Does an infinite game of Beggar-My-Neighbour exist?
Yes!
This question has definitely not plagued scientists for millennia. However, in the event that you think you have found a very long game of Beggar My Neighbour, you might wish to run it through a Beggar My Neighbour simulator written in Python. You can see a full list of record holders here: http://richardpmann.weebly.com/beggar-my-neighbour-records.html
In 2024, Brayden Casella finally found an infinite game. You can read about his methodology in this paper.
Usage:
python test.py
Output:
Paulhus 1999:
Starting hands: ------------KAQ----J------/-JQQK---K----JK--QA-A-JA--
There were 4791 turns
There were 670 tricks
Kleber 1999:
Starting hands: ---JQ---K-A----A-J-K---QK-/-J-----------AJQA----K---Q
There were 5790 turns
There were 805 tricks
Collins 2006:
Starting hands: A-QK------Q----KA-----J---/-JAK----A--Q----J---QJ--K-
There were 6913 turns
There were 960 tricks
Mann and Wu 2007:
Starting hands: K-KK----K-A-----JAA--Q--J-/---Q---Q-J-----J------AQ--
There were 7157 turns
There were 1007 tricks
Nessler 2012:
Starting hands: ----Q------A--K--A-A--QJK-/-Q--J--J---QK---K----JA---
There were 7207 turns
There were 1015 tricks
Anderson 2013:
Starting hands: --A-Q--J--J---Q--AJ-K---K-/-J-------Q------A--A--QKK-
There were 7225 turns
There were 1016 tricks
Rucklidge 2014:
Starting hands: -J------Q------AAA-----QQ-/K----JA-----------KQ-K-JJK
There were 7959 turns
There were 1122 tricks
Nessler 2021:
Starting hands: ----K---A--Q-A--JJA------J/-----KK---------A-JK-Q-Q-Q
There were 7972 turns
There were 1106 tricks
Nessler 2022:
Starting hands: ---AJ--Q---------QAKQJJ-QK/-----A----KJ-K--------A---
There were 8344 turns
There were 1164 tricks
Brayden Casella 2024:
Starting hands: ---K---Q-KQAJ-----AAJ--J--/----------Q----KQ-J-----KA
Game appears to be infinite, loop detected after 474 turns and 66 tricks
If you care about the non-court cards then you have to wait longer for the loop to occur. Passing the substituteValuesForNonCourtCards flag lets you quickly test this by replacing the - with greek and cyrillic letters.
Including unique non-court cards:
Starting hands: αβγKδεζQηKQAJθιλμνAAJξοJπρ/αβγδεζηθιλQμνξοKQπJρστυφKA
Game appears to be infinite, loop detected after 33034 turns and 4654 tricks
We already knew about alternate versions of the game that do not terminate, entering an infinite loop. For example the Italian game of Camicia uses a 40-card deck and no draw-4 cards (aces).
Carmicia
Starting hands: --Q------QJ----JK---/---Q---J-Q-KJ--K-K--
Game appears to be infinite, loop detected after 197 turns and 37 tricks
While this Python code is fine for verifying a single game, if you wish to test large numbers of games to beat the current records, you almost certainly want to use a faster compiled language.