The Effect of Odds For a Controlled Shooter

Recently I wrote an article comparing a pass line bet with placing the 6 or 8 at various levels of dice control. The article compared three different levels of control and the resultant edge for each type of bet. The levels compared were for different sevens-to-rolls-rations (SRRs).

A random shooter will throw six 7s out of every 36 rolls on average or, simplifying, 1 out of every 6 rolls. Saying it more simply, we say a shooter has an SRR of 6. If a shooter is able to eliminate just under one 7 out of every 36 rolls, that shooter will have an SRR of 7. Math has shown that achieving an SRR of just 6.3 (one 7 in every 6.3 rolls) and betting only the best bets will swing the edge to the player. I used SRR's of 6.0 (Random), 6.5 and 7.0 for comparison between the pass line bet and placing a 6.

Many craps players do not know that the low house edge on the Pass Line bet comes from a two-to-one advantage on the come-out. Here is how it works. On come-out a 7 or 11 wins the pass line bet, a 2, 3, or 12 loses. Out of 36 possible combinations of the two dice, there are six ways to throw a 7 (1-6, 2-5, 3-4, 4-3, 5-2, and 6-1) and two ways to throw an 11 (5-6 and 6-5) for a total of eight ways to win the pass line bet on come-out. There is one way to throw a 2 (1-1), two ways to throw a 3 (1-2, and 2-1), and one way to throw a 12 (6-6) for a total of four ways to lose the pass line bet. There are eight ways to win versus four ways to lose, a 2-to-1 advantage on come-out. Once a point is established, the edge swings dramatically to the house.

The results of that comparison are listed in the table below:

By the results above it is clear. Even a slightly improved SRR favors placing the 6 and/or 8 over a pass line bet. But what if we add odds to the pass line bet? How will that change things?

As almost all craps players know, the odds bet carries no house edge. In a random game of craps, no house edge is the best that it gets. All other bets on the table have a built-in house edge, so in a random game of craps betting a small pass line bet with maximum odds is the best way to diminish the impact of the house edge on the money bet. For example, if you bet $10 on the pass line with $50 in odds, the house will take .326 percent. If $60 is bet on the pass line, the house will take 1.414 percent -- 4 1/3 times more.

But a controlled shooter has the ability to reduce the appearance of the 7, thereby reducing the 2-1 edge on come-out and increasing the odds of winning the point. If a controlled shooter has an edge greater than 1.4 percent, he actually has an edge over the house on a pass line bet without odds. Will adding the no-house-edge odds bet dilute his edge? The short answer is no. If the controlled shooter has an edge of more than 1.4 percent, he will win on the odds bet -- not break even!

The table below shows the edges for pass line/come bets with different odds as well as placing the 6 or 8.

As expected the greater the SRR, the higher the player's advantage, regardless of whether the pass line is played or the 6/8 is placed.

Also, from the table we can see that if a SRR 6.5 or better shooter is taking two times odds or less, he is better off placing the 6 or 8. A shooter may only take single or double odds if that is the table maximum, or if the shooter's bankroll dictates he only has $30 to bet per hand. A $10 minimum pass line bet with double odds is $30 as is placing the 6 for $30. With these limits, a 6.5 SRR or better shooter will be better off placing the 6 or 8. If, however, he is playing on a $5 minimum table that allows 5 times odds, he is better off with a pass line bet and full odds. On a 3-4-5 times odds table, it is almost even whether he places a 6 or 8 or bets the pass line.

So there it is. If you have a verifiable SRR of 6.5 or greater, you are better off betting a pass line or come bet with 5 times odds than placing the 6 or 8. If you can only go double odds or less, however, you are better off placing the 6 or 8.

I personally like the idea of playing on a 3-4-5 times odds table so I can decide whether to place the 6 or 8 or go with pass line and come bets and not suffer any decreased edge.

Until the next time...

May all your wins be swift and large and all your losses be slow and tiny.

Jerry "Stickman"