[ExI] 2/3 game, round 1
emlynoregan at gmail.com
Fri Jun 26 05:07:44 UTC 2009
2009/6/18 spike <spike66 at att.net>:
>> ...On Behalf Of Mike Dougherty
>> > I am making up a spreadsheet to do the scoring for you, so you can
>> > decide on a strategy in future rounds without needing to do the
>> > mechanics. More later.
>> I'll continue to watch until I have a better strategy.
> Well damn. I calculated today that there is a trivial strategy for the ESTA
> game. It doesn't even require a spreadsheet; it becomes a simple algebra
> problem. The last to play always wins.
> I though if we used the 1 sigma variation it would be more interesting, but
> I found that version has a closed form solution as well. It is a more
> complicated algebra problem, but same result: there is a particular optimal
> solution regardless of what has already been played, and it can be easily
> calculated. So now, back to the drawing board with me, to see if I can
> dream up a variation on the theme which has no trivial solution.
If the numbers people choose are all public, and the algorithm is
public, then any game of this type should suffer the same problem;
whoever goes last can figure out a winning move and choose it.
You might be able to fix this with iterations. Have a number of
rounds, and allow the results of previous rounds to affect the outcome
of subsequent rounds. Success in each round should probably affect the
outcome (eg: add together points from each round into total points,
use that to decide the winner), but success in previous rounds should
also adversely affect a player's chances in subsequent rounds.
eg: Say you get one turn maximum in the first round. Then, you can
have X turns maximum in subsequent rounds, where X is your position in
the previous round (so the winner gets 1 turn, second place gets 2
turns, 3rd place 3 turns, etc). People still play turns in whatever
order they like, within each round.
(Actually this probably still boils down to algebra; there's probably
a winning strategy that you can a priori just write down.)
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