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roughly in or near the octagon created by the diagonal lines when they reach the
center of the board. Opening moves here are so powerful that modern Twixt has
the ''pie'' rule: ''You cut the pie it into two pieces, and I pick which one I want.'' If
the opening move is particularly strong, on the second move (and only the
second move) the side that did not go first can take the opening move as played as
if it were its opening move and force the other side to make the second move
against it by switching colors. ''I'll play your color, so that makes it your move,
with you switching to my original color.'' Even without the pie rule, three
quarters of the opening board can be eliminated due to symmetry when looking
for an opening move. If we restrict our opening moves to the 80 holes in the
center octagon, symmetry reduces that number to 20, which again is far fewer
than 484. We could probably get by with 10 opening moves.
With a book of moves, our AI will not search at all for an opening move. It will
have opening moves that it likes in the topic of moves, along with the best
counter-move in case the pie rule is invoked. Some of these strong opening
moves can be used as a second move against a weak opening move as well. For
other moves, our search strategies will be guided by the topic of moves. We avoid
a general search of over 400 open holes and concentrate on the few holes that we
think will matter. So how much does this improve the complexity? We might see
something like the following:
One opening move (selected at random from the topic)
One counter-move (based on the opening move)
Twelve holes that are a setup to the opening move
Eight holes to hammer the previous move or 12 holes to do our own setup
One or two holes to complete the setup based on the opening move, or
12 holes to do another setup
What happens when we multiply numbers like these? Our low numbers are 1 and
2; our high numbers are 8 and 12. Let us use 10 to approximate all of them and
compute how expensive six moves of look-ahead would be:
10 * 10 * 10 * 10 * 10 * 10 = 10 6 = 1,000,000
One million is a very tractable number on current hardware. Playing by the topic
using look-ahead should make it possible to create a Twixt AI that is fast enough
to play against, even if it does not ensure that such an AI is powerful against
human players who employ four-move and five-move setups. The topic of moves
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