Take Zendo. Play with two players. Alternate master and student. When master, alongside your rule also write down your probability distribution over number of total examples your student will have seen when he correctly guesses the rule. The master scores the log of the probability she assigned to the actual number of guesses; the student scores the negative of the number of total examples seen. Choose the base of the logarithm to make the two numbers kinda sorta similar, like 1.2ish. After any even number of games, transfer $1 from one player to the other for each point differential and zero their points.
If the student does not guess the rule before seeing 27 positive examples or 27 negative examples, stop the game. Both players must immediately donate $1000 to me. Then restart that game without swapping roles.
Okay, maybe there’s a better way to incentivize the master to bound the difficulty, so that games actually finish. :)
This is problematic for many of the same reasons the sequence game is problematic. “simpler rule” is really hard to define in a way that still makes the game fun.
(I take it as given that you are modifying the game to play two games simultaneously of course)
How’s this? The student may end the game at any point. In this case the master scores 10 and the student 0. Scale the other scoring mechanisms and weight them so that the student in general should gain significantly more than a −10 point differential whenever the master is not trying to make an ubercomplex rule.
Take Zendo. Play with two players. Alternate master and student. When master, alongside your rule also write down your probability distribution over number of total examples your student will have seen when he correctly guesses the rule. The master scores the log of the probability she assigned to the actual number of guesses; the student scores the negative of the number of total examples seen. Choose the base of the logarithm to make the two numbers kinda sorta similar, like 1.2ish. After any even number of games, transfer $1 from one player to the other for each point differential and zero their points.
If the student does not guess the rule before seeing 27 positive examples or 27 negative examples, stop the game. Both players must immediately donate $1000 to me. Then restart that game without swapping roles.
Okay, maybe there’s a better way to incentivize the master to bound the difficulty, so that games actually finish. :)
Indeed. If the game goes on long enough, end the game, and the player with the simpler rule wins.
This is problematic for many of the same reasons the sequence game is problematic. “simpler rule” is really hard to define in a way that still makes the game fun.
(I take it as given that you are modifying the game to play two games simultaneously of course)
How’s this? The student may end the game at any point. In this case the master scores 10 and the student 0. Scale the other scoring mechanisms and weight them so that the student in general should gain significantly more than a −10 point differential whenever the master is not trying to make an ubercomplex rule.
The “simpler” rule is the one with the shortest description, of course...