[ExI] 2/3 game, round 1

[Emlyn]

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.
>
> spike
>

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.)

-- 
Emlyn

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