Don't Fear the 7 and 11

One of the biggest reasons players are uncomfortable with the Don't Pass is the come-out roll. A 7 or 11 immediately loses the bet. There are eight combinations of 7 and 11 out of 36, giving us a 22.22% chance of an immediate loss.

That number can look intimidating, but it only looks at one side of the equation. The Don't Pass also has immediate winning outcomes: the 2 and 3. If we're flat betting one unit and receiving one unit when we win, wins and losses can be compared directly. Every one-unit win adds +1 and every one-unit loss subtracts -1.

Think of it like exchanging pieces in chess. Losing a piece matters, but if you take an equal-value piece in return, the exchange itself is neutral. What ultimately matters is the net difference between what we win and what we lose.

This gives us another useful way to look at the Don't Pass come-out roll.

The 3 has two combinations, and the 11 has two combinations. Over a sufficiently large number of independent rolls, the Law of Large Numbers tells us their observed frequencies should tend toward their equal theoretical probabilities. Because both pay or lose one unit, we can conceptually pair those outcomes:

2 ways to win on 3 vs. 2 ways to lose on 11 = net 0 combinations.

Now consider the 2. There is one combination of 2, producing a one-unit win. We can conceptually pair that against one of the six combinations of the 7:

1 winning combination vs. 1 losing combination = net 0.

After making those comparisons, what remains is the equivalent of five unmatched losing combinations of the 7:

5 ÷ 36 = 13.89%.

This does not mean our actual probability of losing to a 7 or 11 has fallen from 22.22% to 13.89%. A 7 or 11 still appears in 8 of the 36 combinations. The 13.89% represents the net combination disadvantage after pairing the immediate one-unit winning and losing outcomes.

That's an important distinction.

Instead of seeing only eight ways to lose, we're accounting for the three ways to win that help offset those losses under flat, one-unit betting:

8 losing combinations − 3 winning combinations = 5 net losing combinations.

Meanwhile, 24 of the 36 combinations—66.67%—establish a point. Once that happens, the Don't Pass becomes the conditional favorite to resolve on the 7 before the point: 54.55% on 6/8, 60% on 5/9, and 66.67% on 4/10.

That's why the come-out 7 and 11 shouldn't be viewed in isolation. We accept one-unit wins and one-unit losses as exchanges, keep our bet size constant, and allow the mathematics to determine our position.

Flat betting gives the comparison meaning: one unit lost is one unit lost, and one unit won is one unit won. We aren't trying to recover a loss by increasing the next bet. We accept the exchange and move on to the next position.

Gus Santos