Welcome back to our
Craps Learning Series! So far, we’ve covered how to play craps and all the bets you can make. Now, let’s break out the calculators! In this post, we’ll dive deep into the
odds behind Pass and Come bets. We’ll examine what these bets pay versus their odds, and which ones give you the best chance of winning. By the end, you’ll know which bets carry more risk and which ones you should avoid if you want to maximize your chances at the craps table!
🔍 What We’ll Cover:
- Odds of Rolling Each Value
- Pass & Come Line Odds & Math – The Details
- Summary of Pass and Come Bets
💥 Odds of Rolling Each Value
To understand craps odds, we need to first know the probability of rolling each possible outcome with two dice. With 36 possible combinations (6 faces on each die), here’s the breakdown:
| Value | # Ways to Roll | Odds to Roll |
|---|
| 2 | 1 | 2.78% |
| 3 | 2 | 5.56% |
| 4 | 3 | 8.33% |
| 5 | 4 | 11.11% |
| 6 | 5 | 13.89% |
| 7 | 6 | 16.67% |
| 8 | 5 | 13.89% |
| 9 | 4 | 11.11% |
| 10 | 3 | 8.33% |
| 11 | 2 | 5.56% |
| 12 | 1 | 2.78% |
- Note: 7 is the most likely roll, with 6 possible combinations and a 16.67% chance.
- The 7 is the only value that doesn’t depend on the first die rolled. A seven can be made with any combination of the dice.
For each bet, we’ll walk through the odds of winning and the expected profit/loss over 36 rolls, assuming a $10 bet each time. We’ll also assume that each combination gets rolled once.
💥 Pass and Come Line Odds and Math – The Details
Now, let's get into the nitty-gritty of Pass and Come bets. These are some of the most popular bets in craps, but the math behind them can be tricky because they involve multiple rolls.
Initial Roll
On the initial roll, here’s how things break down:
- Pass & Come Bets: You win if a 7 or 11 is rolled, lose if a 2, 3, or 12 is rolled.
- Don’t Pass & Don’t Come Bets: You win if a 2 or 3 is rolled, lose if a 7 or 11 is rolled. A roll of 12 is a push (no win or loss) in most casinos, though some treat it as a loss.
Here are the odds:
| Bet | Odds to Win | Odds to Lose | Odds to Push | Point Established |
|---|
| Pass / Come Bet | 8/36 (22.22%) | 4/36 (11.11%) | 0/36 (0%) | 24/36 (66.67%) |
| Don’t Pass / Don’t Come Bet | 3/36 (8.33%) | 8/36 (22.22%) | 1/36 (2.78%) | 24/36 (66.67%) |
Note: The odds of winning after the initial roll are tied to the establishment of a “point.” The odds of this happening are the same for both Pass and Come bets.
Subsequent Rolls
Once a point is established, we move to the subsequent rolls. Here’s a breakdown of the odds for each possible point (the numbers 4, 5, 6, 8, 9, and 10):
| Point | Odds to Roll Point | Odds to Roll 7 | Pass / Come Win | Don’t Pass / Don’t Come Win |
|---|
| 4 | 3/36 (8.33%) | 6/36 (16.67%) | 1/3 (33.33%) | 2/3 (66.67%) |
| 5 | 4/36 (11.11%) | 6/36 (16.67%) | 2/5 (40%) | 3/5 (60%) |
| 6 | 5/36 (13.89%) | 6/36 (16.67%) | 5/11 (45.45%) | 6/11 (54.55%) |
| 8 | 5/36 (13.89%) | 6/36 (16.67%) | 5/11 (45.45%) | 6/11 (54.55%) |
| 9 | 4/36 (11.11%) | 6/36 (16.67%) | 2/5 (40%) | 3/5 (60%) |
| 10 | 3/36 (8.33%) | 6/36 (16.67%) | 1/3 (33.33%) | 2/3 (66.67%) |
Calculating the Odds of Winning the Bet
To find the total odds of winning a Pass or Come bet, we multiply the probability of establishing the point by the probability of winning once the point is set. Here's how it works for each point:
| Point | Probability of Establishing Point | Probability of Winning After Point is Established | Total Probability (Pass/Come) |
|---|
| 4 | 3/36 = 1/12 | 1/3 | 0.0278 |
| 5 | 4/36 = 1/9 | 2/5 | 0.0444 |
| 6 | 5/36 | 5/11 | 0.0631 |
| 8 | 5/36 | 5/11 | 0.0631 |
| 9 | 4/36 = 1/9 | 2/5 | 0.0444 |
| 10 | 3/36 = 1/12 | 1/3 | 0.0278 |
Total Probability (Pass / Come):
0.2706 or 27.06%
For
Don’t Pass / Don’t Come Bets, we reverse the probabilities and perform the same calculations. The results look like this:
| Point | Probability of Establishing Point | Probability of Winning After Point is Established | Total Probability (Don’t Pass/Don’t Come) |
|---|
| 4 | 3/36 = 1/12 | 2/3 | 0.0556 |
| 5 | 4/36 = 1/9 | 3/5 | 0.0667 |
| 6 | 5/36 | 6/11 | 0.0758 |
| 8 | 5/36 | 6/11 | 0.0758 |
| 9 | 4/36 = 1/9 | 3/5 | 0.0667 |
| 10 | 3/36 = 1/12 | 2/3 | 0.0556 |
Total Probability (Don’t Pass / Don’t Come):
0.3962 or 39.62%
🎯 Summary
- Pass / Come Bets: 49.28% chance of winning
- Don’t Pass / Don’t Come Bets: 47.95% chance of winning
Over the long term, Pass / Come bets are slightly advantageous for players. However, if a 7 or 11 doesn’t come up on the Come Out Roll, these bets can become much harder to win as the point is established. Keep in mind that the Don't Pass / Don't Come Bets will push 2.78% of the time as well if a 12 is hit on the Come Out Roll.
While the math behind craps is complex, it’s designed to maintain a house edge while keeping the game exciting. Next time, we’ll explore the rest of the bets, which are much easier to calculate!
💬 How Do You Play Craps?
Got questions about the math behind Pass, Come, Don’t Pass, and Don’t Come bets? Join the conversation and let's all work to learning the funnest game at the casino together!!
