Here is a card game I thought of while considering how to "chunk"
moves based on mc outcomes...
It is not in any way equivalent to programming go, but there are
significant similarities.
You have a deck of 360 cards numbered sequentially. (This is not as
complex as go, but the tree of potential moves is going to be of
similar size, narrower in places but always extending to 360 moves
total. The size could be changed without significantly changing the
game, so long as the number is even.)
To make a legal move:
1) If your opponent has played a card, and there is a lower card
available, you must play a lower card.
2) If 1) does not apply, you can play any card.
The game ends when all cards are played, and each player scores the
total of the numbers on the cards it has played.
A human player can readily analyze the game, seeing that the first
player wins with correct play, but loses against correct play if he
misses the right first move.
Our computer players, however, are to be limited to whatever
information they can derive from the final scores at the end of the
potential playouts from a particular move. They aren't allowed to read
the actual numbers on the cards or count the number of branches
resulting from a move, although they can of course distinguish
whichever moves they've made in a playout from those the opponent
played, and when, as an aid to choosing which moves are better in the
sense of working more often against limited-information play.
So--How many playouts to find the best line of play against 1) another
computer with the same limitations or 2) a human? At what point in the
game does it become possible for the poor artificially-handicapped
program to find a winning line, if one remains?
If two programs play one another under these limitations, it is
obvious that some moves will be more likely to win than others,
depending on which cards have been played. Some responses, while
falling short of ideal play, will still leave better odds of the
opponent missing whatever winning lines they've left open, and will
thus be objectively better than others. Can an mc player recognize
them? At what point?
Forrest Curo
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