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%