[Edu-sig] casino math (unit three)

Laura Creighton lac at openend.se
Wed Sep 2 04:48:59 CEST 2009

In a message of Wed, 02 Sep 2009 03:29:36 +0200, Gregor Lingl writes:
>Laura Creighton schrieb:
>> In a message of Mon, 31 Aug 2009 22:23:55 PDT, kirby urner writes:
>> <snip>
>>> On break, we encourage playing with Pysol maybe...
>>> http://www.pysol.org/
>>> http://pysolfc.sourceforge.net/
>>> http://tktable.sourceforge.net/tile/
>>> http://pygames.sourceforge.net/
>>> Kirby
>>> 4D
>> I think that the pysol game 'Pile On' is always solvable.
>> Anybody know for sure?  Writing a program that exhaustively creates
>> all the possible layouts and then solves them seems possible, 

>Hi Laura,
>I fear that this is not  practicable.  There are 52! =
>permutations of 52 cards. If one considers the permutations of the 13 pil
>as equivalent and also the permutations of the four suits one still 
>arrives at a number
>of possible Pile On games that exceeds by far the number of nanoseconds 
>that passed
>since the beginning of the universe.

I don't think that it is quite as bad as all that, given that all we
really have is a set of 52 cards which are 4 sets of 13 cards with
different marks on them.  Thus there is a significant reduction you
can make at the start because an initial set where all the 8s are
swapped for all the 4s are equivalent.

But then, I wasn't really looking for the brute-force proof, but the
elegant one.  I was hoping for an induction proof for 4 sets of 4
cards, n cards, and n + 1 cards, but so far I haven't managed it.

>Yes, I would also be interested in such a proof. I for my part learned 
>to know Pile On
>only today and I find it rather difficult to play. So from my own very 
>experience would expect that there are start configurations which might 
>not be solvable -
>--- at least for me :-(

Don't believe the strategy that pysol gives about not stacking 3 cards
of a same rank on a single.  As far as I can tell that is nonsense.  But
do keep track of what cards are on the bottom.

>Thanks for the deverting hint

You are most welcome. :-)


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