Problem 895

[eins.tronix]

What is the exact meaning of "both play optimally"? Is "an optimal move" the best move that one can play in order to beat the other party or any one of the moves that can lead to end of a fair game?

[neverforget]

Problem 895 (View Problem)

What is the exact meaning of "both play optimally"? Is "an optimal move" the best move that one can play in order to beat the other party or any one of the moves that can lead to end of a fair game?

I don't think optimal play is ambiguous here. There is complete information, no randomness, no draws. So optimal play simply means neither player will make a move that forfeits a winning position.

[eins.tronix]

Is this arrangement fair?
G S
S G S
G G S

[neverforget]

Is this arrangement fair?
G S
S G S
G G S

No.

[raiden11]

On Gary's turn he chooses a gold coin and removes it from the game along with any other coins sitting on top. Sally does the same on her turn by removing a silver coin.

Please tell me if I understand the game properly.
It's clear that Gary has to pick up at least one gold coin from the top. But he may or may not pick other coins or he necessarily has to pick up at least one other coin? And the other coins can be picked up from the top of first pile (from which the gold coin was picked up) only or top of any pile is fine?

And the same rules apply to Sally, just with the first coin being silver.

[philiplu]

Please tell me if I understand the game properly.
It's clear that Gary has to pick up at least one gold coin from the top. But he may or may not pick other coins or he necessarily has to pick up at least one other coin? And the other coins can be picked up from the top of first pile (from which the gold coin was picked up) only or top of any pile is fine?

And the same rules apply to Sally, just with the first coin being silver.

No, it's simpler than that. Say it is Gary's turn. If there are no gold coins in any of the piles, Gary loses. Otherwise, Gary can pick any gold coin he wants, and removes that coin. If that chosen coin isn't at the top of a pile, Gary must also remove all the coins which rest on top of his chosen coin, no matter whether they are gold or silver.