[IanCal]

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.

[regularfry]

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.

[IanCal]

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%

[IanCal]

I'll try when I get home but I'd be shocked if that's the case. They're more likely to merge at an earlier point as paths now have shorter jumps.

[throwaway2016a]

I wonder then why not make face cards a 2 or something. Perhaps that would make it more obvious what is going on?