Jonathan Lange wrote:
Of course, the more interesting question is WHY!?!?!

Apologies, I had thought it was obvious.

Keys are often given in a hexadecimal representation.
Each 4 bits is a hex digit, written using 0...9A...F.

So a d16 will generate a hex digit of randomness. Two
d16s will generate two hex digits, which is 2*4=8 bits,
which is commonly called a "byte".

With a pair of d16s a 63-byte key can be generated
in 63 throws, five minutes or so.

The other side of this is (1) it's very hard for
computers to generate random numbers, and using a
computer to generate a "random" key you then use on
the same computer is full of security issues.
(2) it's very hard for humans to generate strings
of random numbers. They avoid number at the extremes
and avoid repeated digits (a 60 byte string would have
a run of 6 repeated digits about one time in five).
The result is very non-random.

So you can see the attraction of a d16 dice.

Secret shared keys are very common in computing
(not just WPA-PSK, but RADIUS and BGP). Having
difficult-to-guess (ie, random) keys is very
important and a vital assumption in their security.
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