Fast Track: the fewest cards home

For a red piece on an empty board: how few cards take it from each square to red's B4, and which cards start such a way. It is worked back from B4 over every card's landing squares, as the rules compute them (roc-apps/fasttrack/Reach.roc). This page is printed by fasttrack/reach_board.roc.

What it assumes.

No opponents, so nothing blocks a piece and nothing sends one home.
One card is one card. Cards that let you play again are not credited yet.
Each card moves the way the rules allow, and a 7 is only ever played whole:

card	what it does here
A, J, Q, K, joker	move 1
4	backwards only ("4 back")
6 from the pen	one square, onto L0
7	seven squares (a split needs a second piece)
A, 6, joker	the only cards that leave the pen
J, Q, K	the only cards that leave the bullseye

The fast track and the bullseye need exact moves. A fast-track hop happens only on a move that starts on a fast-track square. The bullseye is entered only from red's own fast-track square.

How to read a square. L2 3 · 3, 4 back means that from L2 the fewest cards home is 3, and a 3 or a 4 played backwards starts a 3-card way. Each zone is drawn upright, the way the page draws its panel, with the pen at the left and the base up the middle. The other zones' pens and bases are left blank, because a red piece never stands on them.

Things to check

DS is 2, not 1. It is 4 steps from B4, and no card moves 4 forward. Any of A, 2, 3, J, Q, K, joker or a 4 back starts a 2-card way.
So L2 is 3. A 4 back from L2 lands on DS. L0 (to R0) and L1 (to BR) are 2, as you expected, and so is red's HH (to R1).
Red's fast-track square is 2: any card from 5 to 9, hopping to purple's fast-track square and on into red's home stretch.
The pen is 3 (A, 6 or joker to L0, then 2), and so is the bullseye (J, Q or K to purple's fast-track square, then 2).
The worst squares on the board are 4 cards from home: blue's R2–R4 and L1, and green's R2–R4. The rest of enemy territory is 3, except purple's zone, the last before red's: its L side, bottom row and fast-track square are 2, and only its R side is 3.

Red's zone (the mover's own)


	FT 2 · 5, 6, 7, 8, 9
	L4 3 · A, 4 back, J, Q, K, Jo		B4 0		R4 1 · 10
	L3 3 · 2, 4 back		B3 1 · A, J, Q, K, Jo		R3 1 · 9
	L2 3 · 3, 4 back		B2 1 · 2		R2 1 · 8
pen 3 · A, 6, Jo	L1 2 · 4 back		B1 1 · 3		R1 1 · 7
	L0 2 · 4 back	HH 2 · 4 back	DS 2 · A, 2, 3, 4 back, J, Q, K, Jo	BR 1 · 5	R0 1 · 6

Blue's zone (next after red's)


FT 2 · 3, 5, 6, 7, 8, 10
L4 3 · A, J, Q, K, Jo				R4 4 · 3, 4 back, 5, 6, 7, 8, 10
L3 3 · 2				R3 4 · 2, 3, 4 back, 5, 6, 7, 9, 10
L2 3 · 3				R2 4 · A, 2, 3, 4 back, 5, 6, 8, 9, 10, J, Q, K, Jo
L1 4 · A, 2, 3, 4 back, 8, 9, 10, J, Q, K, Jo				R1 3 · 4 back, 10
L0 3 · 5	HH 3 · 6	DS 3 · 7	BR 3 · 8	R0 3 · 9

Green's zone


FT 2 · 2, 3, 5, 6, 7, 9, 10
L4 3 · A, 6, 7, 8, 9, 10, J, Q, K, Jo				R4 4 · 3, 4 back, 5, 6, 7, 8, 9, 10
L3 3 · 2, 7, 8, 9, 10				R3 4 · 2, 3, 4 back, 5, 6, 7, 8, 9, 10
L2 3 · 3, 8, 9, 10				R2 4 · A, 2, 3, 4 back, 5, 6, 7, 8, 9, 10, J, Q, K, Jo
L1 3 · 9, 10				R1 3 · 4 back, 10
L0 3 · 5, 10	HH 3 · 6	DS 3 · 7	BR 3 · 8	R0 3 · 9

Purple's zone (the one before red's)


FT 2 · A, 2, 3, 5, 6, 8, 9, 10, J, Q, K, Jo
L4 2 · 2, 3, 5, 6, 7, 9, 10				R4 3 · 5, 6, 7, 8, 9, 10
L3 2 · 3, 5, 6, 7, 8, 10				R3 3 · 3, 5, 6, 7, 8, 9, 10
L2 2 · 5, 6, 7, 8, 9				R2 3 · 2, 3, 5, 6, 7, 8, 9, 10
L1 2 · 5, 6, 7, 8, 9, 10				R1 3 · A, 2, 3, 4 back, 5, 6, 7, 8, 9, 10, J, Q, K, Jo
L0 2 · 6, 7, 8, 9, 10	HH 2 · 7, 8, 9, 10	DS 2 · 8, 9, 10	BR 2 · 9, 10	R0 2 · 10

The bullseye

bullseye 3 · J, Q, K