[ Editor: Two players each hold all the cards of one suit; on each trick both lay a card face down, the...

My recollection of this game [ Editor: omitted here: "(although I've
not been able to locate the reference)" ] is that it was called GOPS
(standing for Game Of Pure Strategy) [ Editor: omitted here: ", but
that it had an important complication that you don't mention (and one
that makes it MUCH more interesting to play)" ].  A third suit is used as the values for the
tricks.  In the random version, it is shuffled, and the cards in this
suit are revealed one at a time.  For each one, the players "bid" with
the cards remaining in their own suit, and the person bidding the
highest wins the card being bid for.  If we let Ace count as 1, up to
King counting as 13, then the total to be bid for is 91.  Furthermore,
in the version that I play, ties are not discarded but become part of
what is being bid for on the next round.  The only time not all the
cards will be won by some player is when there is a tie on the last
round.

Two comments.  First, in actual play, I have found that the following
strategy works well against beginners: bid two higher than the value
of the card being bid for (bid 3 for 1, 4 for 2, ... 13 for 11, 1 for
12 and 2 for 13).  This will likely result in your losing the 13 and
the 12, but that is only 25 points, and you'll win most of the rest.
Of course, once the game gets near the end, you can exactly analyze
the possibilities to maximize your score (e.g., if you have cards 7
and 8 left, and the other guy has 4 and 7, then obviously you bid 7
first, and you'll win both cards, but if you bid 8 first you might tie
on the last card).  One point of protocol: the cards that have been
used in the bidding are discarded but left face up, so that players
need not have good memories, only good analytic abilities!

Second, several years ago I had a computer analyze this game, under
the assumption that the cards came up in some fixed order, for
n=1,2,3,4,5,6 (rather than n=13), using the techniques of 2-person
zero-sum game theory (see The Compleat Strategyst by J. D. Williams
(revised edition published by McGraw-Hill, 1966) for a good
introduction to the subject).  The results were interesting.  Assume
that the prize cards come up in the order 6,5,4,3,2,1.  Then at your
first turn you should play your 6 58% of the time, your 3 26% of the
time, and your 4 16% of the time.  Using this strategy, your opponent
cannot expect to beat you in the long run (i.e., over many plays of
the game), and if he is not also using the game-theoretic best
strategy, then you will win more often than not.  For example, if the
opponent always plays 5 to the first trick, then the strategic player
will win 62% of the time, if he continues to use the strategy that the
theory calls for (of course, he needs to have the computer analyze
each position as it comes up and compute the probabilities for his
play at each turn).

-- Jerrold W. Grossman <grossman@vela.acs.oakland.edu>

The game is called "gops" (Game Of Pure Strategy) and is best played
with two players although it can be played with three.

The rules of the game are simple: Player A is given all of the
diamonds, player B is given all of the hearts and all of the spades
are placed in a pile between the two players.  Each card is valued as
its pip value, 2, 3, 4, etc. [ Editor: "etc" in the original ], Ace is 1 and Jack, Queen, and King count
11, 12 and 13.

A spade is turned over and shown to both players.  Each player bids
for the spade by taking a card out of his hand and placing it face
down on the table.  The cards are then turned over and the highest
card played (heart or diamond) gets to keep the spade; [ Editor: "," in the original ] if a tie occurs
then the spade is not kept by either player.  Cards are only used
once.  After all 13 cards have been played, the winner [ Editor: "winer" in the original ] is determined
by who has the greatest total spade points.

The strategy is simple: Based on previous play, determine what card
your opponent is going to play and then play 1 higher.  If he plays a
King then play your Ace.  In this manner he will get one trick (at
most 13 points) you will take all the rest and beat him 114 to 13.

[ Editor: the spades total 1+2+...+13 = 91 points, so the score would
be at least 78 to at most 13. ]

The three man game is similar, each player gets all of the hearts,
diamonds, and clubs.  A clear winner keeps the spade, a three way tie
tosses the card out, and if a two way tie occurs, the spade is placed
in a pile between the two winning players.  In the final count, the
value of the pile is split two ways between the winning players, with
each player getting half the points.

-- Bert Sheldon <berts@empros.com>