Looney Labs Icehouse Mailing list Archive

Re: [Icehouse] 2 player Zendo

  • FromJoseph Pate <jpate@xxxxxxxxxxx>
  • DateSat, 12 Jan 2008 12:01:05 -0800 (PST)
Guess I should have read Kory's post before posting my own  ;-)

at least we appear to agree

Ah the joys of responding early before emptying the inbox


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> Date: Sat, 12 Jan 2008 09:00:49 -0800
> From: Kory Heath <kory@xxxxxxxxxxxxx>
> User-Agent: Thunderbird (Windows/20071031)
> To: Icehouse Discussion List <icehouse@xxxxxxxxxxxxxxxxxxxx>
> Subject: Re: [Icehouse] 2 player Zendo
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> X-Barracuda-Bayes: INNOCENT GLOBAL 0.6966 1.0000 1.3431
> X-Barracuda-Spam-Report: Code version 3.1, rules version 3.1.39335 Rule 
breakdown below pts rule name              description ---- 
---------------------- --------------------------------------------------
> 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.
> ---------------------
> 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
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