[pbmserv] Broadcast from kiwibill via PBM Server

[pbmserv@gamerz.net]

BEAT IT OR EAT IT
=================

I am writing to describe a game that I've been quite fascinated by,
for a long time. Not many other folk have been though, and I'm hoping
to get people interested in it, so that we might play some games,
or even do some analysis with like-minded folk.        Hopefully,
we may eventually get it onto the server, if there is enough interest.

It is a game that we used to play quite a bit at coffee breaks back
in the late 60's at Cambridge, when Conway was doing a lot of his
initial investigations into numbers and games.   Although he was
quite interested, he never went far into it, and AFAICS it isn't
even mentioned in Winning Ways.

One of the reasons is, it is a card game; but one with NO ELEMENT OF LUCK,
so (theoretically) it falls with in the purview of CGT. But, being based on
traditional card games, it is still rather more card-like than board-like
in move mechanics, and doesn't really seem to have much overlap with CGT,
even less than does (say) chess.


Well then, to the game.  It was originally called "Besicovitch's Game",
after him who brought it to us (based on similar traditional Russian games),
or "Finchley Central" after a silly joke; but I have dubbed it either
"See-Saw" or "Beat It Or Eat It" - both rather more descriptive.

The rules:-

-----------------
BEAT IT OR EAT IT
-----------------

1.  A half-pack, of 13 cards in each of 2 suits, is dealt randomly and
    arranged so that one player has exactly those spades that the other
    has hearts, and vice versa.

2.  The starter plays any one of his cards onto the table.

3.  The receiver may either, at his own choice,

     (i) cover it with a higher card of the same suit (beating it),
         and play any card of his own, whereupon the other player
         becomes the receiver and continues as in (3);

or  (ii) pick it up, together with any other cards on the table (eating it),
         in which case the other player restarts as in (2).

4.  Play continues thus until one player has no cards in his hand, so winning.
------------------

Note: option 3(ii) is always possible, and may be compelled if the opponent
----  plays a very high card.   Note also that it is possible to win either
by covering the previous card with your last, or by leading your last card.


That describes the "standard version", with two suits.
The original version had all four suits, two of which were "trumps";
I have discarded the trump notion altogether, as it was rather a side issue.
Obviously the game can be played with any length suits, not just 13;
playing with real cards allows "suit" lengths up to 26 long.

It is also possible to play with a different number of suits;
three or four suits are quite feasible, and so is one.
The 1-suit game is particularly intriguing, and in some sense the "purest".

Note rule 1 does induce an element of randomness, but only in the starting
set-up; after that it is complete information (the cards are played face up
if physical cards are being used).  The starting distribution is symmetric,
e.g.  AJt86432 & KQ975   vs   KQ975 & AJt86432,   which can be achieved
(while maintaining randomness otherwise) by various unimportant methods.
One could eliminate the randomness entirely by using a "standard" set-up,
(though this seems unnecessarily restrictive), or by some (joint) choices.

The pile of cards in the middle grows constantly while the players are
covering and leading cards, until someone picks them all up, and the
other one leads off again.   Note that one may elect to pick up all
the table cards even though one might be able to beat the last card played.
Knowing when it is wise to do this, is one of the chief elements of the game!


As I said, we used to play it quite a bit long ago; we discovered a few
various rules of thumb, but nothing very systematic.  I feel there is
quite a heap of theory to be discovered.  I have played some games
by email with a board-game e-friend, but I think a wider clientele
is in order. So I am keenly hoping some of you will be interested.

In any event, may I urge you to play a few games against yourself,
with real cards on a desk? Say with one suit of 13 cards, (traditionally
AKQJt98765432 from high to low).  That way, you may discover some hints
of the depth lurking there.  It is a very tricky game to play well,
and has a lot of NEGATIVE FEEDBACK in it! You have to get rid of all
your cards, but as soon as you get rid of some, this leaves you with
less control over the play!

Hence the negative feedback, as the alternate name "Seesaw" suggests.

If anyone wants to try a game or two with me, please email me directly
with your first lead from this board, altering the board accordingly:-


-------------------------------------------------------------
Bill  -   Hearts: K Q 9 8 7 4 2     Spades: A J t 6 5 3

Table -  .

You   -   Hearts: A J t 6 5 3       Spades: K Q 9 8 7 4 2
-------------------------------------------------------------


It is usually, but not always(!), an advantage to start.

Bill Taylor.   (kiwibill)           W.Taylor@math.canterbury.ac.nz