Leibniz Wrong About Dice!

I was reading a book about Leibniz called “Selections” and then “I, Claudius” by Robert Graves. Emperor Claudius wrote a small pamphlet about throwing dice. Leibniz had a small section about dice odds—that he was using to illustrate some other matter.

 

Two dice references in two different books got me thinking.

 

Leibniz got something wrong! He wrote about someone throwing two six-sided dice and rolling an “11”, and he wrote that there was only one way to roll an “11”.

 

Technically, there are two ways to roll and “11”: you can either roll 5 & 6…but you can also roll 6 & 5. Each die has a different outcome.

 

TWO SIX-SIDED DICE WAYS TO THROW EACH NUMBER

2 = 1+1

3 = 1+2 or 2+1

4 = 1 +3 or 3+1 or 2+2

5 = 1+4 or 4+1 or 2+3 or 3+2

6 = 1+5 or 5+1 or 2+4 or 4+2 or 3+3

7 = 1+6 or 6+1 or 2+5 or 5+2 or 3+4 or 4+3

8 = 2+6 or 6+2 or 3+5 or 5+3 or 4+4

9 = 3+6 or 6+3 or 4+5 or 5+4

10 = 4+6 or 6+4 or 5+5

11 = 5+6 or 6+5

12 = 6+6

 

As you can see, there are more ways (easier) to roll a “7” than any other number. Lucky Seven! 

When Leibniz made his error, he stated there was only one way to roll an “11”. But as you see, there are two ways, which makes “11” easier to roll and “2” or “12”—and the same odds as rolling a “3”. That’s a pretty significant difference-that makes the chances or rolling an “11” 5.56% instead of only 2.78% which is double the odds.

Scribbled notes on an old library catalog card I was using as a bookmark:

Claudius was never as dumb as he pretended to be.