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James_Miller comments on Games for Rationalists - Less Wrong
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Here is a simple game that requires only pen and paper. I've often played it with my young son and I think it helps teach some rationality skills.
Player 1 keeps writing down a different set of three numbers, and for each such set Player 2 says either "Yes" or "No" depending on whether the three numbers conform to a secret rule that Player 2 creates. The rule must be such that the average child in grade X (where X is specified) could easily apply it. If Player 1 keeps getting the same reply to different sets of numbers he can request a counterexample that would elicit the opposite reply. Player 1 eventually tries to guess the rule.
Possible rules: the numbers sum to >20, at least one number has 3 digits, all the numbers are odd, the second number is the biggest,...
A related game I played with my 7 year old asks for all numbers included in a set. It is an extension of the game where you have to guess a single number and the child learns interval halving. He grew out of that some time ago. I didn't yet leave the natural numbers. As with most question and answer games we change roles. Changing roles has the advantage that there is no "teachers password" effect. And the child has to check the rule more often. After a few dozen rounds he was able to find "1, 3, 8". "all numbers > 0" "all divisible by 10 between -100 and +100", And he invented "only -100", "all divisible by 5 between -100 and 0". The advantage is that you don't need paper and pencil but can do this verbally.
This is Zendo, but with numbers instead of shapes. An analogous game can be played with words, e.g.:
Positive examples (these fit a particular rule)
Negative examples (these don't fit the rule):
Solution (rot13): Jbeqf gung raq jvgu gur anzr bs na navzny.