Yahtzee - Odds On A Throw

[Ivan Toono]

Not sure if this the right section, but I'm sure that it will contain people who know a lot more about maths than I do.
Last night, I threw a Yahtzee (all five dice with the same number) in one throw. What are the odds of this happening, please?

[factor-fiction]

1 in 7776

[factor-fiction]

Sorry, i thought it said 6 dice.
For 5 dice the answer is 1 in 2604

[factor-fiction]

Make that 1 in 1296

[factor-fiction]

Chance of 5 consecutive 1s is 1 in (6x6x6x6x6)= 1 in 7776
Ditto for five twos,
Ditto for five 3s
Ditto for five 4s
Ditto for five 5s
ditto for five 6s

Add all these probabilities together and you get 6 in 7776, or 1 in 1296

Anyone agree?

[gen2]

Sorry factor30, I beg to differ.

The possible outcomes from throwing 5 dice is
6 x 6 x 6 x 6 x 6 = 7776
(that was factor30's first figure

of those, six outcomes will be all the same.
6 ones, 6 twos, 6 threes etc.

That makes the odds 6 in 7776
= 1 in 1296
or odds of 1295 to 1 against throwing a Yahtzee

[factor-fiction]

So we agree.

[gen2]

Sorry factor30, I took too long formulating and checking that answer - so "Yes, I now agree"

[factor-fiction]

That's okay ,Gen2. Yes, my initial mistakes were made because I was rushing to submit an answer. I should have taken my time to get it right first time, just as you did.

[Ivan Toono]

Thank you both very much. I'd love to say that I fully understand this but I'd be a liar if I did. :-)
I'm glad to know that there are people around who are able and willing to help others.
Thanks once again.

[beso]

A simpler way is to understand that the first die does not matter so long as the other four are the same as it.

Hence 6 x 6 x 6 x 6 = 1296

[Ivan Toono]

Ok, beso. That is a simpler way to understand it.

Thank you for your time and trouble.