Craps Conditional Probability

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• Conditional Probability Formula
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According to the computation, the probability of winning at craps is almost—but not quite!—50%. This exercise shows that having a matrix and vector language is useful for computing with probabilities. More importantly, however, this post sets the foundations for looking at the interesting case where the two dice are not fair.

Hey Wizard,
I'm a CJ/CIS major working in a Math department, and I've been asked to convert an open ended question test to multiple choice test. I found your site 'The Wizard of Odds', and was directed here to ask my question. What is the probability of rolling a 2 given your roll only being even, when rolling a 20 sided die? Thank you for your help.
-R

Craps Conditional Probability Calculator

• Topics include elementary set theory, techniques for systematic counting, axioms for probability, conditional probability, discrete random variables, infinite geometric series, and random walks. Applications to card games like bridge and poker, to gambling, to sports, to election results, and to inference in fields like history and genealogy.
• You can use probability to figure out the odds of winning and losing in the popular casino dice game of craps. In the game of craps, on your first roll (called the come out roll), three outcomes are possible: Natural: Rolling a total of 7 or 11 — automatically wins. Craps: Rolling a total of 2, 3, or 12 — automatically loses.
• Probability in Craps Game Date: 6/27/96 at 22:44:45 From: Anonymous Subject: Probability in Craps Game Dr. Math, In the game of craps, the shooter rolls two dice and wins if the sum of the dice is 7 or 11 ('natural'); he loses if the sum is 2,3, or 12 (craps). If the sum is 4,5,6,8,9, or 10, then the result is not yet decided.

I know what you probably meant, but you actually need to specify what's on the 20-sided die. If it's 10 through 200 in increments of 10, the probability is zero.
Under the assumption that the d20 contains integers 1..20, here are the answers I'd list on a four-choice pick:
a) 1/2
b) 1/5
c) 1/10
d) 1/20
Edit: What's a 'CJ' major?

I know what you probably meant, but you actually need to specify what's on the 20-sided die. If it's 10 through 200 in increments of 10, the probability is zero.
Under the assumption that the d20 contains integers 1..20, here are the answers I'd list on a four-choice pick:
a) 1/2
b) 1/5
c) 1/10
d) 1/20
Edit: What's a 'CJ' major?

Funny, I read it differently for the same reason. I 'decided' the question stipulated the 20 sides were numbered 2 thru 20, evens only, with 2 identical sides per number, before I read ME's answer. Be interested to see the clarification.
I'm guessing 'Criminal Justice/Crime Scene Investigation' for the major.

If you're saying 'I've got a d20. The next roll will be an even number. What are the odds of that number being a 2?' Then I'd have to say the odds are 1 in 10. But how does one guarantee that no odd number will be rolled?

It's a conditional probability problem. It's guaranteed because the question says it's guaranteed. It's a math question, not a physics question.Designing multiple-choice tests is one of my favorite things to do. I see this question, and all I think is 'gosh, i wonder how they're doing answer placement. Is it randomized? Rotated? both?'

Conditional Probability Formula

My HS world geography teacher was a sadistic guy. He put patterns into all his tests, but he also rotated the correct answers. So my 100% score could go a,b,c,d,a,b,c,d... while my friend could have the same answers but need to respond d,c,b,a,d,c,b,a... Made colluding and/or selling answers a real pain.

Craps Conditional Probability Rules

CJ - Criminal Justice
The numbers on the 20 sided dice are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. If this reply sounds smartalically, I appologize. I don't really understand what you mean needing to 'specify what's on the 20-sided die.' Anyhow, which is the answer; a, b, c, or d?

There are 10 even numbers. If you know for sure that it is even, then the answer is 1/10.
You can also solve this by going through the formula for conditional probability. To be honest I always have to look it up (check wikipedia for conditional probability), but you will end up dividing 1/20 by 10/20 and get 1/10.

Naaah. Just keep rolling 7s and 11s until the casino runs out of chips...

yea but whats the fun in that.. the thrill for me is establishing points taking max odds and making the point... does anyone know what the odds are of actually hitting a fire bet, whether it be for 4,5, or the whole 6 points? I just started playing recently and have made three different points on a roll 3 times so far... just curious.

Check the Wizard of Odds site: here

You list the odds of making the fire bet, which is not the odds of making a point; it is the odds of making multiple points.
This is listed at Fivecardcharlie.net/learning craps.
Assuming there is a point: If the point were 5 or 9, you would be a 3:2 underdog (6 combinations against : 4 combinations each), and your odds would pay 3:2. If the point were 6 or 8, you would be a 6:5 underdog and your odds would pay 6:5. For the four and ten, it is 6 cominations of making a seven out, and 3 combinations each of making the point.
Since the odds bet are at true odds, they also reveal the probability of making the point; it is the odds of making multiple points.

You list the odds of making the fire bet, which is not the odds of making a point; it is the odds of making multiple points.

Craps Conditional Probability Test

Of course. I was specifically replying to the question in the post right above mine.