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Re: Four more "oldies"

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On 26/08/2026 08:08, James Dow Allen wrote:
> 
> 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.

At the time I previously posted I only had the 1/2 solution I'd previously described.

Since then I've written a (pretty naive) program to search for the best strategies, and for the 
3-player game it confirms the best we can do gives a 3/4 chance for the team to win.

For the 4-player game I doubt I will be able to run the program to completion - there are just too 
many potential strategies to enumerate. :(  But as luck would have it, it's found a handful of 3/4 
strategies near the beginning of its search tree - these strategies have one of the players always 
passing regardless of what hats that player sees!

But these results don't really improve my understanding.

Is there an obvious reason why we can't improve on 3/4?  (I see from your hints below that 3/4 can 
be exceeded for 5- or 6-players, so I doubt there's any obvious reason.)

Mike.


>>
>> 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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Thread

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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