One relatively common way to remove first player advantage is to have the first player place one stone, and then after that each person places two stones on their turn. So
After player 1s first move there is one stone in the sequence.
After player 2s first move there are three stones.
After player 1s next move there are five stones.
After player 2s next move there are seven stones.
Etc. Usually this completely removes first player advantage. It’s obvious that this removes player 1s potential advantage since black or white, his move is symmetrical without loss of generality.
Player 2 actually has the first consequential move, with three possible options — again, taking player 1s move as a given color, player 2 can play
DD
DS
SD
where S means “same” and D means “different”. Technically player 2 has four options: he could also play SS and lose immediately :-)
My intuition would be that either there is an infinite game possible and perfect play produces a stalemate, or games must inevitably end, and someone must have a winning strategy — in which case I’m betting its player 2, who makes the first “real” move.
Comments
One relatively common way to remove first player advantage is to have the first player place one stone, and then after that each person places two stones on their turn. So
After player 1s first move there is one stone in the sequence.
After player 2s first move there are three stones.
After player 1s next move there are five stones.
After player 2s next move there are seven stones.
Etc. Usually this completely removes first player advantage. It’s obvious that this removes player 1s potential advantage since black or white, his move is symmetrical without loss of generality.
Player 2 actually has the first consequential move, with three possible options — again, taking player 1s move as a given color, player 2 can play
DD DS SD
where S means “same” and D means “different”. Technically player 2 has four options: he could also play SS and lose immediately :-)
Cool! I haven’t thought about varying the number of stones one could put. It’s definitely a variation to look into!
Would your intuition be that this makes it so that neither player has a winning strategy? That perfect play would yield an infinite sequence?
My intuition would be that either there is an infinite game possible and perfect play produces a stalemate, or games must inevitably end, and someone must have a winning strategy — in which case I’m betting its player 2, who makes the first “real” move.