Nestor and Double Nestor -- Pair Discarding Games

Thanks to Mark Masten, without whom this article would not have been possible.

One of the standard single-deck open games is Nestor, named after a mythological Greek king, one of the Argonauts. The oldest reference I can find in print is William B. Dick's 1884 revision of Games of Patience, or Solitaire with Cards.
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 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 a 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.]

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 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 than 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.]

Variations of Nestor

You can make Nestor as hard or as easy as you like by changing the number of columns; Pretty Good Solitaire includes a variant called Heracles, which is nine columns of five cards with seven reserve cards.   Vertical, which is found in some sources (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.

An interesting version of Nestor is to add jokers to the deck.   These as usual 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 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.
   
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.  [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.]

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).  Nestor, however, does not appear to have been tried as a double-deck game.  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.   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.


Copyright 2011 by Michael Keller. All rights reserved. This file was revised on July 15, 2011.