Craps Dice Probability Explained: Why 7 Appears More Often Than Other Numbers

This article is part of our complete guide on How Craps Really Works: Dice Probability, Bets, and Why Myths Persist, which explains craps probability, house edge, variance, and why common myths fail.

Dice Probability Is About Combinations, Not Totals

Craps is governed by a simple mechanical truth: two dice create combinations, not equal totals.

Players experience the game through totals—2 through 12—but the dice themselves produce ordered pairs. Each roll results in one of 36 equally likely combinations, and probability flows directly from how many combinations produce a given total.

This distinction is critical. Most confusion about craps odds begins by ignoring it.

The Full Distribution of Two-Dice Outcomes

All 36 Outcomes Are Equally Likely

When two fair six-sided dice are rolled, each die has six faces and each face is equally likely.

That means:

There are 36 possible ordered combinations
Each combination occurs with probability 1 in 36
(1,6) and (6,1) are different outcomes

Order matters for probability, even if the total is the same.

How Many Ways Each Total Can Occur

Totals appear at different rates because they can be formed in different numbers of ways.

2 → 1 way
3 → 2 ways
4 → 3 ways
5 → 4 ways
6 → 5 ways
7 → 6 ways
8 → 5 ways
9 → 4 ways
10 → 3 ways
11 → 2 ways
12 → 1 way

This distribution is fixed. It cannot change during play.

Why 7 Appears More Often Than Any Other Number

The Mathematical Reason

The total 7 can be formed in six distinct ways:

(1,6)
(2,5)
(3,4)
(4,3)
(5,2)
(6,1)

No other total has more than five combinations.

As a result, 7 has a probability of 6/36 (1/6) on every roll. Totals like 2 and 12 occur only 1/36 of the time.

This imbalance is the structural center of the game.

Why This Feels Counterintuitive

Many players assume that because there are 11 totals, each one should appear roughly equally.

Dice do not work that way. Totals are labels. Combinations are reality.

The brain notices outcomes, not the combinatorial paths that produce them.

Frequency Does Not Mean Predictability

Common Misinterpretations

Because 7 appears more often, players often conclude that:

it is “due” after a long absence
it is “unlikely” after appearing repeatedly

Both conclusions are wrong.

Frequency describes long-run distribution, not short-run behavior.

Independence Still Applies

Even though 7 has the highest probability, each roll is independent.

The probability of rolling a 7 is always 1/6, regardless of what happened before.

Six rolls without a 7 do not increase the chance of a 7 next time. Three 7s in a row do not reduce it.

The Shape of the Distribution Matters

Why Extremes Are Rare

Totals near the edges—2, 3, 11, and 12—are rare because very few combinations produce them.

Small changes in dice faces push results toward the center of the distribution.

This creates a pyramid-shaped probability curve, narrow at the edges and wide in the middle.

Why This Shapes Player Experience

Because the distribution is uneven:

some numbers feel “active”
others feel dramatic when they appear
long gaps for rare totals are normal

Players often mistake normal distribution behavior for meaningful signals.

Probability vs Short-Term Results

Why Sessions Feel Erratic

In the short run:

rare numbers can appear quickly
common numbers can temporarily disappear
streaks cluster naturally

This volatility does not contradict probability. It is an expected feature of it.

Where Myths Begin

When players expect smooth alternation or quick balance, they misinterpret randomness as:

hot tables
cold tables
changing conditions

The math never changed. Expectations did.

What This Means for Understanding Craps

Craps probability is not hidden or negotiable.

It is fixed, mechanical, and determined entirely by two dice.

Understanding this distribution explains why some numbers dominate the game, why others feel special, and why intuition so often conflicts with reality.

Craps Dice Probability Explained: Why 7 Appears More Often Than Other Numbers

Dice Probability Is About Combinations, Not Totals