How to play
The goal. Defending as Blue, hold Tarn Crossing until 20:00. Attacking as Red, take it: Red wins the moment it holds the crossing with no Blue unit there. The game is 14 one-hour turns; Red's units arrive in waves (each wave is an echelon): .
Each hour. Pick a unit (click it in the list or on the map, or press its key) and click the sector where it should go; clicking an enemy marker sends it to that sector. Click the same sector again to step through a stack. The bar says whether this hour's orders start now or next hour; a clock on a unit means its order waits an hour. Attacking, your units that have not arrived wait in the staging tray below your entry edge: pick one and click a sector on the entry edge to choose where it comes in. Fire your artillery at one sector (press A, or click your battery in the bottom-right corner of the map, then click the sector). The battery is fixed: it cannot move and cannot be attacked. Press End hour: units move, fights happen where both sides meet, and new reports come in.
What you see. Enemy units in a sector you hold are seen exactly. In a sector next to one of your units you see their type, not their losses, and you miss one time in ten; a decoy looks like a tank battalion. Your recon troops also report movement two sectors out, an hour late; a decoy group two sectors out is built to be noticed, so they report it at once as a tank battalion, heard but not seen. Fire watched by a recon troop next to the target shows exactly what is there and how hurt it is.
Decoys. Red has one Decoy Group. It has no combat strength; its job is to make Blue misjudge where the main attack is coming. Seen from a neighbouring sector it looks like a full tank battalion (12 points), and Blue's recon troops hear it as a tank battalion from up to two sectors away, where a real unit shows only as "movement". It is exposed, and shown as a zero-strength decoy for the rest of the game, when a Blue unit is in its sector or when Blue artillery fires on its sector while a Blue recon troop watches. Attacking: send it down a road away from your main effort and keep it two sectors from Blue's recon, so it is heard but never looked at; Blue may send its one reserve the wrong way. Defending: before you commit your reserve, check the road with artillery fire that a recon troop is watching; a "tank battalion" that shows no damage under fire is the decoy.
Winning fights. A unit that has sat in a sector for two hours defends as if it were three times its size. Attack where the defender is thin, or hit a defender that is already fighting from a second direction: then its defense counts for nothing. A unit set to give ground falls back one sector when a stronger enemy attacks it, and an enemy that follows it can run into a prepared position.
Offense–defense balance. The slider above the side buttons sets how much digging in is worth, like a difficulty setting for the scenario: 5 is the standard game, lower settings favor whoever defends a sector (dug-in units hold better), higher settings favor whoever attacks (attacks hit harder). It changes combat only, the same way for both sides; what each side sees and how the other commander thinks stay the same. As Blue you defend most fights, so a low setting is easier for you and a high one harder; as Red it is the other way round. The setting is saved in the share link.
The other commander acts only on what it can see. The Red commander sends its second echelon down the road that looks weakest (it chooses at 08:00) and follows units that give ground. The Blue commander commits its reserve once, to the road that looks strongest when the enemy on it reaches the forward zone, checks contacts with spotted fire first, and counterattacks enemy units that look weak. A decoy it can only hear cannot be checked that way.
How the model works
Fog and friction. Clausewitz wrote that a "great part of the information obtained in War is contradictory, a still greater part is false," and that "everything is very simple in War, but the simplest thing is difficult." Here the fog is what each side can see, and the friction is the order delay and travel time. Boyd's observe–orient–decide–act loop is the hour you play.
Combat. Units in the same sector fight hour by hour under a stochastic version of Lanchester's square law: each side's losses are proportional to the other side's fighting power. The defender's posture multiplies its fighting value by k. The square law breaks even when the attacker's numbers exceed the defender's by √k, so k = 9 for a prepared defense and 6.25 for a hasty one reproduce the U.S. Army's historical minimum planning ratios of 3:1 and 2.5:1 (FM 5-0, Table B-1). In 10,000 one-on-one trials of the model, a prepared defender facing three times its strength holds 55.3% of the time (at the standard balance setting), against FM 5-0's "over a 50 percent probability." A unit breaks at 50% losses, the same threshold for both sides, as in Mearsheimer's reconstruction of the 3:1 rule. Each unit also has a hidden quality factor.
Offense–defense balance. The slider changes one number: the defender's multiplier k for a prepared or a hasty defense is multiplied by 1.1 for every step below 5 and divided by 1.1 for every step above it (k × 1.1(5 − setting)). At 5 the factor is exactly 1, so the game is the calibrated one above. At 0 a prepared defense counts k = 14.5 (it breaks even against 3.8:1); at 10, k = 5.6 (2.4:1). Meeting engagements and flank attacks stay at k = 1, and nothing else changes: sight, order delays, artillery and the scripted commanders' rules are the same at every setting. The step size is notional, set by simulation so that the game's two commanders, playing each other, move by about 15 points at either end, roughly evenly per step (table below).
Flanks. Table B-1 puts a counterattack into a flank at 1:1, so a defender that is already fighting attackers from one sector and is then hit from a second sector fights at k = 1. FM 3-90 pairs a fixing force with an enveloping force this way. The "second sector" test is notional: the map has no facing.
Giving ground. A unit set to give ground falls back one sector, toward its own side, when a stronger enemy attacks it, losing half an hour of the enemy's fire as it breaks contact (notional). It imitates the delay in FM 3-90, which "trades space for time." Any unit that leaves a sector the enemy is in pays the same.
Artillery. Each side fires one mission an hour at any sector. Every enemy unit there loses 8% of its strength (notional; area fire hits a crowded sector harder). The damage report is right 9 times in 10; otherwise it shows no effect, an exaggerated figure, or damage in an empty sector. A friendly recon troop in the target sector is hit half the time; one next to it watches the fall of shot and shows the sector exactly.
The critics. The 3:1 rule is a planning rule of thumb, and it is contested. Mearsheimer defends it for breakthrough battles only, in reply to Joshua Epstein, who offered historical evidence against it; Epstein answered in the same issue, and Dupuy disputed Mearsheimer's corrections to his combat data. Fits of Lanchester equations to the daily records of Kursk and the Ardennes found that none of the basic laws fit well (Lucas and Turkes; Lucas and Dinges). Treat the combat here as a teaching model with a sourced anchor, not a prediction.
The replays. The review reruns your orders on the same scenario with fresh dice, once against the commander you played and once against one who sees everything. The difference is what your hiding, feints and bait were worth: the logic of the value of information (Howard 1966).
Left out. Air power, engineers and obstacles, supply, night and weather, civilians, terrain effects beyond road times, and morale beyond the break threshold.
Balance check
Scripted strategies stand in for players. The doctrinal defender and the feint-and-mass attacker are meant to be what a decent human does: the defender holds about half its games, and the attacker takes the crossing in about two games in three with a feint and a little over half without one. Naive play loses. The numbers below are for the 14 one-hour turns. The rows comparing an opponent who sees everything show what deception is worth (the feint-payoff table at the end sets the two side by side); the artillery rows show what recon spotting is worth.
Offense–defense balance check