[ExI] 2/3 game, round 1

Zelaron zelaron at gmail.com
Fri Jun 26 15:24:18 UTC 2009

On Fri, Jun 26, 2009 at 7:07 AM, Emlyn <emlynoregan at gmail.com> wrote:

> 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
> > 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
> http://emlyntech.wordpress.com - coding related
> http://point7.wordpress.com - ranting
> http://emlynoregan.com - main site
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Perhaps a few ideas from a reasonably simple web-based game that I
programmed about a year ago can somehow be scavenged to introduce stochastic
behavior into the 2/3 game.
In essence, my game publicly displayed the username and password for an
MMORPG account with valuable (append quotes if desired) items. Whoever
logged into the MMORPG account first would effectively win the round (and
the items).

Every 18 hours (on average), a new round started, at which point the account
information for an unclaimed account was published. In the subsequent 8
hours, there was a minute but non-negligible probability that the login
information for the next account would be displayed, or in other words, that
yet another round would start. The chance for a give-away increased (as a
third-degree polynomial function) until 24 hours after the round started, at
which point there was a 100% chance for a giveaway.
The aftermath of the game was a lot of wasted sentience-hours since a large
set of humans claimed to have found it an intriguing pastime to stare at
their screens while an automated AJAX update did its thing.

I figure that a similar system can be used for the 2/3 game, only that
players will submit their single "guess" during the round just before they
think that it will end. If you wait too long, you will fail, but if you try
too early, someone else is likely to render your try obsolete. Of course,
this may perchance more similar to a game of chicken than the 2/3 game, but
oh well.

(Also, the limitation to a single submission per round will, if enforceable,
prevent the consumption (or consummation?!) of time and lives.)
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