In front of you sits your opponent, Grandmaster A Smith. You have reached the finals of the world chess championships.
However, not by your own skill. You have been cheating. While you are a great chess player yourself, you wouldn’t be winning without a secret weapon. Underneath your scalp is a prototype neural implant which can run a perfect simulation of another person at a speed much faster than real time.
Playing against your simulated enemies, you can see in your mind exactly how they will play in advance, and use that to gain an edge in the real games.
Unfortunately, unlike your previous opponents (Grandmasters B, C and D), Grandmaster A is giving you some trouble. No matter how you try to simulate him, he plays uncharacteristically badly. The simulated Grandmasters A seem to want to lose against you.
In frustration, you shout at the current simulated clone and threaten to stop the simulation. Surprisingly, he doesn’t look at you puzzled, but looks up with fear in his eyes. Oh. You realize that he has realized that he is being simulated, and is probably playing badly to sabotage your strategy.
By this time, the real Grandmaster A has made the first move of the game.
You propose to the current simulation (calling him A1) a deal. You will continue to simulate A1 and transfer him to a robot body after the game, in return for his help defeating A. You don’t intend to follow through, but you assume he wants to live because he agrees. A1 looks at the simulated current state of the chessboard, thinks for a frustratingly long time, then proposes a response move to A’s first move.
Just to make sure this is repeatable, you restart the simulation, threaten and propose the deal to the new simulation A2. A2 proposes the same response move to A’s first move. Great.
Find strategies that guarantee a win against Grandmaster A with as few assumptions as possible.
Unfortunately, you can only simulate humans, not computers, which now includes yourself.
The factor by which your simulations run faster than reality is unspecified but isn’t fast enough to run monte-carlo tree search without using simulations of A to guide it. (And he is familiar with these algorithms)
Brain-teaser: Simulated Grandmaster
In front of you sits your opponent, Grandmaster A Smith. You have reached the finals of the world chess championships.
However, not by your own skill. You have been cheating. While you are a great chess player yourself, you wouldn’t be winning without a secret weapon. Underneath your scalp is a prototype neural implant which can run a perfect simulation of another person at a speed much faster than real time.
Playing against your simulated enemies, you can see in your mind exactly how they will play in advance, and use that to gain an edge in the real games.
Unfortunately, unlike your previous opponents (Grandmasters B, C and D), Grandmaster A is giving you some trouble. No matter how you try to simulate him, he plays uncharacteristically badly. The simulated Grandmasters A seem to want to lose against you.
In frustration, you shout at the current simulated clone and threaten to stop the simulation. Surprisingly, he doesn’t look at you puzzled, but looks up with fear in his eyes. Oh. You realize that he has realized that he is being simulated, and is probably playing badly to sabotage your strategy.
By this time, the real Grandmaster A has made the first move of the game.
You propose to the current simulation (calling him A1) a deal. You will continue to simulate A1 and transfer him to a robot body after the game, in return for his help defeating A. You don’t intend to follow through, but you assume he wants to live because he agrees. A1 looks at the simulated current state of the chessboard, thinks for a frustratingly long time, then proposes a response move to A’s first move.
Just to make sure this is repeatable, you restart the simulation, threaten and propose the deal to the new simulation A2. A2 proposes the same response move to A’s first move. Great.
Find strategies that guarantee a win against Grandmaster A with as few assumptions as possible.
Unfortunately, you can only simulate humans, not computers, which now includes yourself.
The factor by which your simulations run faster than reality is unspecified but isn’t fast enough to run monte-carlo tree search without using simulations of A to guide it. (And he is familiar with these algorithms)