Games

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Games
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Numble
The game state is an integer number gt0
Alternatively, a player can - divide by
a prime number if gt1 - subtract 1 if
number gt 1 The player in turn who is left with
the number 1 has lost.
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Numble Game Tree
8
4
7
1
2
6
3
3
5
2
1
2
1
1
2
4
1
1
1
2
3
2
1
1
1
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Numble Game Tree
Green means win position for A
8
A
4
B
7
1
2
6
3
A
2
3
2
5
1
1
B
1
4
1
1
1
2
A
2
3
B
A
1
1
2
1
B
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Evalution function for Numble
Np different prime factors Np0
V - 8 Np1 V 8
NpNgt1 V N Big N gives many
possibilities, which gives more opportunities
when game proceeds to that state.
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Evalution function for Numblestatistical
viewpoint
Let V be an estimate for the probability that A
may win in that position, and let an a priori
probability be ½. Then the probabilty that one
of N nodes is a winner is 1 ½N.
Np different prime factors Np0
V 0 Np1 V 1 NpNgt1
V 1 2(-N) These evaluations give the
same ranking of nodes as the previous evaluation.
Big N gives many possibilities, which gives
higher probabilities for a winning state.
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The game of Cockpit
The players are represented by a position in a
regular grid (in 1,2 or more dimensions). Each
agent has a speed vector in which can be changed
(or unchanged) by 1 step in any direction. The
winner is the one who will land upon the other.
If any player fals outside the field, he has lost
(an then the winner has won even if he also will
fall outside in the next step).
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Cockpit in 1 dimension
A B
A wins
A wins
A wins
..
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Cockpit in 2 dimensions
See
http//www.idi.ntnu.no/emner/tdt4136/JAVA/minmax/m
inmax.html
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Five In A Row
http//www.idi.ntnu.no/emner/tdt4136/JAVA/BONDESJA
KK/fir.html
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(Positive) horizon effect
White pawn b7 will eventually reach 8th line and
become Queen, but that may be postponed by black
so as to fall aout of the event horizon.
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Negative Horizon effect
Pawn (b7) is doomed, but a threat with pawn a3 to
b4 may push the unfortunate event out of the
event horizon.
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Guess second lowest(for classes)
Everyone in a group guesses a number (1-100)
which is supposed to be the next lowest number
that anyone else guesses. When everyone has
decided, they report their number, a winner is
announced, but the game goes on