# [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! =
>80658175170943878571660636856403766975289505440883277824000000000000
>permutations of 52 cards. If one considers the permutations of the 13 pil
>es
>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
>irrelevant
>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
>Gregor

You are most welcome. :-)

Laura

```