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 -Ankhst > X-Spam-Checker-Version: SpamAssassin 3.1.0 (2005-09-13) on lists.looneylabs.com > X-Spam-Level: > X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.1.0 > X-Original-To: icehouse@xxxxxxxxxxxxxxxxxxxx > Delivered-To: icehouse@xxxxxxxxxxxxxxxxxxxx > X-Authority-Analysis: v=1.0 c=1 a=pJKmZVldAAAA:8 a=7UwbLvL8UiXJ_sUWY9QA:9 a=Ho_AuY33pz-mG4trwnsA:7 a=nKQrowuqDJffem8yqkUGqTWnwykA:4 a=oltf0pfCdT4A:10 > Date: Sat, 12 Jan 2008 09:00:49 -0800 > From: Kory Heath <kory@xxxxxxxxxxxxx> > User-Agent: Thunderbird 2.0.0.9 (Windows/20071031) > To: Icehouse Discussion List <icehouse@xxxxxxxxxxxxxxxxxxxx> > Subject: Re: [Icehouse] 2 player Zendo > Content-Transfer-Encoding: 7bit > 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 > > _______________________________________________ > Icehouse mailing list > Icehouse@xxxxxxxxxxxxxxxxxxxx > http://lists.looneylabs.com/mailman/listinfo/icehouse