True Craps!

In every casino you waltz into, at every game and every machine, the casino has an advantage over you. That advantage is called "The Vig", "The Juice", or just plainly "The House Advantage".

The casino makes money because they have the advantage on you. If they did not, they would have to make money from other items, and would soon not exist. If the casino had no advantage over you, they would pay you the patron, at true and correct odds on every bet.

For example, if there were a Pari-Mutual wheel (a wheel of chance) that were perfectly balanced and had 10 selections at which the wheel could be expected to stop, then your chance of hitting any one of them would be 1 in 10. A true and correct payoff for that wheel would be to pay you 10 dollars for every one you gambled. At that rate after several spins, no one would lose and no one would win, except for the sap who had to pay for the wheel and pay the dealer to spin it (the casino). So, the casino is allowed to pay you, say, only $8 for that 10-1 chance. The $2 they keep is called the vig.

So, we know the casino must have some advantage to stay in business. However, if that advantage is too large, few (if any) of the upstanding citizen patrons will ever win and they will then cease to patronize the casino for greener pastures. It is therefore in the casinos best interest as well as the patrons, to make sure the house advantage is moderate enough to recoup operating expenses and a fair profit, while offering a decent chance for the player to cover their expenses and perhaps make a little monetary profit too.

So how do you figure what's good and what's not? By and large, you will find that the games offered in most legitimate casinos come with an edge of between 1% and 20%. That means that over a span of time, the casino will take from 1 to 20% of every dollar placed at risk in their house. Obviously, the player would like to be on the 1% side, and those charged with making a profit for the casino would prefer the player to fork over 20% for their entertainment.

So, how do you know what's good for you? Do you always want to take things as given, or would you like to figure things out for yourself? If you'd like to do the latter, I offer the following calculations for you. Take this math and run with it.

How to calculate the house advantage on any single-event (bet).

Our example is a $6 place bet on the number 6, which pays $7 for a $6 bet.
A craps example, of course!

1. Calculate the total number of winning and losing events. Call it TE.
Example:
For a 6 place bet, there are 5 winning events (1-5, 2-4, 3-3, 4-2, 5-1),
and 6 losing events when 7 rolls (1-6, 2-5, 3-4, 4-3, 5-2, 6-1),
so:
TE = 5+6, TE = 11

2. Calculate the total amount risked (TR) for all events.
Example:
For a 6 place bet of $6 you will have,
TR = $6xTE, TR = 6X11, TR = 66

3. Calculate the total amount to win (TW).
Example:
For a 6 place bet of $6, you will win $7 so,
TW = $7xWinning Combinations, TW = 7x5, TW = 35

4. Calculate the total amount to lose (TL).
Example:
For a 6 place bet you will lose $6, 6 times or,
TL = $6xLosing Combinations, TL = 6x6, TL = 36

5. Find the difference between the Total Won, and the Total Lost.
Example:
Difference = TW - TL, Diff = 35 - 36, Diff = -1

That's one dollar for the House.

6. Now divide that difference by the total you invested because we are examining one bet.
Example:
-1 / $66, -1 / 66 = -.0151
Notice that the amount is negative. This means that the House is making a profit, or Vig.


7. Now turn this into a percentage by multiplying by 100 to come up with a House Advantage on the Place 6 bet of 1.51%.

Another example:

A craps playing amigo asked what the house advantage would be on a combined bet of $50 lay on the 10 plus a $5 hard 10.
Since I am a genius and am rarely wrong and know just about everything and am not ashamed to show it, I will answer the question for the illumination of crapsters everywhere.

Some parameters:

hard 10 pays 7 to 1
lay 10 pays 1 to 2, and costs $1 per 20 bet.
All casinos I know of will charge you $3.00 for a $50 lay 10 bet if they let you make it at all, so betting in full $20 increments is preferable.
This first analysis is for a $40 lay 10 bet. This also assumes you only play at a table that takes the vig on a winning bet (not always the case).

Total winning events: 6 (all sevens)
Total losing events: 3 (all 10's)
Total events: 9
Total to win: $78 (6 * $13)
Total to lose: $95 ((2 * $45) + ($5))
Total risked: $405 (9 * $45)


Total won - total lost = $-17
Total lost for each dollar risked: -17/405 = -.04198
House advantage: 100 * -.04198 = 4.198%

I say anything over a 2% HA is a sucker bet. Don't be a sucker!

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