Dice Probabilities Explained
Two dice are about the friendliest probability lesson there is. There are only 36 things that can happen, every one of them equally likely, and you can count them on paper in a minute. Once you've counted them, the entire craps table — every payout, every edge — suddenly makes sense.
36 equally likely outcomes
Each die has six faces, and the two dice are independent. So the number of combinations is 6 × 6 = 36. The key word is equally likely: rolling a 2 then a 5 is just as probable as rolling a 6 then a 1. On fair dice, every one of those 36 ordered pairs has exactly a 1-in-36 chance.
The catch is that we don't usually care about the individual faces — we care about the total. And totals are not equally likely, because some totals can be made in more ways than others. There's only one way to make a 2 (1+1), but a 7 can be made six different ways.
The shape of the totals
If you count how many of the 36 combinations produce each total, you get a triangle — a little bell. The totals climb from 2 up to a peak at 7, then fall symmetrically back down to 12. The middle is fat; the ends are thin.
| Total | Ways to make it | Probability |
|---|---|---|
| 2 | 1 | 1/36 ≈ 2.8% |
| 3 | 2 | 2/36 ≈ 5.6% |
| 4 | 3 | 3/36 ≈ 8.3% |
| 5 | 4 | 4/36 ≈ 11.1% |
| 6 | 5 | 5/36 ≈ 13.9% |
| 7 | 6 | 6/36 ≈ 16.7% |
| 8 | 5 | 5/36 ≈ 13.9% |
| 9 | 4 | 4/36 ≈ 11.1% |
| 10 | 3 | 3/36 ≈ 8.3% |
| 11 | 2 | 2/36 ≈ 5.6% |
| 12 | 1 | 1/36 ≈ 2.8% |
Add the "ways" column and you get 36 — every outcome accounted for. The 7 sits at the top with six combinations (1-6, 2-5, 3-4, 4-3, 5-2, 6-1), while 2 and 12 are the rarest, with just one each.
The 7 is no accident. It's the only total the size of which the table is built around. It's the most common roll precisely because it has the most combinations — and that's why "seven out" ends so many craps rounds.
How this drives every payout
Craps is just this table dressed up. Consider a Place bet on the 6: you win if a 6 comes before a 7. There are 5 ways to roll a 6 and 6 ways to roll a 7, so among the rolls that matter you win 5 times for every 6 losses — odds of 6 to 5 against you. A truly fair payout would be 6-for-5; the casino pays 7-for-6 instead, and the gap between those two numbers is the house edge.
The same counting explains the come-out roll. A 7 or 11 wins the Pass line because together they have 8 combinations (6 + 2). A 2, 3, or 12 loses with 4 combinations (1 + 2 + 1). Every rule on the felt traces straight back to how many of the 36 outcomes fall where.
Why this beats intuition
People routinely guess that 6 and 8 are "as likely as" 2 and 12 because each is "just one number." The combination count says otherwise: a 6 is five times more likely than a 2. This is the same reason "hard" combinations (rolling a total with a matching pair, like 3-3 for a 6) are rarer than the same total made with mixed dice. The dice don't have memory or momentum — they just have geometry, and the geometry is fixed at 36.
On Riskr you can roll the Craps table as many times as you like with fake chips and watch this distribution emerge: the 7s pile up, the 2s and 12s stay rare, and the bell takes shape. It's the cleanest way to see probability turn into reality.