Please regard the following backgammon position:
(If you don't play this game, I'm sorry, this will take too long to explain.)
As you see, I am playing against the computer.
As you know, backgammon is a sufficiently-limited game such that the computer can,
from any position, work out all of the possible eventual outcomes and
compute the exact probability of winning or losing.
The dice enter an element of randomness into the game.
Now, never mind how we got into this position in the first place.
It had to be an interesting game, such that
the computer and I doubled and redoubled all the way up to 64.
What I want you to look at is the current situation.
It is the computer's turn to play.
Now if you know the game, the computer has a 100.0% chance of losing at this point
but it has a clear majority of a chance to get one man off
before I get all mine off, thus saving itself from the gammon.
I still win the match, probably a very important issue,
because the match is only to 50.
But the computer, instead of either playing it out
or offering a resignation of a single,
has offered a resignation of a double, or gammon!
and you thought only people get depressed ....