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Odds in Craps

The rules vary slightly from one casino to another, but the expected value of most bets is only slightly negative (the most favourable bets with the most favourable rules offer a house advantage of as little as 0.18%). All bets have a negative expectation except for the "free odds" bet that the player is allowed to make after a point is established on a flat (line) bet (this bet has a long-term expected value of 0). Since there is no correlation between die rolls, there is no possible long-term winning strategy. While experienced blackjack players who learn to count cards can gain a small mathematical advantage over extended playing sessions by diligent study, there is no comparable strategy for craps.

Occasionally, players win several bets in a row; such players are said to be "on a roll." Those who increase their bets during a winning series can rapidly win substantial sums. On the other hand, money can be lost back just as quickly, as there is no statistical likelihood of a "hot streak" continuing for any given duration. To counter this, experienced players take full advantage of "free odds" -- bets on which there is zero house advantage. Maximizing the size of your odds bet in relation to your line bet will minimize but never eliminate the house edge. Many casinos have limitation on how large the odds bet can be in relation to the flat bet, with single, double, and five times odds common. Some casinos offer 3-4-5 odds, referring to the maximum multiple of the line bet a player can place in odds for the points of 4 and 10, 5 and 9, and 6 and 8, respectively. During promotional periods, a casino may even offer 100x odds bets, which renders the house edge to almost nothing but dramatically increases volatility. Horseshoe Casino founder Benny Binion once quipped that if every player took the 100x odds, the house "wouldn't be able to keep the lights on," referring to the overhead required to run casino games.

The only casino currently in Las Vegas to offer 100x odds is the Casino Royale located next to Harrah's on the strip. The Stratosphere offers 10x odds and most of the other casinos such as MGM and Bellagio offer 3x4x5. Some casinos such as the Riviera, Orleans and Gold Coast offer 2x odds which is considered an anathema to craps players, in equal footing with 6:5 payouts on single-deck blackjack. Most downtown casinos offer 5x (Binions) or 10x odds (Plaza and Main Street Station, with the Golden Nugget offering the unusual 6x8x10 odds), while a handful of downtown casinos offer the horrible 2x odds (Sam Boyd's Fremont).

Optimal Betting / Bad Bets

One subtlety of craps is that there is a huge variety in the house advantage on the many bets available on the craps layout. Of course the house is guaranteed to win in the long run, but by poor selection of bets, the house can win the player's money many, many times faster. For example,

• A player betting the pass line or come line at $10 per bet, 50 bets per hour, will lose on average $141 over 20 hours of gambling on a gaming trip.

• A player placing the 4 and 10 at the same rates will lose on average $667 over the same period.

• A player betting the "any seven" bet at the same rate will lose on average $1,667 over the same period.

The house percentage advantage is an indication of the expected loss per total amount bet. Note that the total bet amount also drives expected loss, so betting the table minimum will give the slowest rate of average loss. While odds bets lower the house percentage, they do so by increasing the total amount bet. Thus, given a fixed minimum pass line bet, the decision whether to make the odds bet or not does not affect the average dollar loss per game. It does, however, increase the variance, which improves the chance (though still under 50/50) that the player will be net ahead after a finite amount of play, as well as increasing the chance of larger losses or larger wins.

The table below gives house advantage of various bets, as well as expected loss over a typical gaming trip (e.g. 50 bets per hour for 5 hours per day over 4 days = 1000 bets)

In summary, the pass/don't line, come/don't line, place 6, place 8, buy 4 and buy 10 (only when commission is charged only on wins) are the "good" bets, and all other "bad" bets will lose money between 3 and 12 times faster, on average. The Any Seven bet, at 16.7% house advantage, may have the dubious honour of being the worst bet in the entire casino. Many players like to place numbers, but only the 6 and 8 are good bets; buying the 4 or 10 is better than placing it, especially when commission is paid on wins only. The player can work "through" the come line to get money onto the other point numbers at much more favourable returns for the player.

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