Hi Gary,
On Thu, 18 Feb 2016 09:03:26 -0800
"'Gary Campbell' gary_at_numin8r.us [fc-solve-discuss]"
<fc-solve-discuss_at_yahoogroups.com> wrote:
> For me, your paragraph that starts with “if” leaves too much unsaid. I don’t
> know exactly what you mean. Could you spell it out in more detail?
>
Sure, I'll try to explain below.
> From: mailto:fc-solve-discuss_at_yahoogroups.com
> Sent: Thursday, February 18, 2016 8:25 AM
> To: Freecell Solving Discussions
> Subject: Proposed Prune for Black Hole Solitaire and All-in-a-Row Solitaire
>
>
> Hi all,
>
> I noticed one potential prune for
> https://en.wikipedia.org/wiki/Black_Hole_%28solitaire%29 and
> https://en.wikipedia.org/wiki/All_in_a_Row_%28Solitaire%29 while testing the
> Black Hole Solitaire Solver on PySolFC:
>
> if there are two or more isomorphic columns (= columns whose ranks, in order,
> are identical, e.g: ": JH" and ": JD" or ": KH 5C" and ":KS 5H"), then it does
> not matter which column is played first, because they will yield the same
> subsequent state. Therefore, if playing the first column, at a certain stage,
> does not yield a solution, there is no point in playing the remaining ones.
To explain the games: what happens is that the foundation is essentially a
single card and you can move cards to it that are either the rank + 1 or the
rank - 1, with Aces wrapping to Kings and vice-versa. You win by moving all
cards and you can only move cards at the top of columns. In effect, the suits
of the cards do not matter at all - only their ranks.
Now, let's suppose we have the following scenario:
# State 0
foundation = 5H
Col[1] = 6C
Col[2] = 6H
{ other columns here }
Now let's suppose the solver decided to play the 6C card from Col[1] leaving it
empty:
# State 1
foundation = 6C
Col[1] =
Col[2] = 6H
{ same other columns here }
Then it traversed all derived states and found it a dead end. In that case, we
could have also played the 6H card:
# State 2
foundation = 6H
Col[1] = 6C
Col[2] =
{ same other columns here }
But since State 2 is isomorphic to State 1, it will yield the same dead end as
State 1 did, so we should not traverse it.
The same applies if there are two or more cards - with the same ranks in order.
E.g:
Col[1] = KH 5C
Col[2] = KS 5H
Hope you understand it better now.
Regards,
Shlomi
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Received on Thu Feb 18 2016 - 12:21:47 IST