- Probability Of Winning Craps
- Craps Numbers Probability Games
- Craps Dice Roll Probability
- Probability Number Line
- Craps Numbers Probability Calculator
- Calculating Probability Of Winning Craps
N - the number of dice, s - the number of a individual die faces, p - the probability of rolling any value from a die, and P - the overall probability for the problem. There is a simple relationship - p = 1/s, so the probability of getting 7 on a 10 sided die is twice that of on a 20 sided die. If you want to know the probability of rolling a 7, you just divide the number of ways you can get a 7 (there are six ways) by the total number of possibilities (36). Six divided by 36 is the same as 1/6, which is also the same at 16.67%. When it comes to craps, it’s often useful to use odds as your preferred format for expressing probability. To calculate the payout in craps for any bet, convert the payout odds from a fraction to a decimal. Players should then multiply this decimal by the amount they want to wager to determine their potential payout. For instance, a bet on point 4 in craps has payout odds of 9:5. Converted to decimal form, this is 1.8.
If I make 6 consecutive dont' pass/don't come bets, what is the probability that there will be a repeat number (4,5,6,8,9,10) without a seven-out? Two repeats? Show your work! And if you can calculate this, can you recommend a basic book on this type of probability problem? I will study your answer until I sort-of understand it. Thank you.
Wow!You are talking about a lot of states in a Markov Chain.
I am sure someone could do the math, but why?
I would sim this. Would be very easy to do.
Plus, we could get lots of info from it.
Maybe tomorrow if I'm slow at work. Lots of Grad parties this week!
For the 'one-repeat' problem, determine each possible set of six point numbers with one repeat (e.g. {4,8,10,5,8,6}), then calculate each number's probability of both being a point number and not sevening out (for 4, it would be 1/12 (chance of rolling 4 as the point) x 1/3 (chance of rolling another 4 before a 7) = 1/36).
There are 6 possible numbers to be the duplicate; for each one, there are 5 numbers that would now not appear at all; for each of these 30 groups of numbers, there are 360 permutations, although each permutation within a group has the same probability. Figure them out, and then add them up.
This assumes that, by 'a repeat number,' no point appears more than twice. If a point can appear more than twice, you need to check the groups of 3-1-1-1, 4-1-1, 5-1, and 6 as well; it sounds like it's easier to check all 46,656 permutations of six point numbers (which would solve the 'two repeat numbers' problem - and, for that matter, the 'three repeat numbers' problem - at the same time.)
To help you out:
The probability of rolling, and then making, a point of 4 is 1/36, as shown earlier.
For a 10, it is also 1/36.
For a 5 (or a 9), it is 1/9 x 2/5 = 2/45.
For a 6 (or an 8), it is 5/36 x 5/11 = 25/396.
If, in your six rolls, you include the possibility of rolling a 2, 3, 7, 11, 12 as your first number, I get this:
1 duplicate point happens 1 time in 16.3
2 duplicate points happens 1 time in 27.55
3 duplicate points happens 1 time in 583.2
silly
Sally
Do 'repeat numbers' need to be consecutive? That is, if, for example, the six come-out rolls are 6, 4, 7, 6, 10, 11, are the two 6s considered 'one repeat'?
What if the same number is rolled three times - is that considered one repeat or two?
My calculations were based on the answers being (a) no and (b) one repeat. For example, 6, 4, 7, 6, 10, 6 would be 'one repeated number,' as would 8, 8, 8, 8, 10, 4.
This can be solved exactly by a very large Markov Chain. Too much work for me.
By a simulation is faster and easier IMO.
For example, 6, 4, 7, 6, 10, 6.
$5 don't pass bet: roll 6 = point established
$5 don't come bet: roll 4 = bet moves to don't come 4
$5 don't come bet: roll 7 = 7out.
don't come bet loses
wins both don't pass and don't come 4.
The 7 is a 7out. So, no more rolls after the 7 for that shooter.
No repeating numbers to cause a dont pass or a dont come point number to lose
That is how I see the OP question
Sally
Probability Of Winning Craps
silly
Sally
Good idea!
No you are understanding wrong.
The 61% is for all shooters.
That is what the first data table is for.
All shooters with a hand length of 2,3,4,5 and 6.
The second table is just for the shooters (57.7%) that did make it to the 6th roll.
I did not let them roll any further.
So about 62% of the shooters that did roll that 6th roll had at least 1 repeat.
Now I also did not include the natural losers for the dont's.
You only asked about repeats.
Here is a link to my text file and Excel 2007 file if you have Excel for my second simulation. It is 100k shooters in size. I deleated the first one on accident.
text file 4MB right-click to save or click to view in your browser window
Excel file 2.2MB
You can play with the data.
Column Headers
#: shooter number
rolls:
DPLoss: Natural loss (7,11) for DPass
DP12: Push
DPPtL: Point loss for DPass
DCL: DCome natural loss (7,11)
DC4L:
DC5L:
DC6L:
DC8L:
DC9L:
DC10L:
DC12: DCome 12 push
TLoss: total unit loss
TWins: total unit win
DPN: wins DPass 2 and 3
DCN: wins DCome 2 and 3
Sally
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Craps is some of the most fun you’ll have in the casino. However, if you want to be an educated craps player, you’ll need to understand some of the probability and odds involved with rolling a pair of dice.
Craps is always played with two dice, each of which is shaped like a cube less than an inch wide. Unlike the dice you’ll buy at your local game store for board games or RPGs, the dice used in craps have sharp edges and pointed corners.
Craps dice are also bigger than the dice you’ll find in a game like Yahtzee or Monopoly. Most of the time, a casino will imprint their logo on the dice they’re using, too. The dice are red, but they’re also translucent, so you can see that there are no weights attached.
Craps shooters often get on hot streaks. If a shooter gets on too hot a streak, the boxman will pause the game to examine the dice to make sure there’s no funny business going on.
The number of possible combinations on a pair of dice is what the game is built around. That’s also the subject of this post: how the dice combinations work in a game of craps.
What Combinations Are There?
Each die has six sides, and they’re numbered from 1 through 6, using dots. If you add the numbers on opposite sides of the dice together, you always get seven. So the 1 and the 6 are opposite each other, the 2 and the 5 are opposite each other, and the 3 and the 4 are opposite each other.
You have a total of 36 possible combinations – you have six possible combinations on one die and six possible combinations on the other die. Out of these 36 possible combinations, you have 11 possible totals.
Here are the possibilities:
- A total of 2, which can be made up of only one combination: a 1 on each die
- A total of 3, which can be made up of two different combinations: a 1 on the first die and a 2 on the second die; or a 2 on the first die and a 1 on the second die
- A total of 4, which can be made up of three different combinations: 1 – 3, 2 – 2, 3 – 1
- A total of 5, which can be made up of four different combinations: 1 – 4, 2 – 3, 3 – 2, 4 – 1
- A total of 6, which can be made up of five different combinations: 1 – 5, 2 – 4, 3 – 3, 4 – 2, 5 – 1
- A total of 7, which can be made up of six different combinations: 1 – 6, 2 – 5, 3 – 4, 4 – 3, 5 – 2, 1 – 6
- A total of 8, which can be made up of five different combinations: 2 – 6, 3 – 5, 4 – 4, 5 – 3, 6 – 2
- A total of 9, which can be made up of four different combinations: 3 – 6, 4 – 5, 5 – 4, 6 – 3
- A total of 10, which can be made up of three different combinations: 4 – 6, 5 – 5, 6 – 4
- A total of 11, which can be made up of two different combinations: 5 – 6, 6 – 5
- A total of 12, which be made up of only one combination: a 6 on each die
If you look at this closely, you’ll notice that it makes a symmetrical bell curve. Also, the number of combinations that create a specific total can be divided by 36 to get the probability of getting that total.
A Note on Probability
Craps Numbers Probability Games
Probability is a way to measure how likely it is that an event will occur. For our purposes, an event is a total on two dice.
Probability is just a ratio comparing the number of ways something can happen with the total number of possible events.
If you want to know the probability of rolling a 7, you just divide the number of ways you can get a 7 (there are six ways) by the total number of possibilities (36).
Six divided by 36 is the same as 1/6, which is also the same at 16.67%.
When it comes to craps, it’s often useful to use odds as your preferred format for expressing probability. To do that, you just compare the number of ways something can’t happen with the number of ways it can. For example, the odds of rolling a 7 are 5 to 1. They’re actually 30 to six, but you reduce, just like you would a fraction.
You can compare the probability of winning a bet with the payout odds to see what kind of mathematical edge your land-based casino has on a specific bet.
This is the beginning of craps wisdom.
The Point Numbers
The point numbers are 4, 5, 6, 8, 9, and 10.
The 5 and the 9 have four possible combinations, and the 6 and the 8 have five possible combinations.
The odds of a 7 coming up before a 4 is easy to calculate. You have six possible combinations totaling 7 versus three possible combinations totaling 4.
That’s 2 to 1 odds.
The odds are the same for rolling a 10.
The odds of a 7 coming up before a 5 (or a 9) are six versus four, or 3 to 2 odds.
The odds of a 7 coming up before a 6 (or an 8) are six versus five, or 6 to 5 odds.
When the shooter makes a point, it’s his job to roll that point total again before rolling a 7.
Now, you know the odds that he’ll succeed.
Proposition Bets
One of the worst bets you can make at a craps table is a proposition bet. This is usually a bet on a specific total on the next roll. Depending on the number, the odds might look like the following examples.
If you’re looking at a 2 (snake eyes), the odds of winning are 35 to 1.
Craps Dice Roll Probability
If you’re looking at a 12, you face the same odds.
If you’re looking at a 3, the odds of winning are 17 to 1. The same holds true for a total of 11.
If you’re betting on “any 7,” the odds of winning are 5 to 1.
If these bets paid off at those odds, you’d be facing a house edge of zero. If you played long enough, you’d break even or come close to tie.
But the casino isn’t in the business of breaking even. It’s in the money of making a profit.
That’s why they set the payouts for these proposition bets much lower than the odds of winning them.
If you bet on the shooter rolling a 2, you face 35 to 1 odds. If you win, though, you only get a 30 to 1 payout.
Probability Number Line
Statistically, 36 bets of $100 each would mean losing $3500 on your 35 losing rolls and winning $3000 on your one winning roll.
Craps Numbers Probability Calculator
Your net loss is $500.
Average that out by 36 rolls of the dice, and you’ve lost an average of $13.89 per bet or 13.89% of your action.
That’s the house edge, and it’s a huge number.
The “any 7” bet is another proposition bet which is always a one-roll bet, by the way. It’s a bet that the total will be 7 on the next roll.
The odds of winning this one are 5 to 1, but the payout is only 4 to 1.
You can calculate the house edge on this bet easily, too.
Assume six perfect rolls betting $100 each.
You’ll lose five of those bets for a total of $500 lost.
On the one bet you win, you’ll get a $400 payout.
Your net loss over six rolls of the dice is $100.
Divide that by six, and you can see that the house edge on the any 7 bet is 16.67%.
The pass line bet has a house edge of 1.41%.
On average, over enough rolls of the dice, you should lose $1.41 every time you place a $100 bet on the pass line.
But if you bet that same $100 on any 7, you’d lose $16.67.
Which one of those sounds like the better bet to you?
Calculating Probability Of Winning Craps
Conclusion
That’s as good an introduction to the dice combinations in craps as you’ll find. Once you understand the math in this blog post, you can figure out everything you need to know about every bet at the table.