OpenFront Troop Cap and the 42.2% Rule

If your troops seem to have stopped growing, you are almost certainly sitting above 42.2% of your cap. Growth rate peaks exactly there and falls away after it, reaching roughly zero once you press against the ceiling.

So the correct loop is not to save troops but to spend them: attack, drop back to around 40%, refill, attack again. The +troops/s readout turns orange the moment you cross the peak, so there is no arithmetic to do in game.

Why growth stalls

growth per second ∝ (troops^0.73) × (1 − troops ÷ cap)

The first term grows with your army; the second collapses toward zero as you approach the cap. They cross at 42.2%, and past that the second term wins.

“My troops aren’t growing” therefore has three usual causes:

1. You are above 80% of cap — growth has all but stopped. Spend
2. Your cap itself is low — you need land and cities. See the formula below
3. Too many troops are out on attacks — troops away from home do not generate growth

The Troop Cap Calculator will tell you what your ceiling actually is from your map and land share.

The troop cap formula

maxTroops = 2 × (tiles^0.6 × 1000 + 50,000)
          + (sum of city levels) × 250,000

The two terms behave very differently.

Land scales at ^0.6, so it has diminishing returns. Quadrupling your tiles raises the cap by only about 1.7×.

Cities are linear at +250,000 per level. The tenth city level gives exactly as much as the first.

A “+25,000 per city” figure circulates in some community writeups. The actual code says +250,000 — a factor of ten.

Rather than working this out by hand, put your map, your leaderboard Owned %, and your city levels into the Troop Cap Calculator — it returns both your ceiling and where 42.2% of it falls.

Where 42.2% comes from

Troops gained per tick (one tick = 100 ms):

gain = (10 + troops^0.73 / 4) × (1 − troops / maxTroops)

The first term grows with your troop count; the second collapses toward zero as you approach the cap. Solving for the balance point:

d/dr [ r^0.73 × (1−r) ] = 0
→ 0.73 × (1−r) = r
→ r = 0.73 / 1.73 = 0.4220…

That derivative is the origin of the “42%” number the community passes around as folklore.

Using it in a real game

Peacetime band is 35–55%. Below 30% you cannot defend; above 60% you are throwing away growth.

Only fill to 70–80% when you are staging a single decisive push.

The first minute is an exception. Early expansion raises the cap, and the larger cap compounds into more growth, so openers should sit lower — around 20–30% — and spend more aggressively. See the 1-Minute Build Order, or run it yourself in the Opening Simulator.

The color tells you

The +troops/s indicator in the control panel is green while the growth rate is still rising and orange once it starts falling.

Orange means you just crossed 42.2%. No math required — when it turns orange, click.

Common mistakes

1. Hoarding troops. At the cap, your growth engine is switched off.
2. Taking land and never building cities. You cannot out-expand the ^0.6 curve.
3. Placing cities on the border. Buildings transfer with the territory — build them deep inland.
4. Pushing the attack slider to 100%. Past a 2:1 troop advantage, extra troops buy you nothing.