Do you remember the first time you played craps? I remember mine. I had no idea what I was doing and didn’t have a clue about what the best bet options were. I did some homework and used math before I played again, and now, I always know exactly what to do when I play craps.
In this article, I’m going to share the mathematical facts that I learned about shortly after my first craps experience. Using the same principles that I used, you can play craps in the most mathematically sound way every time you play.
1 – The Odds of Rolling Any Number in Craps
You can only roll 11 numbers when you play craps. But the 11 possible numbers don’t have an equal chance of being rolled. This is important because it directly influences each of the available bets.
To understand why each possible number has a unique chance of being rolled, you need to understand how the dice combinations create each total. This is simple once you know how dice work.
How many combinations result in a total of 7? The answer is six combinations, and here’s how it works. If the first die is a 1, the second has to be a 6. If the first die is a 2, the second has to be a 5. If the first die is a 3, the second has to be a 4.
This is only three combinations, but you have to also include the combinations for when the first die is a 4, 5, or 6. This is why there are six combinations that produce a total of 7.
Five combinations produce a total of 6 and 5 more produce a total of 8. Four combinations produce a total of 5 and a total of 9. Three combinations are possible for 4 or 10, and two combinations produce 3 or 11.
This creates a total of 36 combinations when you play craps. You can determine the percentage odds of rolling any number by dividing the number of combinations by 36.
2 – Come Out Roll Math
If you’re a craps beginner, you have to must learn that every craps game starts with something called a come out roll.
You have two options when you make a come out roll wager—the pass and don’t pass. Come out rolls start every series of rolls at the craps table, and one of three things happen on a come out roll. You can win your bet, lose your bet, or a point can be set.
After a point is set the series continues until the point is rolled again or a 7 is rolled.
None of this is especially important from a mathematical point of view when you’re trying to determine what the best wager is to make. The only thing that’s important is which of the two bet options offers the lowest house edge. The bet with the lowest house edge also provides the highest return.
The pass wager has an edge of 1.41%, which means it has a return of 98.59%. Don’t pass has an edge of 1.36%, which means it has a return of 98.64%.
What this means is the best come out wager mathematically is don’t pass. Don’t pass is always the best wager according to craps math.
3 – Odds Bet Math
When a point is set, which happens any time a come out roll results in a total of 4, 5, 6, 8, 9, or 10, you have other bet options. You’re going to learn about most of these options in the next section. But if you use math to determine the best wager option, there’s only one option. This option is called the odds.
You need to know about a rule that every craps table has regarding odds wagers. You aren’t allowed to place an odds wager until after you place a come out roll wager and a point gets set. In other words, they don’t let you just make odds wagers.
This means that there are exactly two bets that you should make playing craps based on the math. The first wager is don’t pass and the second wager is on the odds.
4 – Other Craps Bets Math
All of the other bets available when you play craps offer worse odds and a higher house edge than the three bets you’ve learned about so far. This means that when you use math, you should ignore all of the other craps wager options.
Some of the other options are better than others, but they’re all worse than the two wagers I already covered that you should make. The places 6 and 8 have a house edge of 1.52%, which is a return of 98.48%. This is the next best option, but you never have to make this wager, so you shouldn’t.
Many of the other craps wagers have a house edge of over 9%. This is worse than many slot machines, which means that it’s terrible. These wagers include any 7, all the hop wagers, all the hard wagers, the big 6 and 8, and any craps.
All of the other craps wagers have a house edge that falls between 2.78% and 6.67%. In other words, these wagers are all bad.
5 – Math Shows You How Much to Bet
You can also use math to determine the optimum bet size for every craps bet that you make. This is simple to do now that you know what the house edge is for each wager.
When you know what the house edge is, you can multiply it by the size of your bet to figure out your average loss. This tells you that the bigger your wager size, the more you’re going to lose on average on any wager that has a house edge.
When it comes to betting on the odds, the correct bet size is the largest possible. This makes a dangerous assumption that you can afford to make the largest odds bet without the risk of losing all of your money. You need to have enough money so if you lose several odds wagers in a row that you don’t go bankrupt before the long term odds even out.
The reason why the maximum odds wager is correct even though it pays out 100% over time is because it reduces the average amount you lose on don’t pass compared to the total amount you bet overall.
6 – Live Craps Rolls and Digital Craps Roll Math
When you play digital craps, like on mobile casinos online, the results of the dice rolls are always random. The rolls are as close to truly random as you can get. But is the same thing true when you play craps in a land-based casino?
The truth is that the dice used in the casino aren’t perfect. The dice are close to perfect, but they’re not 100% perfect. This means that there’s a small chance the dice aren’t completely random.
But this doesn’t mean that you can use this information mathematically to make a profit. You’re not going to be able to get enough data to make a mathematically accurate prediction based on imperfect dice because the casinos replace the dice too often.
What all of this means is that the dice used in land-based craps are so close to random that it’s a waste of time to try to use math to predict the future results.
Our Thoughts on Using Math in Craps
The best way to play craps can be determined by using math. It turns out that most of the available wager options are terrible, and that you can make exactly two bets every time you play that give you the best return.
You can also use math to figure out exactly how much you should risk on each of these wagers.
No other bet amount gives you the same return.
While there might be a small statistical difference between live rolls and digital rolls, the truth is that in the long run, it’s not enough to make a difference.