What deal of two-player Beggar Your Neighbor gives the longest game (the most tricks), and can a game go on...

As far as I know very little is actually known about Beggar Your
Neighbor.  A short note appears in Beasley's _The Mathematics of
Games_, and rumor has it that John Conway offers $100 for an infinite
trick hand (or proof that none exists).  The official rules of the
Great Usenet Beggar Your Neighbor Contest and the results are given
below.

{Rules}

There have been some more questions as to the exact rules to BYN, so
I'll rewrite what Beasley wrote for greater clarity.  I'm only going
to handle the two-player version, since the contest I'm running only
deals with that.

  Each person is dealt 26 cards from a standard deck.  Each player
  places their cards in a stack face-down in front of themselves.
  The play: the player turns the top card in their stack face-up
  in the middle of the playing area onto the trick stack.  If this
  card is a plain card (two to ten inclusive), play passes to the
  next player.  If this card is a court card (Jack, Queen, King,
  Ace) the other player must now play repeatedly until they either
  have laid down a certain number of plain cards (one if the court
  card was a Jack, two if a Queen, three if a King, and four if an
  Ace) or until they play a court card.  In the former case the
  player who played the court card picks up the trick, puts it on
  the bottom of their stack, and plays again; in the latter, the
  other player must now play to the new court card in the same way.
  The first person who can't play is the loser, the other player
  is the winner and wins the remaining cards as the final trick
  (if the trick stack is empty consider them as winning a trick
  anyway - this is a very minor point).

Beasley had a slightly different end condition, but the one above
makes more sense (and is the end condition I learned as a kid).
Again, this makes little difference in actual play.

{Question}

Q: If a player can't make a move, does the winning player take the
cards left in the trick stack and count that as a trick?
A: Yes.  In fact, even if there aren't *any* cards left in the trick
stack count the winning player as winning a trick (if there aren't
any cards in the trick stack, they win the "empty" trick).

{Results - in the initial hands 4 is an ace, 3 is king, etc., 0 is
plain}

The winner:

Mark S. Manasse (msm@pa.dec.com) with 713 tricks:

20010000300301000200040004
00030300140240010000020000

In close second was Truman Collins (tcollins@std.mentorg.com) with 703
tricks:

00320201403100020004000400
00020000100000400130300000

ath@linkoping.trab.se was third with 623:

04000030330000001000120000
00024000024000201040030001

Scott "TCB" Turner (srt@aero.org) claims to have a 610 trick hand,
which would make him fourth, but I have been unable to verify this.

Mark wins a year subscription to _Games Magazine_, _The Journal of
Recreational Mathematics_, or _The Fibonacci Quarterly_ (his choice),
and I've also decided to award puzzles and books to the top four
finishers.

-- Chris Long <clong@cnj.digex.com>  (November 1993)