everyone should know the work of George PĆ³lya on how to solve problems
Marvin Minsky (in Steps Toward Artificial Intelligence)
solve a simpler problem ?
restriction of dark hex
first stone must touch own edge
each subsequent stone must touch own previous stone
must reach other side within 4 moves
can we solve this ?
*p1 * * * * p1 p2 ~ ~ ~ ~ D+ C+ B+ A+ d- a+ ~ ~ ~ ~ c- b+ ~ ~ ~ ~ b- c+ ~ ~ ~ ~ A- B- C- D- a- d+ * * * *
a- b- c- d- a+ b+ c+ d+ A- ? 1 ? ? ? 1 1 1 D+ C+ B+ A+ B- c- b+ C- b- c+ D- A- B- C- D- A+ B+ C+ D+ what should we assume if player sees opponent stone? minimax ? equiprobable ? eg: A-a- .5 if p2 plays minimax = equiprob. {d-,a+} eg: A-d- .25 if p2 moves 2,3 uniform {left/right}
A-- move 2 towards opponent - A-+ " " " " + a- c- d- a+- a++ A-- ? 0 0 1 .5 A-+ ? 1 .5 1 0 so if p2 plays a- and sees a stone at A-, then p2 minimax is equiprob {d-, a++}, 1p win rate .25