Dice Probability In Craps for Beginners

Here is a sentence I wish someone had drilled into my head before I ever stepped up to my first craps table. The whole game is built on one simple piece of math. Two dice can roll a 7 more easily than they can roll any other number. That is it. That single fact is the engine that makes craps work the way it does, and once you understand it, every bet on the table starts making sense.

You do not need to be good at math to play craps well. You do not need to memorize tables or carry around a probability chart. But you do need to understand why a 7 is special and why the dice favor some numbers over others. This article is going to walk you through that in plain English, with a chart that makes the whole thing visual.

If you have read our articles on the come out roll and the point and basic rules, you have heard me say the 7 is the most common roll a few times now. This is the article where I actually show you why.

Two dice, 36 possibilities

Start here. 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 will ever see.

Each of those 36 combinations is equally likely. The dice do not have memory or preference. The first die is just as likely to come up 3 as it is to come up 5, and the second die is just as likely to come up 4 as it is to come up 1. Every roll is independent. The dice do not know what they did last time. They do not owe anyone a number. They are completely random.

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. The number 7, for example, can be made by rolling a 1 and a 6, a 2 and a 5, a 3 and a 4, a 4 and a 3, a 5 and a 2, or a 6 and a 1. That is 6 different combinations that all add up to 7. The number 2 can only be made one way, by rolling a 1 and a 1. The number 12 can only be made one way too, by rolling a 6 and a 6.

That asymmetry is everything in craps.

The 36 combinations laid out

Here is the chart that we have made for you to look at. This visual is 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. The numbers at the edges, 2 and 12, are the rarest. Everything else falls somewhere in between in a predictable pattern.

The thing to note is that the further you get away from 7, the more the odds decrease that you will hit that number.

The full count of every total

Here is the breakdown of every possible roll and how many ways there are to make it.

The number 2 can be rolled 1 way out of 36. That is a probability of about 2.78 percent. Translation: a 2 will show up roughly once every 36 rolls. Some weeks you will see 2s back to back. Other weeks you will not see one for an hour. But long term, 1 in 36.

The number 3 can be rolled 2 ways out of 36, which is about 5.56 percent.

The number 4 can be rolled 3 ways out of 36, or 8.33 percent.

The number 5 can be rolled 4 ways out of 36, or 11.11 percent.

The number 6 can be rolled 5 ways out of 36, or 13.89 percent.

The number 7 can be rolled 6 ways out of 36, or 16.67 percent. This is the highest probability of any single roll. A 7 will show up about one out of every six rolls on average.

The number 8 can be rolled 5 ways out of 36, the same as the 6, at 13.89 percent.

The number 9 can be rolled 4 ways out of 36, the same as the 5, at 11.11 percent.

The number 10 can be rolled 3 ways out of 36, the same as the 4, at 8.33 percent.

The number 11 can be rolled 2 ways out of 36, the same as the 3, at 5.56 percent.

The number 12 can be rolled 1 way out of 36, the same as the 2, at 2.78 percent.

You will notice the symmetry. The 6 and 8 have the same probability. The 5 and 9 have the same probability. The 4 and 10 do too. The 3 and 11 are tied. So are the 2 and 12. The numbers pair up, with 7 sitting alone in the middle as the most common roll. This is just a property of how dice math works, and it has consequences all over the table.

Why this changes everything about the bets

Now that you can see how often each number comes up, the bets on the table start telling a different story.

Take the pass line. We have already covered why this bet works the way it does, but let me put it in probability terms. On the come out roll, you win on a 7 (6 ways) or 11 (2 ways), which is 8 ways out of 36. You lose on a 2 (1 way), 3 (2 ways) or 12 (1 way), which is 4 ways out of 36. Eight wins, four losses, twice as many wins as losses. That is why the come out is favorable to pass line bettors.

Now take a single point cycle. Say the point is 6. You win on a 6, which is 5 ways out of 36. You lose on a 7, which is 6 ways out of 36. Every other number does nothing. So during the point cycle, you have 5 winning rolls against 6 losing rolls. The 7 is more likely than your point. That is why pass line bets lose more than they win during the point cycle.

The casino's edge on the pass line is the difference between those two phases, after you do the math on how often a point gets established and how often each point gets made. The full calculation works out to about a 1.4 percent house edge. Not bad. But every penny of that edge comes from the math we just walked through.

Why the 6 and 8 get all the love

Look at the chart again and notice that the 6 and 8 are the second most common rolls. Five ways each, just one less than the 7. This makes them the most attractive numbers to bet on directly, in the form of place bets, because they hit so often.

Compare a place bet on the 6 with a place bet on the 4. The 6 has 5 ways to come up versus 6 for the 7, which means the 6 will hit about 45 percent of the time when you put a place bet on it. The 4 has only 3 ways to come up versus 6 for the 7, which means the 4 will hit only about 33 percent of the time. The 6 is winning roughly 4 of every 9 attempts. The 4 is winning only 1 of every 3 attempts.

The casino adjusts the payouts to compensate for this. The 4 pays more than the 6 on a place bet because the 4 hits less often. But the casino does not pay you the full true odds, which is where their edge comes from. We will get into the details on each specific bet in the bet articles, but the underlying probability is what determines what they pay and what edge the casino takes. The place bets article covers it all.

The 4 and 10 problem

The 4 and 10 are the hardest point numbers to make. They have only 3 ways each. When the point is 4 or 10, you have 3 ways to win versus 6 ways to lose to a 7. That means the 4 or 10 only hits as a point about one out of three times. The other two thirds of the time, the round ends on a 7.

This is why some experienced players do not love seeing a 4 or 10 set as a point. The math is against you on those numbers more than on any other point. You can still win, you can still bet odds and have a good time, but the probability is heavier against you when the point is 4 or 10.

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 is paying you more for the harder point because the harder point is less likely to come through. The math works out to be perfectly fair, which is why the free odds bet has zero house edge regardless of which point you are taking odds on. The free odds article goes deeper.

The longshot bets and why they are bad

Now look at the chart and find the 2 and 12. Each one has only one combination that makes it. The probability of either is 1 out of 36, or about 2.78 percent.

The casino will let you bet on a 2 or 12 hitting on the very next roll. These are called the aces (for 2) and boxcars or midnight (for 12). The fair payout, the true odds, would be 35 to 1. You are betting 1 chip and the dice are 35 to 1 against you, so a fair payout would be 35 chips back if you win.

The casino actually pays 30 to 1 on these bets. That is 5 chips less than the fair payout. Over many bets, that 5 chip gap is where the house edge comes from on the prop bets. The edge on aces and boxcars works out to nearly 14 percent, which is brutal. For comparison, the pass line is 1.4 percent. You give up ten times the edge for the chance at a flashy 30 to 1 payout.

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

The gambler's fallacy and why it gets people in trouble

I want to spend a minute on this because it costs people real money at craps tables.

The gambler's fallacy is the belief that past dice rolls somehow influence future dice rolls. If a 7 has not come up in 20 throws, the gambler's fallacy says a 7 is "due" and you should bet on it. If the shooter just rolled three 11s in a row, the gambler's fallacy says another 11 is unlikely because they have already happened.

It is wrong. Completely wrong. The dice do not have memory. They do not know what they rolled five minutes ago. Every single roll is independent of every roll that came before it. The probability of rolling a 7 on the next throw is exactly 6 out of 36, regardless of whether the last roll was a 7 or not. Regardless of whether the last 10 rolls were 7s or not. Regardless of anything else that has ever happened at any craps table anywhere.

This is hard to internalize because the human brain is bad at randomness. We see patterns where there are none. We feel like a streak has to end, or a hot run has to keep going. But the dice do not feel anything. They just bounce.

The practical takeaway is this. Do not increase your bet because something seems "due." Do not decrease your bet because the table seems "cold." The next roll is going to do whatever the next roll is going to do, and your job as a player is to make smart bets with the right math, not to chase patterns that are not actually there. We talk more about this in our common craps mistakes article.

How probability translates to real sessions

Probability is a long-term concept. It tells you what will happen over many thousands of rolls. It does not tell you what will happen on the next roll, or in the next 20 minutes, or even in the next hour at a single table.

This is important because in any individual session, anything can happen. You can sit at a table where the 7 does not come up for 30 minutes. You can also sit at a table where the 7 comes up four times in a row right after a point gets set. The dice do not even out over short stretches. They even out over millions of rolls, which is why the casino, with its giant volume of action across all of its tables, gets reliable returns. You, playing one session, are subject to whatever the dice happen to do that night.

This is part of what makes craps fun. In any given session, you can win. You can win a lot. The math says the casino has the edge in the long run, but the long run is a lot longer than a single Friday night. A single session is short. Your bankroll is finite. The dice can be on your side for hours at a time. The casino's edge becomes visible over millions of rolls, not 200 rolls.

That is why bankroll management matters more than probability theory for an individual player. If you bet smart and quit while you are ahead, the math has not had time to catch up to you. If you keep betting forever, the math wins. Our article on bankroll management goes into this.

Things you do not need to memorize

Before I wrap up, let me tell you what you do not need to know. You do not need to memorize all 36 combinations. You do not need to know the exact percentage on every roll. You do not need to do mental math at the table.

What you do need to know is this. The 7 is the most common roll. The 6 and 8 are next. The 4 and 10 are the hardest point numbers. The 2 and 12 are the rarest rolls and any bet that depends on them is going to lose more often than it wins. The dice have no memory. That is the whole probability picture.

Everything else is detail. Once you understand those few facts, you understand enough to make good decisions at the table. The specific percentages matter to people who design bets and casinos. They do not matter to a player making basic strategic choices. Bet the pass line. Take odds. Avoid prop bets. Done.

What this all adds up to

Craps is a game of probability, and the probabilities are not even. The 7 is favored over every other number. That asymmetry is built into every bet, every payout, every house edge. Once you can see the chart in your head and understand why some numbers come up more than others, the rest of the game makes sense.

You do not need to be a math person to play smart craps. You just need to know that the 7 is special, the 6 and 8 are friendly, and the longshots are traps. With those three pieces of intuition, you can navigate the table without getting burned.

The next article gets into the pass line bet in detail. This is the foundation bet, the one almost everyone makes, and now that you understand the probability behind it, the math will make a lot more sense.

Read next: The Pass Line Bet