Add a finiteness test

[alessandro-gentilini]

Hello Mr. Mayer,
thank you for your program that is the standard de facto for the quest to infiniteness of Beggar my Neighbour.

I am from Italy where we play "Camicia" which is described by Marc M. Paulhus^a in this way:

For the record, the Italian game of "Camicia" is played with a 40 card deck with 12 court cards (4 each of values 1, 2, and 3). Playing a billion random deals of Camicia also failed to produce any cycles.

Some years ago I was an avid seeker but then I stopped the quest and now to my surprise I found that Camicia was declared non terminating in 2016^b and in 2017^c.

My ancient C++ code confirmed the infiniteness but it is a rat nest and so I am proposing you to add a finiteness test to your program, my proposal is very simple but I am not 100% sure it is correct.

P.S. I forgot a print(finite) as a last line.

All the best,
Alessandro

^a_{Marc M. Paulhus (1999) Beggar My Neighbour, The American Mathematical Monthly, 106:2, 162-165, DOI: 10.1080/00029890.1999.12005024}
^b_{See https://cstheory.stackexchange.com/questions/22175/does-this-game-terminate/52560#52560}
^c_{See see https://github.com/drago-96/cavacamisa/blob/master/infinite/20170217.txt and https://github.com/drago-96/cavacamisa}

[matthewmayer]

Thanks! do you have a sample of a starting hand which causes an infinite loop?

[alessandro-gentilini]

Hello!
Starting hands: --3-2-2-3-31-----31-/--1--2----2-------1-.

Since Camicia has different cards, in order to test it, I modified your penalty_value_of function in this way:

def penalty_value_of(card):
    values = {"1":1,"2":2,"3":3}
    return values[card]

[LeoDog896]

By the way, I made a faster simulator (written in Rust): https://github.com/LeoDog896/beggar-my-neighbour

It handles these cases a lot faster.

[matthewmayer]

For sure python is a terrible choice if you want something fast enough to check large numbers of games!