Fast Track: ranking the squares

Every square a red piece can stand on, ranked best first. The squares count the way to B3, as once B4 is taken, with a free face card allowed first. The table is printed by roc-apps/fasttrack/rank_board.roc from Reach.routes_with.

The rules, in order:

1. Fewer cards to B3, with every card but the joker.
2. Among equals, a base square first, the deeper first.
3. More routes. A route is every shortest sequence of moves, where a move is a card, or a face card then a card. For a square one card out, that is just its ways in: R1's two are F+5 and 6.
4. While still tied, rules 1 and 3 again (fewer cards, then more routes) with a smaller deck at each stage: - without the 6; - without the 7; - without the 4; - without the J, Q and K, which also takes away the free face card. This comes late, so that face + 8 still counts as a cheaper play than face + 7; - last, without the 9 and 10, so a square reached with a 2 or 3 beats one reached with a 9 or 10.

Each cell below is cards / routes with that stage's deck. A - means the square cannot reach B3 at all with that deck: the bullseye needs a J, Q or K to leave.

What still ties

• Green's fast-track square and purple's L4, and blue's fast-track square and purple's L3: identical at every stage.
• The four pen squares, which are the same square.

How the last two stages split things:

• R4 beats R3. At the "no 7" stage R3 loses its face + 7 route, and R4 keeps face + 8.
• DS, then purple's fast-track square, then R4. Without the 9 and 10, DS is still one card, a 3. Purple's fast-track square needs 2 cards, with 3 routes. R4 needs 2 cards, with 2 routes.

The ranking

square	no joker	no 6	no 7	no 4	no J/Q/K	no 9/10
rB3	0 / 1	0 / 1	0 / 1	0 / 1	0 / 1	0 / 1
rB2	1 / 4	1 / 4	1 / 4	1 / 4	1 / 1	1 / 1
rB1	1 / 5	1 / 5	1 / 5	1 / 5	1 / 1	1 / 1
rDS	1 / 2	1 / 2	1 / 2	1 / 2	1 / 1	1 / 1
pFT	1 / 2	1 / 2	1 / 2	1 / 2	1 / 1	2 / 3
rR4	1 / 2	1 / 2	1 / 2	1 / 2	1 / 1	2 / 2
rR3	1 / 2	1 / 2	1 / 1	1 / 1	1 / 1	1 / 1
rR1	1 / 2	1 / 1	1 / 1	1 / 1	2 / 3	2 / 3
rR2	1 / 2	1 / 1	2 / 25	2 / 22	2 / 2	2 / 2
rR0	1 / 1	1 / 1	1 / 1	1 / 1	1 / 1	1 / 1
gFT	1 / 1	1 / 1	1 / 1	1 / 1	2 / 6	2 / 2
pL4	1 / 1	1 / 1	1 / 1	1 / 1	2 / 6	2 / 2
rBR	1 / 1	1 / 1	1 / 1	1 / 1	2 / 3	2 / 3
bullseye	1 / 1	1 / 1	1 / 1	1 / 1	-	-
bFT	2 / 48	2 / 43	2 / 39	2 / 39	2 / 4	3 / 12
pL3	2 / 48	2 / 43	2 / 39	2 / 39	2 / 4	3 / 12
rFT	2 / 44	2 / 38	2 / 34	2 / 34	2 / 4	2 / 2
pL2	2 / 34	2 / 28	2 / 24	2 / 24	2 / 4	2 / 2
gL4	2 / 31	2 / 29	2 / 27	2 / 27	3 / 12	3 / 2
pL1	2 / 24	2 / 17	2 / 14	2 / 14	2 / 2	3 / 9
pL0	2 / 22	2 / 14	2 / 10	2 / 10	2 / 2	3 / 7
pHH	2 / 22	2 / 14	2 / 7	2 / 7	2 / 1	2 / 1
bL4	2 / 21	2 / 18	2 / 16	2 / 16	3 / 4	4 / 12
pDS	2 / 20	2 / 14	2 / 6	2 / 6	2 / 2	3 / 3
rL4	2 / 18	2 / 15	2 / 13	2 / 13	3 / 4	3 / 2
pBR	2 / 16	2 / 14	2 / 8	2 / 8	2 / 3	3 / 6
pR0	2 / 12	2 / 12	2 / 10	2 / 10	2 / 2	3 / 3
pR1	2 / 9	2 / 9	2 / 9	2 / 8	2 / 1	4 / 31
gL3	2 / 5	2 / 5	2 / 5	2 / 5	3 / 12	3 / 2
pR2	2 / 5	2 / 5	2 / 5	2 / 4	3 / 21	3 / 3
rHH	2 / 5	2 / 3	2 / 2	3 / 60	4 / 16	4 / 6
rL1	2 / 4	2 / 4	2 / 4	2 / 1	4 / 24	4 / 6
rL0	2 / 4	2 / 3	2 / 3	2 / 1	3 / 4	3 / 2
rL2	2 / 3	2 / 3	2 / 3	2 / 1	3 / 4	3 / 2
gL2	2 / 2	2 / 2	2 / 2	2 / 2	3 / 13	3 / 2
gR1	2 / 2	2 / 2	2 / 2	2 / 2	3 / 6	4 / 6
gR0	2 / 2	2 / 2	2 / 2	2 / 2	3 / 6	4 / 4
rL3	2 / 2	2 / 2	2 / 2	2 / 2	3 / 4	3 / 2
gBR	2 / 2	2 / 2	2 / 1	2 / 1	3 / 6	3 / 2
gHH	2 / 2	2 / 1	2 / 1	2 / 1	3 / 1	4 / 6
gDS	2 / 2	2 / 1	3 / 69	3 / 63	4 / 76	4 / 4
pR3	2 / 1	2 / 1	2 / 1	2 / 1	3 / 15	4 / 18
gL0	2 / 1	2 / 1	2 / 1	2 / 1	3 / 9	3 / 2
gL1	2 / 1	2 / 1	2 / 1	2 / 1	3 / 6	4 / 6
gR2	2 / 1	2 / 1	2 / 1	2 / 1	4 / 56	4 / 4
pR4	3 / 374	3 / 269	3 / 203	3 / 189	3 / 12	4 / 16
bL3	3 / 346	3 / 301	3 / 266	3 / 266	3 / 4	4 / 14
bL2	3 / 221	3 / 190	3 / 164	3 / 164	3 / 4	4 / 12
bR1	3 / 182	3 / 160	3 / 144	3 / 110	3 / 4	5 / 38
bR2	3 / 152	3 / 132	3 / 118	3 / 71	4 / 24	5 / 24
bDS	3 / 142	3 / 65	3 / 20	3 / 20	4 / 8	5 / 30
bBR	3 / 139	3 / 105	3 / 40	3 / 40	3 / 4	4 / 12
bR0	3 / 138	3 / 122	3 / 94	3 / 94	3 / 4	5 / 24
bHH	3 / 125	3 / 69	3 / 63	3 / 63	4 / 18	5 / 36
bL1	3 / 106	3 / 93	3 / 79	3 / 79	4 / 30	5 / 48
gR3	3 / 96	3 / 86	3 / 78	3 / 62	4 / 43	5 / 24
bL0	3 / 81	3 / 73	3 / 65	3 / 65	3 / 4	4 / 12
bR3	3 / 41	3 / 35	3 / 31	3 / 16	4 / 16	6 / 164
gR4	3 / 34	3 / 28	3 / 24	3 / 24	4 / 40	4 / 4
rHP1	3 / 8	3 / 3	3 / 3	3 / 1	4 / 4	4 / 2
rHP2	3 / 8	3 / 3	3 / 3	3 / 1	4 / 4	4 / 2
rHP3	3 / 8	3 / 3	3 / 3	3 / 1	4 / 4	4 / 2
rHP4	3 / 8	3 / 3	3 / 3	3 / 1	4 / 4	4 / 2
bR4	3 / 5	3 / 5	3 / 5	4 / 1610	4 / 16	5 / 24