Pool Checkers - Movement of Pieces

It always better to show the rules by example.
1.c3-d4 White moves first. d6-c5
2.b2-c3 c7-d6
3.c3-b4 b6-a5
4.d4:b6 a5:c7 Checkers can jump both forward and backwards.
5.a1-b2 h6-g5
6.g3-h4 f6-e5
7.h4:d4 d6-c5
8.d4:b6 c7:a1
9.f2-g3 a7-b6
10.g3-f4 b6-a5
11.d2-c3 a1:f2 [ 11...a1:g3 is fine too. 12.h2:f4 ]
12.g1:e3 g7-f6
13.e1-d2 d8-c7
14.h2-g3 f8-g7
15.e3-d4 f6-g5
16.f4:d6 A checker does not become a king when the jump passes through the king row.
c7:e1 A checker becomes a king when jump ends in the king row.
17.g3-f4 h8-g7
18.f4-e5 e1-g3
19.a3-b4 a5:c3 There is no "jump-the-most". Choose which jump to make, but of course jump all available checkers on the chosen way.