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Games

Games. Numble. The game state is an integer number >0 Alternatively, a player can - divide by a prime number if >1 - subtract 1 if number > 1 The player in turn who is left with the number 1 has lost. Numble Game Tree. 8. 4. 7. 1. 2. 3. 6. 2. 3. 5. 1. 1.

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Games

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  1. Games

  2. Numble The game state is an integer number >0 Alternatively, a player can - divide by a prime number if >1 - subtract 1 if number > 1 The player in turn who is left with the number 1 has lost.

  3. Numble Game Tree 8 4 7 1 2 3 6 2 3 5 1 1 2 1 1 2 4 1 1 2 3 2 1 1 1

  4. Numble Game Tree Green means win position for A 8 A B 4 7 1 2 3 6 A 2 2 3 5 1 1 B 1 4 1 1 2 1 A 2 3 B A 1 1 2 B 1

  5. Evalution function for Numble Np = # different prime factors Np=0 V= - ∞ Np=1 V= + ∞ Np=N>1 V= N Big N gives many possibilities, which gives more opportunities when game proceeds to that state.

  6. 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 – ½**N. Np = # different prime factors Np=0 V= 0 Np=1 V= 1 Np=N>1 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.

  7. 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).

  8. Cockpit in 1 dimension A B A wins A wins A wins …..

  9. Cockpit in 2 dimensions See http://www.idi.ntnu.no/emner/tdt4136/JAVA/minmax/minmax.html

  10. Five In A Row http://www.idi.ntnu.no/emner/tdt4136/JAVA/BONDESJAKK/fir.html

  11. (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.

  12. 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.

  13. 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 …

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