Dice Odds

[nailit]

can anyone tell me what the odds are of throwing 5 dice and getting them all to have the same number face up? (and how would you work this out?)

Just been playing yahtzee (a dice game) with friends and wondered what the odds would be.
Thanks.

[Quizmonster]

No idea where the word, 'quote', came from. I suppose I messed up my attempt to make the 5 italic! Let's try again: 5.

[Old_Geezer]

Yes you are right Quizmonster, but at those odds prefect accuracy may be overlooked :-)

Perhaps more to the point, it is stated as 1 in whatever, rather than 1 to whatever.

[mibn2cweus]

Approximately 1/22 for a 'three roll turn' - http://en.wikipedia.org/wiki/Yahtzee#Probabilities

[nailit]

Can *anyone* please give me a definitive answer?
Didnt think it was THAT a difficult question.
5 dice. (any number) same side up.
Odds?
I'm running out of parecetomol.

[Prudie]

I agree with calibax, 1 in 6^4 which is 1296.
it is easier to see with just 2 dice, the probability of throwing a double is 1 in 6 which is 1 in 6^1
With n dice it's 1 in 6^(n-1)
so with 5 dice it's 1 in 6^4

[New Judge]

To be pedantic (I have been known for it) and to agree with QM, there is one chance in 1,296 of five dice all showing the same non-specific number so the odds against it happening are 1,295 to 1.

[BlackadderV]

NJ is correct. The probability is 1/1296 which, translated to bookies' odds, is 1295 /1

[nailit]

ok thanks guys. Just waiting now for someone to throw a spanner in there. (again)

[BlackadderV]

Odds and probability are two different things. If you have three different balls, red blue and green, then the probability of picking a red one is 1/3 giving odds of 2 to one against.

[Old_Geezer]

Just so.

[BlackadderV]

Similarly, the chance of NOT picking a red ball is 2/3 or 2 to 1 one on (1/2)