Dale Newfield wrote:

Student picks a number, X.

`The master picks a rule that they think will take the student X turns
``to figure out.
`

The Student gets points for guessing in less than or equal to X turns,
and is given one anyway if the master made the rule too hard:
(1 point if not solved at X, 2 if solved at X, 3 at X-1, etc.)
The Master gets two points if it's solved in exactly X turns.

`On turn X, as the Student, I will purposely not guess the rule
``correctly, because if I guess it correctly, I gain no points over the
``Master, while if I fail to guess correctly, the game ends and I gain a
``point. You could just give the Master a single point instead of two
``points if it's solved in exactly X turns. But then neither player cares
``what happens on turn X, because the Student gains a single point either
``way. Since that's the best result the Master can hope for, the best
``strategy is just to purposely come up with a rule that's too hard. You
``could tweak the scoring further to insure that the Student always gains
``two or more points over the Master for guessing the rule correctly, and
``gains exactly one if the rule is too hard, but then once again the best
``strategy for the Master is to purposely come up with a rule that's too
``hard. I'm not seeing any obvious way around all of this.
`

`I'm intrigued by Guy's idea of keeping X hidden from the Student. Here's
``my variation on that theme. Interestingly, this suggestion actually
``works for any number of players, and provides a kind of cap to keep
``games from going on too long.
`
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`The Master secretly comes up with a rule, and secretly comes up with a
``target range of rounds during which he or she hopes a Student will guess
``the rule. (A round means a full round of play, with each Student taking
``one turn.)
`

`If a Student correctly guesses the rule in fewer rounds than the
``beginning of the Master's target range, the game ends and that Student
``gets a point per round played.
`

`If a Student guesses the rule correctly on a round within the target
``range, the game ends and the Master gains a number of points equal to
``the start of the target range minus the size of the target range.
`

`If no Student has guessed correctly after the last round of the target
``range, the Master announces this fact, and no one gets any points for
``this game. (However, the Students may continue playing for fun.)
`
---------------------

`So if, as the Master, I choose the range 10-15, the size of my range is
``6. I will win exactly 4 points (10 minus 6) if any Student guesses
``correctly on a round within my range, while Students can win between 1-9
``points by guessing correctly before that. If I choose the range 20-20, I
``will gain 19 points if any Student guesses correctly on exactly round
``20, and Students can win between 1-19 points by correctly guessing
``before that.
`

`I can increase my chances of winning by increasing the size of my range,
``but that reduces the number of points I might win. Notice that there's
``no point in making the size of my range equal to or greater than the
``bottom end of my range. Choosing the range 10-30 is silly (and should
``probably just be illegal), because I will then win negative points if
``any Student guesses correctly within my range.
`

`As a Student, my potential payoff for a correct guess becomes greater
``and greater as the game progresses, but of course, I'll wonder whether
``or not we've moved within the Master's range. If I become convinced that
``we have, I'll just stop making good guesses (and should probably just
``explicitly announce this fact and start passing my turns). This will
``keep the Master from suddenly becoming "helpful" in too obvious a way
``(or simply blurting out the answer!) when the game enters the target
``range. However, I would consider it perfectly legal and within the
``spirit of this game for the Master to start building more helpful
``counter-examples once the game moves into the target range. It's up to
``the Students to think about this and decide whether they want to risk
``guessing.
`

`One potential way to salvage Mondo for the single-Student game would be
``to institute what I've called "Risky Mondo". You start the game with no
``stones, and you need to spend stones to guess. You win a stone by
``calling Mondo and answering correctly, but if you answer incorrectly,
``you lose all your stones. This wouldn't change the single-Student game a
``lot, but it would have some subtle effects, and perhaps it's more
``pleasing than just getting an infinite number of stones. A slightly more
``complex version of Risky Mondo can also be used in multi-Student games.
``See
``http://lists.looneylabs.com/pipermail/icehouse/2007-February/001324.html .
`
I have no idea if this would be fun. I'd like to try it sometime.
-- Kory