Beggar-my-neighbour

{{Short description|Card game}} {{about|the card game|the British sitcom|Beggar My Neighbour (TV series)|the economic policy|Beggar thy neighbour}} {{Use British English|date=December 2024}} {{Infobox card game | title = Beggar-my-neighbour | subtitle = | image_link = Pack of playing cards whitebg.jpg | image_caption = Cards are dealt from face-down stacks | alt_names = Strip jack naked, draw the well dry, beat your neighbour out of doors, beat jack out of doors | type = Adding-up-type | players = 2+ <ref name=Guardian20081122>[https://www.theguardian.com/lifeandstyle/2008/nov/22/rules-card-games-beggar-neighbour Beggar my neighbour], The Guardian, 22 November 2008</ref> | play = Clockwise | card_rank = | ages = | num_cards = 52 | deck = [[Playing card#French|French]] | origin = | related = [[War (card game)|Battle]]{{*}}[[Egyptian Ratscrew]] | playing_time = usually <15 minutes per hand | random_chance = Complete | skills = [[Counting]] | footnotes = }} '''Beggar-my-neighbour''', also known as '''strip jack naked''', '''beat your neighbour out of doors''',<ref name=Guardian20081122 /> or '''beat jack out of doors''',<ref>{{cite web|url=http://www.hipsfinder.com/finder_2fish.php?record=1117 |title=HIPS Finder Ltd |access-date=2020-09-20}}</ref> or '''beat your neighbour''',<ref>"Beat Your Neighbour" in {{cite book|date=2018|title=50 Card Games: 50 Popular Card Games for Hours of Fun|publisher=Igloo Books|page=17|isbn=9781784409852}}</ref> is a simple choice-free [[card game]]. It is somewhat similar in nature to the children's card game [[War (card game)|War]], and has spawned a more complicated variant, [[Egyptian Ratscrew]].

== Origins == The game was likely invented in [[United Kingdom|Great Britain]] and has been known there since at least the 1840s.<ref>{{cite web|url=https://archive.org/details/disgracetofamil00jerrgoog |title="his shop-boy, seated across an empty sugar-tub, was playing a game of 'Beggar-my-neighbor'" ''The Disgrace to the Family'' Chapter IV |access-date=2016-09-09}}</ref>

It may be the same as '''beat the knave out of doors''' or '''knave out o' doors''', in which case it is much older as this game is mentioned as early as 1755.{{sfn|Smith|1755|p=15}}

Beggar-my-neighbour appears as a children's game in 19th-century British novels such as [[Charles Dickens]]'s ''[[Great Expectations]]'' (1861).<ref>{{cite web |url=http://www.19thnovels.com/greatexpectations.php?c=8 |title="I played the game to an end with Estella, and she beggared me." ''Great Expectations'' Chapter 8 |publisher=19thnovels.com |access-date=2009-10-29 |archive-url=https://web.archive.org/web/20090925153042/http://www.19thnovels.com/greatexpectations.php?c=8 |archive-date=2009-09-25 |url-status=dead }}</ref>

== Play == A [[standard 52-card deck]] is shuffled and then divided equally between two players, and the two stacks of [[playing card|cards]] are placed on the table face down. The first player lays down their top card face up to start a central pile, and the opponent plays their top card, also face up, on it, and this goes on alternately as long as no [[Ace]] or [[court card]] ([[King (playing card)|King]], [[Queen (playing card)|Queen]], or [[Jack (playing card)|Jack]]) appears. These cards are called "penalty cards".

If either player turns up such a card, their opponent has to pay a penalty: four cards for an Ace, three for a King, two for a Queen, or one for a Jack. They do this playing the required number of cards to the central pile. When they have done so, if all the cards are numerals, the player of the penalty card wins the hand, takes all the cards in the pile and places them under their pack. The game continues in the same fashion, the winner having the advantage of placing the first card. However, if the second player turns up another Ace or court card in the course of paying to the original penalty card, their payment ceases and the first player must pay to this new card. This changing of penalisation can continue for some time. When a single player has all of the cards in the [[Playing card|deck]] in their stack, they have won.

For more than two players, play proceeds clockwise. If a player reveals a new penalty card while paying their penalty, the next player around pays the tax.<ref name=Guardian20081122 />

== Game theory == There are 653,534,134,886,878,245,000 (approximately 654 quintillion) possible initial states for a game of beggar-my-neighbour.<ref>Remy, [https://math.stackexchange.com/a/2688359/1184658 Beggar-my-neighbour possible games]. Retrieved 2023-08-07</ref> {{asof|2024|2}}, the longest game known that does terminate is 1164 tricks long, where the cards of the deck are played a total of 8344 times. It was found by Reed Nessler.<ref name=":0"> {{cite web |author=Richard P Mann |title=Known Historical Beggar-My-Neighbour Records |url=https://richardpmann.com/beggar-my-neighbour-records.html |archive-url=https://web.archive.org/web/20250727012249/https://www.richardpmann.com/beggar-my-neighbour-records.html |archive-date=2025-07-27 |access-date=2024-02-10}}</ref>

Whether there is a game of beggar-my-neighbour that goes on forever was a longstanding question in [[combinatorial game theory]]. Some smaller decks of cards have infinite games, such as [[Camicia (Card Game) | Camicia]],<ref>Alessandro Gentilini, [https://github.com/matthewmayer/beggarmypython/pull/5#issue-1617788484 I found that Camicia was declared non terminating]. Retrieved 2023-08-07</ref> while others do not. [[John Horton Conway|John Conway]] once listed this among his anti-[[Hilbert problems]],<ref> {{cite encyclopedia |url= https://archive.org/details/moregamesofnocha0000unse |title= Unsolved Problems in Combinatorial Games |format= PDF |last1= Guy |first1= Richard K. |author-link1= Richard K. Guy |last2= Nowakowski |first2= Richard J.  |encyclopedia= More Games of No Chance |isbn= 0521808324 |series= MSRI Publications |volume= 42 |date= 25 November 2002  |access-date= 2018-12-03 |publisher= [[Cambridge University Press]]  |quote= This problem reappears periodically. It was one of Conway’s ‘anti-Hilbert problems’ about 40 years ago, but must have suggested itself to players of the game over the several centuries of its existence. |url-access= registration }}</ref> open questions whose pursuit should emphatically ''not'' drive the future of mathematical research.

For a two-player game, a starting distribution of cards that leads to an infinite game was first found by Brayden Casella and reported on 10 February 2024.<ref>{{Citation |last=Casella |first=Brayden |title=A Non-Terminating Game of Beggar-My-Neighbor |date=2024-03-19 |url=http://arxiv.org/abs/2403.13855 |access-date=2024-03-23 |last2=Anderson |first2=Philip M. |last3=Kleber |first3=Michael |last4=Mann |first4=Richard P. |last5=Nessler |first5=Reed |last6=Rucklidge |first6=William |last7=Williams |first7=Samuel G. |last8=Wu |first8=Nicolas}}</ref><ref name=":0" /> The cyclic game begins {{Code|---K---Q-KQAJ-----AAJ--J--}} and {{Code|----------Q----KQ-J-----KA}}. This happens because the game is eventually periodic—that is, it eventually reaches some [[state (computer science)|state]] it has been in before.

==In popular culture==

In the 1854 novel [[Hide and Seek (Collins novel)|''Hide and Seek'']] by [[Wilkie Collins]], Zach Thorpe and Matthew Grice kill time by playing beggar-my-neighbour "for [[Sixpence (British coin)|sixpence]] a time."

In [[Charles Dickens]]' 1861 novel ''[[Great Expectations]]'', the game is the only one known by the boy protagonist ([[Pip (Great Expectations)|Pip]]) as a child.

== References == {{reflist}}

== Bibliography == {{Wikisource1911Enc|Beggar-my-neighbour}} * {{cite journal | author=Marc Paulhus | title=Beggar My Neighbour | journal= The American Mathematical Monthly | year=1999 | volume=106 | issue=2 | pages= 162–165 | doi=10.2307/2589054 | publisher=Mathematical Association of America | jstor=2589054}}. * {{Cite book | last1 = Morehead | first1 = Albert H. | last2 = Frey | first2 = Richard L. | last3 = Mott-Smith | first3 = Geoffrey | title = The New Complete Hoyle Revised: The Authoritative Guide to the Official Rules of all Popular Games of Skill and Chance | publisher = [[Doubleday (publisher)|Doubleday]] | year = 1991 | location = London, New York, Sydney, Auckland, Toronto | page = 456 | isbn = 0-385-40270-8 }} * {{cite book |last1=Smith |first1=Gyles |title=Serious Reflections on the Dangerous Tendency of the Common Practice of Card-playing;: Especially of the Game of All-Fours, as it Hath Been Publickly Play'd at Oxford, in this Present Year of Our Lord, MDCCLIV. in a Letter from Mr. Gyles Smith, to His Friend Abraham Nixon, Esq; of the Inner Temple. |date=1755 |publisher=W. Owen, at Homer's Head near Temple-Bar. |location=London |url=https://books.google.com/books?id=IYJbAAAAQAAJ&pg=PA15 |language=en}}

== External links == * [https://www.pagat.com/war/beggar_my_neighbour.html ''Beggar My Neighbour''] at [[pagat.com]].

[[Category:Catch and collect games]] [[Category:Card games introduced in the 1860s]] [[Category:War group]] [[Category:Round games]] [[Category:Card games for children]]