Aloril wrote:
Actually given *enough* games "fully random including
eye filling and passing moves" will win against a pro player.
That is "true", at least as it is true that a monkey would
write Hamlet typing at random long enough.
That probability is in the range of 1 to (x·100)^(y·100)
where x and y are > 1. x represents the number of available
moves in hundreds (more than 100 typically) and y represents
the number of consecutive moves the random player has to
"guess". (The whole game and, therefore, also more than
hundred.) This number is below the probability of breaking
any type of cryptographic system (private key or public key)
by a fluke in the first guess. For practical reasons that
number is called zero. ;-)
The problem of "towards infinite shift" of Elo rating of
programs vs random is a different one. It is caused because
the probability formula never returns zero (except for
infinite difference), but it does return very small values
(not as small as those of my previous argument).
One possible solution would be to force this value to zero
(statisticians do that for problems related with goodness
of fit) when the number of expected wins is below 5 in n.
Where n a reasonable guess for the number of games
the bot can play. Using this, there would be a maximum
Elo difference above which nothing should be computed
or, even better, the game should not be played at all.
But there is, of course, the possibility of a win due
to an Internet fail, a bug, the operator resigned to
power off the computer .. and the this probability is
equal for both. So probably doing nothing is also an
wise option. ;-)
Jacques.
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