(adsbygoogle = window.adsbygoogle || []).push({}); Yahtzee involving Mathematical Probabilities...

First off, has anyone played this game before?

I haven't, but it would be of great help if someone who knows the game, could answer some questions. (I don't need anyone to solve anything. I solved all the computations, I just want confirmation on the rules, or if my reasoning is flawed.)

If you don't know about the game, but would still like to help, read on.

It's not a requirement, but I guess it would help.

Why do I need to know about this game?

Well, it's about a question about Yachtzee that can be misinterpreted in many ways.

Let me state how you start off Yachtzee to those who do not have a clue what the game is about.

First, you just simultaneously roll 5 dice, and then a bunch of numbers appear in the face value of all 5 dice.

What I am asking is, is order of the dice numbers important?

Ie. If you rolled a 1,2,3,3,4,5, could it also be interpreted as, 1,3,3,2,4,5, or 5,4,3,3,2,1, or 4,3,3,2,1,5?

If the previous sets are all the same with one another, then order is of no importance, but if they are important, then each previous set mentioned in the example is not considered the same with the other aforementioned set.

I think you get the point now.

I'm supposed to calculate the permutations (the possible outcomes) of all the outcomes.

If order IS important, the total outcome, or sample space would be 6^5 = (6x6x6x6x6) = 7776 outcomes.

But if order IS NOT important, then the total outcome would be 10!/(5!)(5!) = 252 total outcomes. (Note: 5! = 5x4x3x2x1)

So is order important in this game, or not?

Also, I got one last thing to say,

The probability of getting two pairs (order important) is 25/108 = 0.23148 = 23.15%.

Yet, the probability of getting two pairs (order not important) is 15/63 = 0.23809 = 23.81%.

The percentage of both probabilities is very close. Why is this? Wouldn't something as making the dice results order important or unimportant causes the two values to be different?

So which result is correct, and why? Also, why are the percentage of both probabilities of getting two pairs of order important and order unimportant so close?

What's your opinion on this matter?

PS: If the answers for the sample space, or probabilities mentioned in this post were wrong, I apologize, and I will try to remedy the problem immediately.

Thank you, Everyone.

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# Yachtzee involving Mathematical Probabilities

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