Craps - Optimal Betting

Optimal Betting

All bets have a house advantage; one can reduce (but not eliminate) one's average losses by only placing bets with the smallest house advantage.

The pass/don't line, come/don't line, place 6, place 8, buy 4 and buy 10 (only under the casino rules where commission is charged only on wins) are the best bets with the lowest house edge in the casino, and all other bets will, on average, lose money between three and twelve times faster because of the difference in house edges.

The place bets and buy bets differ from the pass line and come line, in that place bets and buy bets can be removed at any time, since, while they are multi-roll bets, their odds of winning do not change from roll to roll, whereas pass line bets and come line bets are a combination of different odds on their first roll and subsequent rolls. The first roll of a pass-line bet is 2:1 advantage for the player (8 wins, 4 losses), but it's "paid for" by subsequent rolls that are at the same disadvantage to the player as the don't pass bets were at an advantage. As such, they cannot profitably let you take down the bet after the first roll. Note that, if it didn't make it hard to track what the initial bet was, they would gladly let you increase your pass/come bet after the come-out roll, since you'd be getting even money on a bet that should pay odds. They will just remind you to place the point instead and get your extra payout (over even money) of 1:6 (on points 6/8), 1:2 (on points 5/9), or 1:1 (on points 4/10).

Conversely, you can take back (pick up) a don't pass or don't come bet after the first roll, but you shouldn't, because you already endured the disadvantaged part of the combination - the first roll. On that come-out roll, you win just 3 (1-1, 1-2, 2-1) out of 36 possible rolls, while losing on 8 (6 7s, 2 11s) (2.6:1 against). On the other 24 rolls that become a point (push on the 1 12), your don't pass bet is now a favorite of between 2:1 (on points 4 and 10) and 6:5 (on points 6 and 8). It's no wonder that they will gladly allow you to take down such a bet.

Among these, and the remaining numbers and possible bets, there are a myriad of systems and progressions that can be used with many combinations of numbers.

An important alternative metric is house advantage per roll (rather than per bet), which may be expressed in loss per hour. The typical pace of rolls varies depending on the number of players, but 102 rolls per hour is a cited rate for a nearly full table. This same reference states that only "29.6% of total rolls are come out rolls, on average," so for this alternative metric, needing extra rolls to resolve the pass line bet, for example, is factored. This number then permits calculation of rate of loss per hour, and per the 4 day/5 hour per day gambling trip:

• $10 Pass line bets 0.42% per roll, $4.28 per hour, $86 per trip
• $10 Place 6,8 bets 0.46% per roll, $4.69 per hour, $94 per trip
• $10 Place 5,9 bets 1.11% per roll, $11.32 per hour, $226 per trip
• $10 Place 4,10 bets 1.19% per roll, $12.14 per hour, $243 per trip
• $1 Single Hardways 2.78% per roll, $2.84 per hour, $56.71 per trip
• $1 All hardways 2.78% per roll, $11.34 per hour, $227 per trip
• $5 All hardways 2.78% per roll, $56.71 per hour, $1134 per trip
• $1 Craps only on come out 3.29% per roll, $3.35 per hour, $67.09 per trip
• $1 Eleven only on come out 3.29% per roll, $3.35 per hour, $67.09 per trip