number of decisions per hour.
Most casual players will typically bet $5 on the pass line. You can expect in most well run games the dice will roll about 100 times per hour. The number of pass line decisions that occur in those 100 rolls is 30. Therefore the cost per hour is simply
$5 times 1.41% times 30 decisions per hour = $2 (rounded)
By doing similar calculations for every bet you can compute each bet cost per hour and then rank them (Table 2).
Table 2 – Ranking of Crap Bets by Cost per Hour (rounded)
(assumes 100 rolls per hour)
|Bet||$ Wagered||# Decisions/hr||Cost/hr|
|pass/come/don’t pass/don’t come||$5||30||$2|
|place 6 and 8||$6||30||$2.70|
|hardway 6 and 8||$1||30||$2.70|
|big 6 and 8||$1||30||$2.70|
|field (3x 12)||$1||100||$2.80|
|hardway 4 and 10||$1||25||$2.80|
|field (2x 12)||$1||100||$5.50|
|place 5 and 9||$5||28||$5.60|
|3 and 11||$1||100||$6.70|
|2 and 12||$1||100||$6.70|
|place 4 and 10||$5||25||$8.30|
|buy 4 and 10||$21||25||$25|
|lay 4 and 10||$41||25||$25|
|buy 5 and 9||$21||28||$28|
|buy 6 and 8||$21||30||$30|
|lay 5 and 9||$41||30||$30|
|lay 6 and 8||$25||30||$30|
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. Such is the case with the hardway bet on the 6 and 8. Even though the bet is ranked low in Table 1 because of its high casino edge, it suddenly becomes a better bet when you look at its cost per hour ranking in Table 2. Why is this? Simply because it’s possible to bet low amounts ($1) and the number of decisions per hour (30) is relatively low. Remember it’s the combination of casino’s edge and number of decisions per hour, which determines the ranking in Table 2.
Take a look at the hourly cost of some of the proposition bets in Table 2. If you are prone to making prop bets, you should confine your betting to the hardway 6 and 8 compared to say any craps, any seven, or a bet on the 2/12 and 3/11 because the hourly costs are lower. If you like to bet the field, please do so in a casino which pays double on the 2 and triple on the 12. Your hourly costs will decrease from $5.50 to $2.80. Also note how the place bet on the 6 and 8 ranks high in both tables. If you like betting on the numbers you better pay close attention to Table 2. The numbers clearly show how much more it will cost you to buy a number vs. placing it.
Keep in mind that the cost per hour calculations and rankings in Table 2 is 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 the Table 2 (40 cents vs. $2). Likewise if you decide to bet $5 in the field instead of $1 your hourly costs would jump from $2.80 to $14.00.
You must also keep the cost per hour rankings in perspective. Obviously one way to keep your hourly costs to as low as possible is to bet the smallest amount ($1) on a bet which doesn’t have many decisions per hour. But that leads to a lot of rolls of the dice in which you would not be participating much and it won’t be fun playing.
So what about the odds bet which is noticeably missing from Table 2? Shouldn’t it reduce the cost per hour for the pass/come/don’t pass/ don’t come wagers because it lowers the casino’s edge for these bets (see table 1)? Well let’s see.
Table 2 tells us that the $5 pass line bettor’s hourly cost is $2. Suppose the player wagers doubles odds. The casino’s edge for the combined pass line plus double odds is reduced from 1.41% to 0.61% 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 the player betting double shells out another $10 on the odds every time a point number is thrown (about two thirds of the time). His average bet is about $11.67 per decision. If you multiply $11.67 times the 0.061% casino edge times the 30 decisions per hour, you arrive at an hourly cost of $2 – the same as the pass line player that doesn’t make the odds bet. Putting it another way, the casino’s edge on the odds bet is 0 so the hourly costs for the pass line bet is the same as a pass line bet with odds assuming the same amount of money is riding on the pass line bet. Therefore whether you bet pass line or pass line with single, double, triple, even 100-times odds, your hourly cost for the basic $5 pass line bet is always $2.
Review the numbers in Table 2 before you hit the crap tables to determine what it is really costing you to play. And remember when it comes to playing craps, time is really money.
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