What is the probability of rolling a Yahtzee given that your first roll yielded 2 of a kind?

Question

Say you roll a 6-6 on your first roll. What is the probabilty that by the end of your turn (the next two rolls) you will have acheived a Yahtzee?

Answer 1

Assuming you rolled a 6-6 and the other three dice were all different, and different from 6, then you'll roll three dice next time. The probability of hitting 3 6s is 1/216. The probability of hitting exactly 2 6s is 3 x 1/36 - 1/216. The probability of hitting exactly 1 6 is 3 x 1/6 minus the probability of hitting 2 or 3 of them. The probability of hitting no 6s is what's left over.

The probability of making Yahtzee is the sum of

prob of being at N 6s after 2 turns x conditional prob of hitting Yahtzee on the third turn given that you were at N after two turns,

summed up as N goes from 2 to 5. That conditional probability is 1, 1/6, 1/36, or 1/216, depending on whether N was 5, 4, 3, or 2.

You can take it from there.

Answer 2

+ added:
I see from the other answers that the game is played with more than 2 dice.


Tell me what a Yahtzee is and I can answer your question.

P( 2 of a kind ) = sum up (2 ones, 2 twos ,...)

36 possible combinations with 2 dice. You can get two of a kind one way -> 1/36

So, add up for the 2 ones, 2 twos., ..., 2 sixes

= 6/36
So, P ( two on a kind ) = 6/36

Now, add detail of what a Yahtzee is....

Answer 3

the 1st roll there are 36 mixtures a million is double sixs and there are 10 others that conatin a six. So the spectacular of rolling a minimum of one 6 is 11/36 for the 1st roll. So it extremely is 25/36 against on the 1st roll. the 2nd roll is the comparable if no 6s are rolled the 1st time and a million/6 if a six is rolled. So finished odds are a million/36 for one roll +(10/36 of a million six)*(a million/6 for a six on the 2nd roll) a million/36+10/216 a million/36 + sixteen/216 22/216 11/108

Answer 4

The odds of you getting Yahtzee with the first throw is 1080-1

Answer 5

I think it's around 1 in 135 to 1 in 140. I made some strange assumptions and did some unorthidox math to come to that conclusion, but I'll bet it's pretty close to being accurate.