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Mathematics of Odds

The Only Fair Bet

In any casino, every game is tilted in favor of the house. This built-in advantage is called the house edge. Every bet you make, from blackjack to roulette, has a small statistical cost. Except for one.

The 'Odds' bet in craps is unique. It's a side bet you can only make after a point is established on a Pass Line or Come bet. It pays out at true mathematical odds, meaning the casino has exactly zero advantage. It's the only truly fair bet in the entire building.

Lesson image

When a point is established (4, 5, 6, 8, 9, or 10), the game changes. The goal is now for the shooter to roll that point number again before rolling a 7. A roll of 7 ends the round, and Pass Line bets lose. The probability of rolling the point versus rolling a 7 dictates the true odds.

PointWays to RollWays to Roll a 7True Odds AgainstCasino Payout
4 or 10362 to 12 to 1
5 or 9463 to 23 to 2
6 or 8566 to 56 to 5

As you can see, the casino pays you exactly what the bet is worth. There's no commission or statistical haircut. This is why it's such a powerful tool.

Taking the Odds

After a point is established, you can place an additional wager behind your original Pass Line bet. This is called "taking the odds." The maximum you can bet is determined by the table limits, often advertised as "3-4-5x Odds."

This isn't a strategy, but a rule of the table. It means:

  • You can bet up to 3 times your Pass Line bet when the point is 4 or 10.
  • You can bet up to 4 times your Pass Line bet when the point is 5 or 9.
  • You can bet up to 5 times your Pass Line bet when the point is 6 or 8.

A 💲10 Pass Line bet with a point of 8 allows you to take up to 💲50 in odds (5 x 💲10). If the 8 hits, your Pass Line bet pays 💲10 (1:1) and your odds bet pays 💲60 (6:5 on 💲50).

By betting more on the 0% house edge odds bet, you drastically lower the effective edge on your total action. The original 1.41% edge on the Pass Line bet gets diluted by the larger, fair odds bet behind it. The more odds you take, the closer your total wager gets to a 0% house edge.

Laying the Odds

This same principle works in reverse for players betting against the shooter with a Don't Pass bet. If a point is established, you are betting that a 7 will be rolled before the point. Since it's more likely for a 7 to appear, you must offer odds instead of receiving them.

This is called "laying the odds". You wager more to win less, reflecting the true probability. For example, to win $10 on a point of 4, you must lay $20 (1:2 odds).

Payout=Wager×Ways to roll the PointWays to roll a 7\text{Payout} = \text{Wager} \times \frac{\text{Ways to roll the Point}}{\text{Ways to roll a 7}}

Just like taking odds, laying odds is a 0% house edge bet. It lowers the effective edge on your Don't Pass bet (originally 1.36%) the more you lay. For players who prefer to bet against the shooter, this is the most powerful tool available.

Quiz Questions 1/5

What is the term for the casino's built-in statistical advantage in its games?

Quiz Questions 2/5

What makes the 'Odds' bet in craps unique compared to virtually all other bets in a casino?

Mastering the odds bet is the single most important step in moving from a casual player to an informed one. It turns a game of pure chance into one where you can actively minimize the house's advantage.