Odds Of Rolling A 7 In Craps

The Game

• Rolling A 7 In Craps
• Odds Of Rolling Craps
• Should I Fold Set Of Aces Because Of Possible Straight Here?

The odds are 5 to 1 against you rolling a 7. You will roll a 7 one in every six rolls. The odds of actually rolling a 7 are 6 in 36 or 5:1. The house pays out 4:1 on a winning bet, which brings up an outrageous house edge of 16.67%. This is the absolute worst bet you can make in craps. This is actually one of the worst bets a player can make in any casino game at the casino. The odds of rolling a 7 which you will remember is the most likely number, is 6 times more likely than rolling a 2. So think about the odds of rolling a Hard-way bet like hard 4, hard 10, etc. One chance in 36, just like a 2 or a 12! C-E or Craps-Eleven bets have true odds of 5 to 1. The payouts vary at 3 to 1 for craps (2, 3, 12) and 7 to 1 on eleven. This also carries an 11.11% house edge. Any 7 bets have true odds of 5 to 1 with payout odds at 4 to 1. Any 7 has the largest house edge on the table at 16.67%. Horn bets carry a higher house edge of 12.5%. Using Probability to Calculate the Odds in the Game of Craps. Natural: Rolling a total of 7 or 11 — automatically wins. Craps: Rolling a total of 2, 3, or 12 — automatically loses. Point: Rolling a 4, 5, 6, 8, 9, or 10 — establishes the point for the next round of rolling.

Craps is a dice game where two dice are rolled and the sum of the dice determines the outcome.

• If the sum is a 7 or 11, you win and the game is over.
• If the sum is a 2, 3, or 12, you lose and the game is over.
• If you roll a 4, 5, 6, 8, 9, or 10, that value becomes your 'point' and you continue to roll until you re-roll your point or a 7. If you roll your point, you win; if you roll a 7, you lose.

Video: Use Real Player to listen to the instructions and watch several games to make sure you understand the game. (56k - DSL/Cable)

Some of the probabilities are easy to find. The fundamental counting principle tells us there are 6*6=36 ways to roll two dice, all of them equally likely if the dice are fair. There is only one way to roll a sum of 2 (snake eyes or a 1 on both dice), so the probability of getting a sum of 2 is 1/36. There are 4 ways to get a five (1-4, 2-3, 3-2, 4-1) so the probability of getting a five is 4/36. The probabilities of obtaining any of the first roll sums can be found fairly easily and are shown in the table below.

We can find the probability of winning, losing, or obtaining a point on the first roll of the game by adding up the probabilities for the sums that go with winning, losing, or getting a point. For example, since a 7 or an 11 is a winner on the first roll and their probabilities are 6/36 and 2/36, the probability of winning on the first roll is 6/36+2/36=8/36.

Probabilities of Winning, Losing, or Getting a Point on First Roll

The Point

Rolling A 7 In Craps

The main problem with game of craps is that it can theoretically go on forever when a point is obtained on the first roll. Now, in actual practice, it doesn't. Eventually, you are going to either re-roll that point and win or roll a 7 and lose.

But, becasue you could theoretically go on forever, finding the probabilities involve an infinite geometric series. As an example, consider the case when the point is a 9 that is shown in the tree diagram to the right. Once you roll a 9, there is a 4/36=1/9 chance of rolling it again on any roll and a 6/36=1/6 chance of rolling a 7 and losing. However, there is a 13/18 chance that you will roll neither and the game will continue for another round.

There is a 1/9 chance of winning on the second roll (the first after the point), a 13/18*1/9=13/162 chance of winning on the third roll, a 13/18*13/18*1/9=169/2916 chance of winning on the fourth roll. But it doesn't stop there, it keeps going, and going, and going. Then you have to add all those probabilities up and that involves an infinite geometric series. That might not be difficult for you, but since the prerequisite for the applied statistics course is just intermediate algebra, most of the students have never seen an infinite geometric series.

So, there has to be another way.

The Simulation

This is a game that is most fun when it is simulated using actual dice. Sure, it would be possible and quicker to simulate it using a computer, but it wouldn't be nearly as fun.

Here's how the simulation works. Roll a pair of dice and record the sum in the table where it says 'Sum on first roll'. We are then going to record the result of the first roll as 'Win', 'Lose', or 'Point' in the table where it says 'Result of first roll'. If the sum is a 2, 3, 7, 11, or 12, go ahead and copy the first roll results into the overall results column and move on to the next game. If you have rolled a point, continue to roll the die until you roll either that point or a 7, but do not record the value of each of those rolls. Once you have rolled your point or a 7, then record either 'Win' or 'Lose' in the table for the overall results. You may wish to abbreviate the results as 'W', 'L', or 'P'.

The Analysis

The virtual casino bonus codes. After you have played several games (I recommend 36 since there are 36 different outcomes possible and it makes the probabilities nicer), it's time to sit back and look at what you have gathered.

First Roll Probabilities

Go through and count how many times each sum appeared as the first roll of the dice. Record it in the table below as a fraction over the total number of rolls and compare it to the theoretical probabilities we found earlier.

Are the observed probabilities close to the theoretical probabilities? They should get closer as you simulate more crap games (law of large numbers).

First Roll Outcomes

Empress of time. Now add the number of times you got a win, lose, or point on the first roll of the dice and write that as a fraction. If you played the game right, this can also be found by adding the probabilities of getting a win (7 or 11), lose (2, 3, or 12), or point (all else) together.

Record them in the table below and compare them with the theoretical probabilities found by adding the theoretical probabilities as mentioned in the last paragraph or that we found earlier in this document.

Final Results

You're probably thinking to yourself that this has been pointless. So far, we haven't found anything that we couldn't find through simple probabilities and it was much quicker and more accurate (exact instead of an approximation).

Odds Of Rolling Craps

What we're really interested in finding is the final outcomes of the game; that is, the probabilities of winning or losing the whole game. Count how many times you won and lost for the overall results and write that as a fraction over the total.

Did your results come out close to the theoretical results (found using infinite geometric series or absorbing markov chains)? You should have lost a few more games than you won. Well, after all, the casinos want to make money, don't they?

Type of Simulation

This is a simulation used to find probabilities. In this kind of simulation, you conduct an experiment and ultimately find the number of successes divided by the number of trials to find the relative frequency or the empirical probability. Success is defined as whatever you're trying to find the probability of. So, if you're looking for the probability of rolling a 6, then it is the number of 6's over the total number of rolls. If you're trying to find the probability of losing the game, then it is the number of losses divided by the total number of games.

Return to Simulation Page

Casino Craps Odds

Knowing the mathematical odds of the dice achieving a certain outcome is the essence of the game. If you are going to play for money, then try and remember these odds.

For a description of the kind of bets you can make playing Craps, see instructions from a real casino or dice-play's Craps guide. If you want to understand more about how odds work, see dice odds.

You will be at a slight disadvantage with the Pass Line bet since the odds of the dice winning are only 970 times out of 1980. The edge against the dice passing works out as 1.414%.

Palace of chance casino. The following table illustrates the bets found on Vegas/Nevada, Atlantic City, etc., Bank Craps tables. Bets in red can be made in other ways at better odds.

British casinosare tightly regulated and pay better odds on some bets. The following table illustrates the differing bets found in British casinos.

Should I Fold Set Of Aces Because Of Possible Straight Here?

Bar 1-2 Some greedy casinos (on cruise ships perhaps) bar 1-2 and not 1-1 or 6-6. This gives them a greater edge on Don't Pass/Don't Come bets.

There are 36 possible outcomes of two dice. The following tables show the true odds for the specified outcome of the dice.

(A) This column gives the number of possible ways of making the dice total.

(B) This column gives the odds against making the dice total in a single roll.

(C) This column gives the odds against rolling the dice total before a 7.

(D) These columns give the odds against making the higher dice total before the lower dice total. e.g. 12 before 6 = 5 - 1. For making the lower number before the higher, reverse the odds. e.g. 6 before 12 = 1 - 5.

Hardway Odds of making a number as a double, before a 7 or as another combination.

Odds against rolling a specified double are 35 - 1

Odds against rolling a specified combination of two differing numbers are 17 - 1

Odds against rolling craps are 8 - 1