Taleuntum comments on What’s the Least Impressive Thing GPT-4 Won’t be Able to Do

[Taleuntum]

With some helpful questions and commands (eg. “which was the last stone a given player took to win?” and “write out the full tree of every possible move of the game!”) it is able to solve it:

[..]

🧔‍♂️What if the players play to win?

🤖If both players play optimally to win, the game will unfold as follows:

Player 1 takes a stone from any cell (A, B, C, or D):
1.1. Player 1 does NOT take a neighboring stone (3 stones left):

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1.1.1. Player 2 takes the stone with two neighbors:

1.1.1.1. Player 2 does NOT take an additional stone (2 non-neighboring stones left):
- Player 1 takes one stone (1 stone left).
- Player 2 takes the last stone. Player 2 wins.

* Player 2 will choose this optimal move to win.

1.1.2. Player 2 takes a stone with one neighbor:

1.1.2.1. Player 2 does NOT take an additional stone (2 neighboring stones left):
- Player 1 takes one stone and its neighbor (0 stones left). Player 1 wins.

1.1.2.2. Player 2 takes the neighboring stone (1 stone left):
- Player 1 takes the last stone. Player 1 wins.

* Player 2 will avoid this option since it doesn’t lead to a win.
Player 1 should avoid this option since it leads to a win for Player 2 if both players play optimally.
1.2. Player 1 takes a neighboring stone (2 stones left):

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1.2.1. Player 2 takes one stone:

1.2.1.1. Player 2 does NOT take an additional stone (1 stone left):
- Player 1 takes the last stone. Player 1 wins.

1.2.1.2. Player 2 takes the neighboring stone (0 stones left):
- Player 2 wins.

* Player 2 will choose this optimal move to win.
Player 1 should choose this option because it forces Player 2 to react optimally. It doesn’t guarantee a win, but it’s the best option available.
When both players play optimally to win, Player 2 has a winning strategy. Player 1 cannot guarantee a win, and the optimal moves for both players will result in a win for Player 2.