Beggar-My-Neighbour Records

An infinite game of Beggar-My-Neighbour has been found!

Brayden Casella (10-02-2024). ∞ tricks, ∞ cards: 1: ---K---Q-KQAJ-----AAJ--J-- 2. ----------Q----KQ-J-----KA

Game loops after 474 turns and 66 tricks

We must know. We will know. We do know.

The preprint describing the infinite game and the historical search can be found here

A video description in French

Below is the historical archive of previous records for posterity.

From July 2007 to May 1 2012, I held the world record, with Nicolas Wu, for the longest ever discovered game of Beggar-My-Neighbour. Since then, Reed Nessler, Nicolas Wu, Philip Anderson and William Rucklidge have improved on the record.

I've compiled a list of known current and previous records, which you can find below.

John Conway once described the search for an infinitely-looping game of Beggar-My-Neighbour as an "Anti Hilbert Problem", one that absolutely should not drive the future of mathematics.

Michael Kleber, another previous record holder, has said, 'This is almost entirely uninteresting'.

Nonetheless, the search for a longer, or even infinite game continues. Recently Sam Williams has updated me on his progress with a novel approach.

Known Historical Beggar-My-Neighbour Records

Please let me know if you believe these are inaccurate or you have discovered a new record. Test the length of games using Matt Mayer's BeggarMyPython script.

Mark Manasse(06-06-1992). 713 tricks, 5104 cards 1. Q--J----K--K-J---Q---A---A 2. ---K-K--JA-QA--J-----Q----

Michael Kleber (before 1999). 805 tricks, 5791 cards: 1. ---JQ---K-A----A-J-K---QK- 2. -J-----------AJQA----K---Q

Michael Kleber (c. 2002). 841 tricks, 5977 cards: 1. ----QJ-A-KK--------K--QQJ- 2: ---J---K--A-----Q-AJ-A----

Michael Kleber (c. 2005). 893 tricks, 6321 cards: 1. -J--KA----A-Q--Q-A----KJ-- 2. A------QKJ--Q-------KJ----

Truman Collins (2006). 960 tricks, 6914 cards: 1. A-QK------Q----KA-----J--- 2. -JAK----A--Q----J---QJ--K-

Richard Mann and Nicolas Wu (16-07-2007). 1007 tricks, 7157 cards: 1. K-KK----K-A-----JAA--Q--J- 2. ---Q---Q-J-----J------AQ--

Reed Nessler (01-05-2012). 1015 tricks, 7207 cards: 1. ----Q------A--K--A-A--QJK- 2.-Q--J--J---QK---K----JA---

Reed Nessler (04-05-2012). 1016 tricks, 7224 cards: 1. -J-------Q------A--A--QKK- 2. -A-Q--J--J---Q--AJ-K---K--

Nicolas Wu (17-05-2012) & Philip Anderson (23-07-2013, independently). 1016 tricks, 7225 cards: 1: --A-Q--J--J---Q--AJ-K---K- 2: -J-------Q------A--A--QKK-

Reed Nessler (20-09-2013). 1014 tricks, 7259 cards: 1: ---AK-Q--J----J--QKJ-Q---- 2: ------JK-----A--K--Q---AA-

William Rucklidge (17-01-2014). 1024 tricks, 7269 cards: 1. A-AQ-----Q--K--AQ-------JJ 2. -J-A-KKJ--K-----------Q---

Philip Anderson (03-02-2014) . 1032 tricks, 7323 cards: 1. -AJ--QK--K----Q--J-A-KKJ-- 2. ---------JQ----------A-AQ-

William Rucklidge (05-03-2014). 1122 tricks, 7960 cards: 1: -J------Q------AAA-----QQ- 2: K----JA-----------KQ-K-JJK

Reed Nessler (31-08-2021). 1106 tricks, 7972 cards: 1: ----K---A--Q-A--JJA------J 2: -----KK---------A-JK-Q-Q-Q

Reed Nessler (09-06-2022). 1164 tricks, 8344 cards: 1: ---AJ--Q---------QAKQJJ-QK 2: -----A----KJ-K--------A---