Warning: This is probably one of the most boring pages ever created. I generated the data for this page as part of a contest I entered in 1991. On the slight chance that anyone is ever interested I figured I might as well put it on the net. Incidentally, I came in second place in this contest and won a year's subscription to a journal.
Beggar Your Neighbor (also know as Beggar Thy Neighbor or Beggar My Neighbor) is a British card game for two people. It's similar to the kid's card game War, where the winner is pre-determined by the deal and no skill is involved. The game is played by Pip and Estella in the book "Great Expectations" by Charles Dickens.
The rules are very simple and are summarized here:
A standard deck of cards is fully dealt between the two players. A person is chosen to start play and from then on the players alternate.
The person whose turn it is (player1) takes the top card off of his deck and places it face up in the middle of the playing area onto the trick stack. If this card is a normal card (from two to ten), play passes to the next player (player2).
If the card is a court card (Jack, Queen, King, or Ace), then things get a bit more interesting. Player2 now must place up to a predetermined number of cards on the trick stack. The number is determined by the court card played by the previous player (one for a Jack, two for a Queen, three for a King, four for an Ace). He plays cards one by one off of his deck. If each one is a normal card, then as soon as he's done playing these cards, his opponent (player1) takes the trick stack, places it on the bottom of his deck, and plays again. If while playing the cards, player2 plays a court card himself, then the other player (player1) is in the same position as player2 was after player1 played the first court card.
The first person who runs out of cards is the loser, and the other player takes any cards in the trick stack.
Another explanation of the rules is available at a site associated with the book "Great Expectations".
In November of 1991, Chris Long initiated a contest to see who could find the initial hand that would go the highest number of rounds before the game ended. A round was counted whenever the trick stack was picked up. I believe his interest was to find if it was possible for there to be a card configuration where there was a cycle so that the game would never end.
I wrote a program to churn through random hands, playing them out and keeping track of how many rounds each resulted in. The contest ran for about 6 weeks, and I managed to find one that went 703 rounds. It turned out that I came in second to someone who found one that went 706 rounds. I later improved my program a little and have run it occasionally in the background on my computer. I have since found two initial deck configurations that result in a game going 769 rounds and lots of others that are shorter than that but still very long. I'm quite sure that the 769 round games are the longest ever found. I thought I'd make them available on the net on the off chance that anyone's interested.
I've actually run two separate programs. One generates purely random hands, while the other generates hands that have about the same number of court cards in each hand. The second tends to generate somewhat longer running deals on average.
With the program that generated purely random hands, I kept track of the length in rounds of each game. After analyzing 369,400,000,000 games, here are some interesting statistics: The most common number of rounds for a game is 11, which happens 2.70150068% of the time. In 0.00001602% of the time, the game ends after only one round! I've put an example of one of these one round games at the bottom of this page. Just over 50% of the time, the game ends after from 6 to 28 rounds. Incidentally, the total number of possible deals that are distinct from the game's point of view (swapping a 9 of hearts and a 2 of clubs wouldn't change the outcome) is 653,534,134,886,878,245,000. It's equal to 52!/(4!*4!*4!*4!*36!), which is the number of permutations of 52 cards divided by the number of permutations of the aces and of the kings, and of the queens, and of the jacks, and of the other cards.
In total, my programs played through 738,640,000,000 randomly generated games. Below are all of the ones I found where the resulting games go on for 700 rounds or more. The deck order is top to bottom. Aces, Kings, Queens, and Jacks are denoted by 'A', 'K', 'Q', 'J', respectively, and all other cards are denoted by a '0'.
Tricks taken = 769 Winning player = 2 Player 1 Deck = 00000J000Q000A00JJ00QKQ000 Player 2 Deck = K00AK000000A00A00K0Q0J0000 Tricks taken = 769 Winning player = 1 Player 1 Deck = A000Q00JQ00A000J00000Q000K Player 2 Deck = A0JJKK00A00000Q00000000K00 Tricks taken = 757 Winning player = 1 Player 1 Deck = 00000QKJ0J0JK00QA0000J0Q0Q Player 2 Deck = 000000K000000000AAK0000A00 Tricks taken = 746 Winning player = 1 Player 1 Deck = 0A0Q00JAA00Q000000J0K000KK Player 2 Deck = 000J00000Q00000000K000JQA0 Tricks taken = 734 Winning player = 1 Player 1 Deck = Q00A0K000A0J000K00Q0000K00 Player 2 Deck = Q00J0000Q0JJ00000A0K000A00 Tricks taken = 731 Winning player = 1 Player 1 Deck = 00K0K0J000000J00QA00A0000J Player 2 Deck = A0JK0000000QQ0000Q000KA000 Tricks taken = 728 Winning player = 2 Player 1 Deck = 0QQ0A0000Q000KJA000J000000 Player 2 Deck = 00000000JKK0A00JK000A0Q000 Tricks taken = 727 Winning player = 2 Player 1 Deck = 00K0000000Q00J0A000Q000JKJ Player 2 Deck = 0A0K000Q000J00Q0A00K0000A0 Tricks taken = 726 Winning player = 2 Player 1 Deck = Q0Q0K000JJ0J00K00000000000 Player 2 Deck = 000K0A00K0000J0QA0Q0000AA0 Tricks taken = 722 Winning player = 2 Player 1 Deck = 0000JJA000A00K00000000KQ0A Player 2 Deck = AK00000J000000J0Q0K000Q0Q0 Tricks taken = 718 Winning player = 1 Player 1 Deck = 000000QJ00K0K0Q0Q0J0000000 Player 2 Deck = J0A0A00000000KA0QJ000A0K00 Tricks taken = 714 Winning player = 2 Player 1 Deck = 000000QQ000A00J000K000K0JA Player 2 Deck = 0000000K0000Q00JA0A00JK00Q Tricks taken = 713 Winning player = 1 Player 1 Deck = A000K000J0KJ00JJ0000000Q0K Player 2 Deck = QQ000K000A0Q00A00000000A00 Tricks taken = 713 Winning player = 1 Player 1 Deck = 00Q000000QK0A0J00A0J0000A0 Player 2 Deck = KQKQ00J00J0K0000000000000A Tricks taken = 713 Winning player = 2 Player 1 Deck = 000Q000JK0000000JAQ00000A0 Player 2 Deck = 000000Q0KQK0000AAK0000J0J0 Tricks taken = 712 Winning player = 1 Player 1 Deck = A000000QJ0A0000000000J0K0A Player 2 Deck = 0AQQK0000J00000JK0000KQ000 Tricks taken = 712 Winning player = 1 Player 1 Deck = 000A000A0J000QA0Q0K000K0A0 Player 2 Deck = JK0JK0JQ0000Q0000000000000 Tricks taken = 708 Winning player = 1 Player 1 Deck = 00A00JAK000J00K000000Q00A0 Player 2 Deck = 000A00Q00KJ000QK000J0000Q0 Tricks taken = 707 Winning player = 2 Player 1 Deck = J00KQ000000000QA0K0000A00J Player 2 Deck = KK0J0000000QJ0AQ00A0000000 Tricks taken = 706 Winning player = 1 Player 1 Deck = 000A000J00000000KJ00JQA0AK Player 2 Deck = 00000000QJ0000QK0QK000000A Tricks taken = 704 Winning player = 1 Player 1 Deck = AQ000000J00000J0K0Q0Q00000 Player 2 Deck = 00AK0Q00JJ000000000K0A0A0K Tricks taken = 703 Winning Player = 2 Player 1 deck = 00KQ0Q0JA0KJ000Q000A000A00 Player 2 deck = 000Q0000J00000A00JK0K00000 Tricks taken = 701 Winning player = 1 Player 1 Deck = 00JA00Q000K0JA0000000K00A0 Player 2 Deck = 0K0000Q0JJQ00000000QAK0000 Tricks taken = 701 Winning player = 2 Player 1 Deck = 0A000J0J000AK000J00A000KK0 Player 2 Deck = JA0000Q00QK00000Q00Q000000
Here are four examples of configurations where one of the players wins by taking all of the other's cards in the first round:
Tricks taken = 1 Winning Player = 1 Player 1 deck = 0000000K00Q000J00Q00JQK000 Player 2 deck = 00000000K0AA0AQJA000000KJ0 Tricks taken = 1 Winning Player = 1 Player 1 deck = 0000000000000KA00J0JJ0K00Q Player 2 deck = 0000000000000Q00AKKA0AQJQ0 Tricks taken = 1 Winning Player = 2 Player 1 deck = 0000000000KA00Q00KAAQ0J00Q Player 2 deck = 000000000J00J00KA0Q0K000J0 Tricks taken = 1 Winning Player = 2 Player 1 deck = 0000000000A0Q00JAKKQ00A0J0 Player 2 deck = 000000000000Q0KK0J0J0Q0A00
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