Each die has 6 sides. Two dice rolled together can land in 6 times 6 different ways, which is 36 total combinations. That number, 36, is the foundation of every craps bet you'll ever see. Each combination is equally likely; the dice have no memory or preference, and every roll is independent.

So if every combination is equally likely, why are some totals more likely than others? Because some totals can be made more than one way. A 7 can be made by rolling 1-6, 2-5, 3-4, 4-3, 5-2, or 6-1, six different combinations that all add up to 7. A 2 can only be made one way (1-1), and so can a 12 (6-6). That asymmetry is everything in craps.

Here's a chart worth staring at for a minute, because once your brain absorbs it, the rest of craps probability becomes intuitive. The numbers in the middle (6, 7 and 8) are the most common, and the numbers at the edges (2 and 12) are the rarest. The further you get from 7, the lower the odds of hitting that number.

Here's the breakdown of every possible roll and how many ways there are to make it. Notice the symmetry: the 6 and 8 are tied, the 5 and 9 are tied, the 4 and 10, the 3 and 11, and the 2 and 12, with the 7 sitting alone in the middle as the most common roll.

A 7 will show up about one out of every six rolls on average. That's the highest probability of any single roll, and it's the fact the entire game is built around.

Now that you can see how often each number comes up, the bets start telling a different story. Take the pass line. On the come out roll, you win on a 7 (6 ways) or 11 (2 ways), which is 8 ways out of 36, and lose on a 2 (1 way), 3 (2 ways) or 12 (1 way), which is 4 ways. Eight wins, four losses, twice as many wins as losses. That's why the come out is favorable to pass line bettors.

Now take a single point cycle with the point at 6. You win on a 6 (5 ways) and lose on a 7 (6 ways); every other number does nothing. So you have 5 winning rolls against 6 losing rolls: the 7 is more likely than your point. That's why pass line bets lose more than they win during the point cycle. The casino's edge is the difference between those two phases, working out to about 1.4 percent.

The 6 and 8 are the second most common rolls, five ways each, just one less than the 7. That makes them the most attractive numbers to bet on directly as place bets, because they hit so often. Compare a place bet on the 6 with one on the 4: the 6 has 5 ways versus 6 for the 7, hitting about 45 percent of the time, while the 4 has only 3 ways, hitting about 33 percent.

The casino adjusts payouts to compensate, paying more on the 4 because it hits less often, but it doesn't pay the full true odds, which is where its edge comes from. The underlying probability is what determines every payout and edge. The place bets article covers it all.

The 4 and 10 are the hardest point numbers to make, with only 3 ways each. When the point is 4 or 10, you have 3 ways to win versus 6 to lose to a 7, so it only hits about one out of three times. This is why some experienced players don't love seeing a 4 or 10 set as a point.

It also explains why the free odds bet pays 2 to 1 on a 4 or 10 point versus only 6 to 5 on a 6 or 8 point. The casino pays more for the harder point because it's less likely to come through. The math works out perfectly fair, which is why the free odds bet has zero house edge regardless of the point. The free odds article goes deeper.

The 2 and 12 each have only one combination, a probability of 1 out of 36, or about 2.78 percent. The casino lets you bet on a 2 or 12 hitting on the very next roll, called the aces (2) and boxcars or midnight (12). The fair payout, the true odds, would be 35 to 1. The casino actually pays 30 to 1, five chips less, and over many bets that gap is where the house edge comes from. The edge on aces and boxcars works out to nearly 14 percent, versus 1.4 percent on the pass line.

This is the math behind why prop bets are bad. They look exciting because the payouts are huge, but the dice almost never produce those numbers, so even when you hit one, you've already lost more on the bets that didn't hit than the win pays out. The flashier the payout, the worse the math is for you.

This one costs people real money at craps tables. The gambler's fallacy is the belief that past dice rolls influence future ones. If a 7 hasn't come up in 20 throws, the fallacy says a 7 is "due." If the shooter just rolled three 11s, the fallacy says another is unlikely. It's completely wrong. The dice have no memory. Every roll is independent, and the probability of a 7 on the next throw is exactly 6 out of 36 regardless of anything that came before.

This is hard to internalize because the human brain is bad at randomness; we see patterns where there are none. The practical takeaway: don't increase your bet because something seems "due," and don't decrease it because the table seems "cold." Make smart bets with the right math, not chase patterns that aren't there. More in our common craps mistakes article.

Probability is a long-term concept. It tells you what happens over many thousands of rolls, not what happens on the next roll or in the next hour. In any individual session, anything can happen: you can sit at a table where the 7 doesn't come up for 30 minutes, or where it comes up four times in a row after a point. The dice don't even out over short stretches; they even out over millions of rolls, which is why the casino, with its giant volume, gets reliable returns while you, playing one session, are subject to whatever the dice do that night.

This is part of what makes craps fun. In any given session you can win, and win a lot. The casino's edge becomes visible over millions of rolls, not 200. That's why bankroll management matters more than probability theory for an individual player: if you bet smart and quit while ahead, the math hasn't had time to catch up. Our article on bankroll management goes into this.

You don't need to memorize all 36 combinations, know the exact percentage on every roll, or do mental math at the table. What you do need to know: the 7 is the most common roll, the 6 and 8 are next, the 4 and 10 are the hardest point numbers, and the 2 and 12 are the rarest, so any bet depending on them loses more than it wins. The dice have no memory. That's the whole probability picture.

Once you understand those few facts, you understand enough to make good decisions. Bet the pass line. Take odds. Avoid prop bets. Done. The next article gets into the pass line bet in detail, and now that you understand the probability behind it, the math will make a lot more sense.