Can you help me with a dice probability problem?
If there are 3 standard die which are numbered as follows:

die A - 1,2,3,4,5, and one blank face
die B - 5,6,7, and 3 blank faces
die C - 7,8 and four blank faces

If the highest number was the winning throw which die is the most likely winner?
If A,B and C were all thrown? or If A and B only were thrown, A and C or if B and C only were thrown?

The way you have phrased this makes it hard to understand. This is my guess at what you were trying to ask.

If A, B, and C were all thrown, obviously C is more likely to have the highest number- A can be no higher than 6, B no higher than 7 while C is no lower than 7.

If "A and C" or "B and C" are thrown, the answer is still obviously C.

If "A and B" are thrown, the expected value for A is (1+ 2+ 3+ 4+ 5)/6= 2.5 while the expected value for B is (5+ 6+ 7)/6= 3. B is more likely to have the higher number.

There are indeed several problems with that wording.
What happens in the case of the dice showing the same outcome?
B & C could both be 7, in that case is there a winner?
All three could be blank. Then what?

Sorry that my wording is a bit wooly and confusing.
I will try to simplify the question .
The dice are numbered:

Die A - 1, 2, 3, 4, 5 and one blank face
Die B - 5, 6, 7 and three blank faces
Die C - 7, 8 and four blank faces

Give there are three people and three dice -
Which die would you choose to give the greatest chance of rolling a winning number ( highest number wins, in the event of a tie die are rolled again until there is a winner )

If A is against B: B wins and A wins .

If A is against C: A wins and C wins .

If C is against B: B wins and C wins .

I don't know if that is what you mean.

Hi Snowman,

I'm assuming a blank face effectively counts as a zero.

I'll take the first case, where all three players throw.

A wins only if B and C both roll blanks and A rolls a non-blank. So P(A wins) = (3/6) * (4/6) * (5/6) = 0.09259.

B wins if C rolls a blank and B rolls a non-blank, except for the case where A and B both roll 5s. So P(B wins) = (4/6) * [(3/6) - (1/6) * (1/6)] = 0.3148.

C wins if C rolls an 8, or if C rolls a 7 and B rolls a non-7. So P(C wins) = 1/6 + (1/6) * (5/6) = 0.3056.

So B has the greatest probability of winning.