I learned about this from the "metamagical" section in a Scientific American magazine from the 80s, good times. Apparently Uri Geller did it on tv and didn't work.
The Kruskal Count Card Trick
41–43 of 43 posts
Re: The Kruskal Count Card Trick
#42When I was a graduate student, in the late 80s, I was waiting for a flight to Los Alamos in Albuquerque. There was only one other person in the lounge, obviously also going to Los Alamos. I started chatting and he introduced himself as Martin Kruskal. Idiot me had no idea whom I was speaking to. I said “The only Kruskal I know invented this amazing card trick having to do with dynamical systems.” He stared at me, obv…
What was the advice?
One of the conversations was about reading. Let the kids read anything: comic books, fun novels, fantasy picture books. He re-assured me that they would eventually expand into other things. Martin was right.
Re: The Kruskal Count Card Trick
#43Earlier quoted context omitted.
I put together a small simulation and I think you have an 82% chance of winning with the setup described (though I welcome repeats). Replacing the J/Q/K with a score of 10 and the win rate drops to ~68%. Intuitively anything that makes you take shorter steps should increase the chance of merging with another path.
Try running it again with them set to 2. My bet would be that's also less good than 5 (but not as bad as set to 10). I'd be very interested to know if that's right or not.
I think it goes up to ~86%.
The procedure I'm using is to follow the jumps starting at each top card until you can't go any further, and count how often each following card is landed on. Then taking the max count on the last 7 cards and dividing by 9 (the max you can get to). That should be the chance you both land on the same card in the final row.
Here's a table of the results with different face card values:
Face value: 1, chance of winning 86.2%
Face value: 2, chance of winning 85.6%
Face value: 3, chance of winning 84.5%
Face value: 4, chance of winning 83.3%
Face value: 5, chance of winning 82.0%
Face value: 6, chance of winning 80.7%
Face value: 7, chance of winning 79.1%
Face value: 8, chance of winning 75.1%
Face value: 9, chance of winning 71.4%
Face value: 10, chance of winning 68.0%