Nestor and Double Nestor --
Rank Pair Discarding Games
by Michael Keller and Mark Masten
One of the standard single-deck open games is Nestor, probably
named after a
mythological Greek king, one of the Argonauts. The game dates back at
least to the German book Illustrirtes
Buch der Patiencen,
first published in 1877, and later translated
into other languages including English. (It's also one of a
handful of very early games to be named without a definite
article). It is
called Matrimony in some older books (e.g. New Games of Patience
(1911) by
Mary Whitmore Jones), an unfortunate name which has been applied to
other games. Nestor is the most common of the family
of rank pair discarding games. In the standard one-deck version, the
deck is dealt out row-by-row into a tableau of eight columns and six
rows. The remaining four cards are dealt face up below the
tableau columns as an open reserve. The uncovered card in each
column, as well as the four cards of the reserve, are available at any
time. Cards are discarded in pairs of the same rank; each
discard uncovers new cards in the tableau. The object is to
discard all 52 cards in pairs of the same rank. [Some
older sources specify that the last four cards are dealt as a
closed reserve, in which the four cards can be only be used in order,
which is unnecessarily harsh and adds nothing to the strategy of the
game.]
Above left: an unrectified deal of
Nestor, number 59970 in Solitaire Virtuoso. Note that six
of the eight rows contain repeated ranks. Above right: how
the deal comes out when rectified. Both versions are winnable.
If the cards were dealt randomly, the game would become very
difficult (with a win rate less than 1 out of 7, according to Mark
Masten's computer analysis of 100,000 sample deals, reported to the
Card Solitaire Forum mailing list in 1999. The reason for this is
that cards of the same rank tend to be to be dealt to the same
column. Somewhere around 40% of deals would be impossible
by inspection because they have three of the same rank in the same
column. The standard procedure for dealing, which I call rectification,
is to deal row by
row, placing on the bottom of the deck any card which would duplicate
ranks in the same column. The last four cards (almost always would-be
duplicates) then become the
reserve, which may contain duplicate ranks. This is how the game
is invariably described in print; careless computer adaptations
sometimes leave out the rectification. Dealt in the
standard way, the game has a win rate of just above 4 in 7 with
perfect play. [The standard rectification scheme
fails on rare occasions; the easiest way to handle it is probably just
to reshuffle.]
A reasonable rule to follow in unrectified versions of Nestor is to allow overlap discards: two cards can be removed together if one is uncovered and directly covers the other. In the unrectified version of 59970 above, four pairs can be
removed under the overlap discard rule once all the cards above them are
removed: 9's in column 1, 3's in column 3, 6's in column 6, and 2's in
column 7. (We also look at overlap discards in the Pyramid article).
Variations of Nestor
You can make Nestor as hard or as easy as you like by
changing the number of columns: BVS Solitaire includes two unrectified versions without reserves: Turkish Kerchief deals the entire deck into 10 columns (the first two get an extra card); Full Parade is 9 columns (seven get an extra card). These games come from the 1998 book Pasiasny
(in Russian) by N.IU. Rozaliev. Both games specifically
allow overlap discards, but are nevertheless quite difficult to win. Pretty Good Solitaire includes a
variant called Heracles, which
is nine rectified columns of five cards with seven reserve cards, and Alcides, which is ten unrectified columns of five cards and two reserve cards. Vertical,
a game found in some older books (and which is sometimes confused with
Nestor itself),
has one fewer column of cards in the tableau: seven columns of six
cards each, with ten reserve cards. Sometimes an extra card is dealt to
the center (fourth) column, and only nine cards to the reserve.
Doublets is a
closed version of Nestor, with only the last card in each tableau
column dealt face up (cards are turned up as they are uncovered).
Doublets is usually dealt to a tableau of 12 columns of four cards each
(non-rectified). The last four cards are a closed stock, which is
used to fill empty columns -- when the last card in a column is
discarded, deal the top card of the stock face up to replace
it.
This makes the reserve less useful than in standard Nestor, as the four
cards cannot be used until you start clearing columns, and a critical
card may not be available at the right moment.
Mark Masten's solver found that the win rate in standard Closed
Nestor, eight columns of six, but with a normal open reserve, is about
1 in 4 if the deals are rectified.]
An interesting version of Nestor is to add jokers to the
deck. An available joker can be matched with any card (though
the second joker must then be matched with a card of the same rank as
the first if all of the cards are to be discarded). This was
first suggested by Walter B. Gibson in his excellent 1964 book How To
Win At Solitaire (where Nestor again appears as
Matrimony). He suggests
just adding the two jokers to the reserve. But Mark Masten
suggests just shuffling them into the deck as usual, and dealing a
six-card reserve with the usual rectification. His variation Nestor's Revenge
has no reserve at all, just nine rectified columns of six cards each,
with two jokers shuffled in randomly. His solver won about 1 deal
in 6.
Double Nestor
There seems to be a widespread idea, which I don't entirely
agree with, that any good single-deck solitaire can be made into a good
double-deck game (this idea is more persistent in computer solitaire
packages; two-deck games which have appeared in the literature are more
likely to have stood the test of time). For a long while, Nestor, however, did not
appear to have been tried as a double-deck game (not counting Mah Jong solitaires). I originally
experimented with this using the game editor in Solitaire Antics
Ultimate, trying out various layouts for a two-deck Nestor. What
I was aiming for is a game which can be won most of the time, but
provides challenging play, particularly towards the end of the game. My
first attempt was 12 columns of 8 (rectified), with eight reserve
cards. This seemed too easy, so I tried 10 columns of 10, with four
reserves. I only won one out of five tries, though that might have been
due to poor play (later I won three out of seven). I then tried 11
columns of 9, with five reserves. I won eight of ten, but it was not as
challenging as I would like -- the winnable deals seem on the easy
side. I have also tried a non-rectified
deal of 12 columns of 8 -- this would be the most consistent with the
original Nestor, and easier to deal by hand, but I won every try and it
also didn't seem hard enough.
In 2003 I asked the members of the Card Solitaire Forum for help,
and
Mark Masten wrote a new solver to handle double-deck variants of
Nestor. He found that rectification got harder as the columns got
longer. It appears that 10 columns of 10 is a very good game,
even without rectification. His solver won about 92 percent
of the time. One interesting version he devised is 7
columns of 13 cards, with rectification, and a 13 card reserve: each
column will contain one of each rank, as will the reserve. I have included the 10x10 unrectified game as
one of the standard games in Solitaire
Virtuoso.
I like this even more than regular Nestor,
though I am still not good at it yet. BVS Solitaire also
included 10x10 unrectified as Double Nestor. Pretty Good
Solitaire adopted 12x8 unrectified for its version of Double Nestor.
Mah Jong
A form of computer solitaire using a set of 144 Mah Jong tiles instead
of playing cards was first developed for the PLATO system in 1981 by
Brodie Lockard. The tiles are arranged in one of a number of
three-dimensional patterns (most notably a pattern called the Turtle)
where many of the tiles are hidden. The object is to remove the
tiles in identical pairs; it is essentially a closed version of
Nestor. Since then hundreds of versions have been published
under various names on every platform imaginable, including many online
versions. The game has been analyzed by Michiel de Bondt.
There is also a similar game called Shisen-Sho (or Four Rivers) where
the pattern is a flat rectangle, but the choice of tiles is restricted
to pairs connected by a path with no more than two right-angle turns.
In recent years, versions of closed Nestor with regular cards, using long piles of cards
with only the top card face up, have become commonplace in commercial
packages of thematic solitaire. Sometimes the piles branch off into subpiles, both
branches blocked by a single card. Nestor now trails only Golf as the dominant
mechanism in campaign solitaires.
Copyright ©2011, 2021 by Michael
Keller.
All rights reserved. This file was revised on May 31, 2021.