Beeswax and Beehive --
Building in Ranks
There are only a handful of solitaires in which cards are packed on the
tableau by rank. In a couple of these, packing by
rank is only a means to an end. David Parlett's ingenious Curds and
Whey is essentially a one-deck variation of Spider; it allows
packing on the
tableau in rank, and also downward in suit; the object being to form
four complete suites
(sequences running from king down to ace in suit). Steve
Meretzky's Barbershop Quintet uses
packing by rank to facilitate discarding in sequence as in
Golf. In the
two games we describe in this article, cards are packed on the tableau
in rank only, the object being to form thirteen sets of four.
Beeswax and Beehive are both available in Solitaire
Virtuoso.
Beeswax is the name I am now
using for an excellent open
solitaire I have never seen in a book, though there are a fair number
of computer versions.
Among
the computer versions still available are Maurice Abraham's Patience Pack
(where it is called Pile Sort), a freeware package of 120 games and
puzzles first published in 1994 (the current version 8.0, written in
2005, still runs under Windows 7). The Linux solitaire collection
AisleRiot
implements it as Pileon. Pretty
Good Solitaire calls the game
Fifteen
Puzzle: not a particularly good name, as this solitaire is unrelated to
the
well-known sliding block puzzle popularized by Sam Loyd (fifteen
numbered pieces in a 4x4
grid, which have to
be arranged in order by sliding blocks into the one space in the grid).
In Beeswax, the
entire deck is dealt out in a tableau of 13 columns of 4 cards each,
with two empty
columns. It is usually
presented as thirteen fans of four cards each, with two empty spaces,
the fans and spaces
being arranged in a 3x5 or 4x4 array. I am not a fan of
fans: I prefer to have 15 parallel
columns, so that it is easy to see which columns have room left. In
Beeswax a
card may
only be moved onto a card of the same rank, or into an empty
column.
Each column can hold a maximum of four cards, so the
first play must be to one of the two empty columns. The
object is to form thirteen quartets of the same rank; completed
quartets are not discarded.
Let's play through a deal, number 52923, from Solitaire Virtuoso. Usually
the player wants to move, if possible, three (or even on occasion four)
cards of the
same rank to one of the two empty columns, trying to keep one column
empty as much as possible. Often there are no ranks with three
available cards, so we try to find a pair which will expose two more
playable cards. In this case moving the two aces to the first
empty column will uncover a queen and a three, both of which can be
played on. The moves are notated, as in other column-packing
games, using a hexadecimal extension of the standard FreeCell
notation. The
columns are numbered 1-9 and A-F, and each move is specified by giving
the starting and ending columns. So moving the ace of diamonds to
the first empty column is denoted 5E (this can be done
quickly by right-clicking the
AD, as in many Virtuoso games).
Moving the ace of clubs onto the ace of diamonds is DE. We now have three queens
free, and we can see that the fourth is in
column C; if we can find places to put the seven of spades and nine of
diamonds, we can get the four queens together. We move all
three queens into the last empty column, put the ten of diamonds on the
ten of hearts, and complete a quartet by putting the queen of hearts on
the
other three queens. Note the automatic recording of the solution.
Now we could regain a space by putting the nine of hearts on the nine
of spades, but we can also clear column 2 if we can find a place for
the two tens. We can put them in column 9 if we can move the two
jacks, so we put the nine of spades onto the nine of hearts, move the
two jacks onto the jack of spades, the two tens onto the ten of spades,
and the ace of spades and nine of clubs onto their respective
columns. Now we have an empty column again, and four clean columns (columns with cards
all of the same rank). We can also move the
three of hearts onto the three of clubs and complete the quartet of
nines with the nine of diamonds. Sequences of plays like this are
not hard to visualize with practice.
We can now clear column 3 by putting the sixes in column 2 and the twos
in column 8; look for opportunities to clear columns with only two
ranks in them whenever possible. We also move the six of
clubs and jack of diamonds onto their corresponding columns. You
should always move free cards into clean
columns
(columns containing only one rank) whenever possible,
unless you have no empty columns and can create one by moving all of
the cards from a clean column onto another column. We also move
the
five of diamonds onto the five of clubs, uncovering the ten of clubs
and setting up another set of maneuvers. If we move all four tens
into the empty column 3, and the eight of spades into the eight of
diamonds, we can clear column 4 by putting the two sevens onto the
seven of diamonds, the three of spades on the three of diamonds, and
the five of hearts on the five of diamonds. But instead of moving
the five of hearts, we put the two fives from column 1 onto it, and we
can instead clear column 7 by moving each of the four cards onto a
different column (I call this a fountain,
and try to finish a deal with a fountain when I can). We're
almost finished now:
If we move all four threes (from columns 5 and A) into the empty column
7, we can clear column 6 (king of spades to column 1, four of diamonds
to column 5; finish three quartets with king of clubs, ace of hearts,
and six of hearts). The last three quartets are easy -- all four
twos to an empty column, then finish the eights and fours). Our
completed solution is:
52923
5E
DE 2F CF DF 42 C4 CF DC 9D
29
2E 2C 85 8C 32 38 32 38 12
1D
B1 93 B3 AB 49 4A 14 71 7B
79
74 57 A7 51 65 61 6E 62 86
A6
B8 A5 B5
Like many open solitaires, Beeswax has a very high win rate with
expert play. I have been
able to win 98% of a block of 100 Solitaire Virtuoso deals given
enough attempts,
though I have only won about 1 in 3 on the first try (and without
undos). I'm also working on a second block, with 87 solved so far.
There is plenty
of skill involved; I
would rate this as one of the best open solitaires. I
decided to give it a new name because it is something of an open
version of the second game we are looking at...
Beehive
is a storehouse game rarely
seen in books; my only sources are books on card games for children,
Joseph Leeming's Games and Fun With
Playing Cards
(1980 Dover abridgement of an 1949 original), Alfred Sheinwold's
101 Best Family Card Games
(Sterling, 1992), and Vernon Quinn's 50 Card Games for children (USPCC 1946,
where it appears as Honeybee). It is also rare as a
computer game: until recently, I had only seen one version, no longer
available, by
NZP Games (their website no longer exists, but my 2005 copy of the game
still runs in Windows 7). 10 cards are initially dealt to a
storehouse (only the last card is face up; others are turned face up as
they are uncovered). Six cards are dealt, one each, to six
columns to
start the tableau; the remaining 36 cards form a stock. The stock
is dealt, three at a time as in Demon (Canfield) or Klondike, to a
wastepile
(NZP and Leeming both specify that the stock be dealt with only one
card at a time visible, but I find games using the Demon deal much more
strategic if you spread each group of three). If the top of the
waste matches any of the tableau columns in rank, it may be moved
there,
uncovering another waste card. When the stock is exhausted
(possibly after dealing one or two leftover cards as a group), the
waste can be turned over (without shuffling) and redealt, as many times
as necessary. When the fourth card of the same rank is moved to a
tableau column, the quartet of four cards are discarded, and the empty
column can be filled at any time with a card from the storehouse or
waste. Leeming specifies that an empty column must be immediately
filled from the storehouse, or from the top of the waste after the
storehouse is empty. But the game is also more strategic if a
column may be left empty (NZP and Solitaire Virtuoso both allow
this). The object is to form and discard all
13 quartets of the same rank. NZP uses a
storehouse of 16 cards, but the game is probably too hard that
way. There is now a good version in BVS Solitaire,
with the same 10-card storehouse specified in
Leeming. Solitaire Virtuoso uses a 13-card storehouse
as a default; this can be changed to any value between 7 and 16.
Beehive is a good game for practicing strategic manipulation of the
stock, which may help in other games (such as Demon or the
three-at-a-time version of Klondike: Robert Abbott's site
has a discussion of how to use this strategy in playing Klondike).
Copyright ©2021 by Michael Keller.
All rights reserved. This file was revised on June 5, 2021.