Tempo and the Race: Counting Who Is Actually Ahead

The beginner's guide asks you to read the board as two races rather than as a maze: your shortest path to your goal edge, their shortest path to theirs. That habit is worth nothing if the two numbers are wrong. This page is only about producing them — the fast method, the cases where the fast method lies, and the discipline that keeps a count from going stale a move after you made it.

Distance is rows remaining plus a surcharge

Tracing a route square by square is slow, error-prone, and you have to do it twice. There is a faster decomposition. Sort every step on a route into three kinds: forward, meaning one row closer to your goal edge; sideways, along a row; and backward, away from the goal.

Forward steps you were always going to pay for, so count them once and forget them. The rest is surcharge, and the two kinds are not priced the same. A sideways step costs exactly one, because your goal is an entire edge and not a particular square (the rules are explicit about that) — you never have to return to the column you left, so the step is paid once. A backward step costs two: one to give up the row and one to retake it, since you still have to cross that row again to finish.

So the honest identity is:

moves = rows remaining + sideways steps + 2 × backward steps

That doubling is the whole reason a wall behind you hurts more than a wall beside you, and it is the arithmetic the rest of the series prices things against — Endgames turns it into a budget of free turns, and Traps and Cages uses it to explain why a door on the wrong side of your pawn is so expensive.

Finding a surcharge without tracing the whole route

Walk the line you intend to take and stop at each wall crossing it. Ask what the cheapest way past costs: one lateral step if the square beside you is open and the way forward from there is clear, two if you have to shift twice. Add those up.

This works only while the walls are independent of one another, and it is worth seeing it fail once. Suppose your pawn is on e4 heading north to row 9, so five rows remain. A horizontal wall lies across the north side of e5 and f5, closing both of those squares' way forward. Priced locally, you step e4–e5, find the wall, and look sideways: d5 is open and d5–d6 is clear, so the detour is one lateral step and the total is six.

Now add a second wall, a vertical one in the groove between the d and e columns, spanning rows 5 and 6. Price it locally again and the answer gets worse: from e5 you can no longer slip west, so you go east to f5, which is also walled to the north, then to g5 and up — two lateral steps, total seven. But seven is not the answer. The route e4–d4–d5–d6–d7–d8–d9 costs one lateral step and five forward ones. Six.

The local method missed it because it assumed you meet the wall before you react to it. Once walls interact, the cheapest detour often starts behind the obstruction, on a square you have not reached yet, where the sidestep is still free. This is the single most common way an intermediate player overcounts their own position and talks themselves into a panic wall.

When walls sit close enough together to interact — sharing a post, overlapping in the same two or three columns, or forming any kind of corridor — abandon the shortcut and use the slow method, which is always right. Mark every square of your goal edge zero. Then repeatedly give each unlabelled square one more than the cheapest labelled neighbour it can legally reach, honouring walls. Stop when your pawn's square has a number; that number is your distance, and the labels you generated on the way are the map of every alternative route you have. Do it for the opponent too, from their goal edge. A player who only ever recounts their own path spends the whole game being surprised.

Folding the turn into the total

Two distances still are not enough, because the players do not move simultaneously. The bookkeeping is one line: their distance, minus your distance, plus one if it is your move. One or more and you win the race as it stands; zero or less and you lose it. Level on distance is therefore not level — the player on move is effectively half a turn ahead, and a tie on the two numbers is a win for whoever moves next. Endgames proves that from the parity of the arrival plies.

Record the count with the turn already folded in rather than adding it as an afterthought, because the folded number is the stable one. While both players simply walk, both distances fall at the same rate and the move alternates, so the tempo-adjusted difference does not change at all. That is what makes it a lead rather than a snapshot: only three things move it, and each of them is somebody's decision.

What actually invalidates a count

A wall. Recount both sides, not just theirs — a wall is terrain, and terrain lengthens whoever has to cross it. The rate a wall has to clear is set elsewhere: it competes against walking, so it needs a net two squares to beat a step (Wall Economy derives that, and Wall or Advance turns it into a five-step procedure). What matters for counting is narrower: a wall changes the number only by the gap between the route it closes and the next-best route still open, so if you cannot name that second route, you cannot predict what your own wall will do.

A jump. A count is only stable while the pawns cannot become adjacent, since the jump is the one move that crosses two rows in a single turn. Before you commit to a number, check whether the pawns can meet on it; Openings works through the meeting square and who wins it.

Your own carelessness. The count decays the moment you stop maintaining it. Update both numbers every turn — it costs a few seconds once you are decomposing rather than tracing.

The count is a measuring instrument, not a plan. Its use is that it tells you which kind of game you are in: ahead on the folded number, walking is already the winning move; behind it, walking is the one guaranteed loss, and the answer is structure rather than a scattered wall or two (Traps and Cages). If a term here was unfamiliar, the Glossary has it.