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Re: Four more "oldies"

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Mike Terry <news.dead.person.stones@darjeeling.plus.com> posted:

> On 24/08/2026 18:04, James Dow Allen wrote:
> > 
> > Mike Terry <news.dead.person.stones@darjeeling.plus.com> posted:
> > 
> >> On 23/08/2026 18:44, James Dow Allen wrote:
> >>>
> >>> (2)  ...
> >>> With optimal strategy, what is the probability that the team wins?
> >>> This is tricky. First try it with 3 players.
> >>> Or two with 'pass' not an option.
> > 
> > "Tricky" in an almost perverse way.  Do try it first with only 3 players.
> 
> For 3 players I see similar sorts of strategies, except they are a little simpler.
> 
> Specifically, players can effectively bet on a 2-1 split which occurs with probability 3/4, and in 
> doing so the team wins with that probability.  E.g. the strategy can be:
> -   if a player sees team mates with hats RR then choose G
> -   if a player sees team mates with hats GG then choose R
> -   (otherwise pass)

Beautiful!

> 
> But I don't feel that's helped me with the 4-player game.  (I suppose that I could write a program 
> to enumerate what I consider plausible strategies, but I'm doubting I'm going to get anything better 
> than 3/4 for the 3-player game...)

I assume you DO have a 3/4 solution for the 4-player game?
Gur "gevpx" vf gung gurer vf ab jnl gb vzcebir ba gung.
> 
> I'm probably overlooking some key insight!

For N=5 or larger the puzzle becomes horrifically tedious and difficult.
(I'll supply keywords for Google search if you wish.)

You have been warned.  If you do pursue N=5 despite my admonition
do NOT call me a sadist.

Sbe svir cynlref gur punapr bs fhpprff vf gjragl-svir bhg bs guvegl-gjb.
Sbe fvk  cynlref gur punapr bs fhpprff vf gjragl-fvk bhg bs guvegl-gjb.

> 
> Mike.
> 

James.

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Four more "oldies" James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-08-23 17:44 +0000
  Re: Four more "oldies" David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> - 2026-08-24 07:40 +0000
    Re: Four more "oldies" David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> - 2026-08-25 07:27 +0000
      Re: Four more "oldies" ram@zedat.fu-berlin.de (Stefan Ram) - 2026-08-25 12:33 +0000
  Re: Four more "oldies" richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-08-24 09:45 +0000
    Re: Four more "oldies" James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-08-24 10:33 +0000
    Re: Four more "oldies" Phil Carmody <pc+usenet@asdf.org> - 2026-08-27 22:45 +0300
  Re: Four more "oldies" Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-08-24 16:25 +0100
    Re: Four more "oldies" James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-08-24 17:04 +0000
      Re: Four more "oldies" Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-08-25 00:41 +0100
      Re: Four more "oldies" Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-08-25 01:08 +0100
        Re: Four more "oldies" James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-08-26 07:08 +0000
          Re: Four more "oldies" Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-08-26 23:18 +0100
            Re: Four more "oldies" Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-08-27 00:48 +0100
            Re: Four more "oldies" James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-08-27 10:42 +0000
              Re: Four more "oldies" Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-08-28 04:55 +0100
  Re: Four more "oldies" Charlie Roberts <croberts@gmail.com> - 2026-08-24 13:27 -0400
  Re: Four more "oldies" James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-08-29 00:04 +0000

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