Direct answer: when should you stop expanding?
Stop spending troops on optional land when the next capture creates another active border, drops you below roughly 30% of troop cap with an enemy nearby, or buys less safety than rebuilding would. With quiet borders, the strongest raw growth band is usually about 35–50% of cap; the formula peaks near 42% for normal large caps. Under pressure, holding 50–70% is often worth slower growth because the reserve prevents a collapse.
Use this mechanics page for troop cap, growth ratios, and the expand-versus-rebuild decision. Use Economy Fundamentals for the broader question of which protected investment to buy next. Keeping those jobs separate avoids two pages competing for the same answer.
The troop sweet spot is a band, not a permanent target
- Population cap base
- 2 × (tiles^0.6 × 1000 + 50,000) + Σ(cityLevel × 250,000)
- Population type multiplier
- Human ×1 / Bot ÷3 / Nation Easy ×0.5, Med ×0.75, Hard ×1, Imp ×1.25
- Troop growth rate
- toAdd = (10 + troops^0.73 / 4) × (1 - troops / maxTroops)
The final factor, 1 - troops / maxTroops, removes growth as the bar fills. The troops^0.73 term rises with your current army, so the fastest raw generation is not at zero troops. Across common human caps, the maximum sits close to 42% of cap. That is a planning signal, not an order to dump troops whenever the bar passes 42%.
| Current troops | What the formula says | Practical decision |
|---|---|---|
| Below 30% | Plenty of headroom, but little deterrence | Pause optional wars. Take only cheap neutral land or a capture that immediately removes danger. |
| 35–50% | Near the raw troop-growth peak | Use quiet windows for efficient expansion and short, decisive attacks. |
| 50–70% | Slower growth, stronger immediate reserve | Prefer this band on a contested chokepoint, before betrayal, or when two rivals can reach you. |
| 70–80% | Growth is visibly throttled | Bank this much only for a known timing, credible threat, or expensive follow-up. |
| Above 80% | The cap factor is 0.20 or less | If the border is safe, convert troops into useful land or raise the cap instead of idling at a full bar. |
Four checks before one more expansion
- Is the land cheap? A short neutral edge or weak disconnected pocket may pay for itself. A long attack into defended land is not “growth”; it is a war budget.
- What remains after the capture? Judge the post-attack ratio, not the number before you click. Below 30% with a live enemy border is a rebuild warning.
- Does the shape improve? A compact choke, coast connection, or closed pocket can be worth slower recovery. A thin corridor or new second front can make a larger country poorer.
- Is cap actually the bottleneck? If troops are near 80% and the position is safe, more cap helps. If troops are low because you keep losing fights, another City does not repair the real problem.
Three match situations
Quiet outer frontier
You hold about 45% of cap, the nearest opponent is separated by neutral land, and each capture keeps one coherent border. Continue taking low-cost tiles while the ratio remains near the growth band. Stop when the route opens another opponent, stretches into a corridor, or pushes the next attack below a safe recovery floor.
Contested chokepoint
You hold 55–65% of cap and a rival can attack the same narrow border. Do not spend back to 42% merely because it is the mathematical peak. The rival can turn your “efficient growth” into an immediate loss. Preserve the reserve, use a Defense Post if it solves the choke, and expand elsewhere only if the new land reduces rather than multiplies pressure.
Post-war rebuild
You won land but fell below 25% of cap. Cancel small attacks, keep Gold liquid, and let the army recover before buying exposed infrastructure. A safe City can be prepared if the cap will soon bind; a City on a frontier that is about to fall converts Gold into an enemy asset.
When is a City worth the Gold?
A completed City level adds a fixed 250,000 troop cap. The first City costs 125,000 Gold, but that is not a direct “profit”: you trade liquid Gold for cap, a train station, and a structure that must survive. Build or upgrade when cap is restricting recovery, the site is defensible, and the Gold is not needed for an immediate border or nuclear answer.
| Owned tiles | Cap without City | Cap with one City level | What it means |
|---|---|---|---|
| 10,000 | ≈602,000 | ≈852,000 | A large +42% increase; useful if the early site is safe. |
| 50,000 | ≈1,420,000 | ≈1,670,000 | About +18%; still meaningful, but compare it with defense and route income. |
| 200,000 | ≈3,131,000 | ≈3,381,000 | About +8%; the City is predictable cap, not automatically the best purchase. |
The tile term has diminishing returns, but the fixed City bonus also becomes a smaller percentage of a large existing cap. Its strategic advantage late is different: it raises cap without widening the frontier.
Gold sources and when they fit
- Base gold income
- Players 100 / tick, Bots 50 / tick (× goldMultiplier)
- City troop bonus
- Each City level provides +250,000 troop cap
- Train revenue
- baseGold (ally 35k / team 25k / self 10k) − distPenalty (5,000 × max(0, citiesVisited − 9)), floor 5,000
- Trade ship revenue
- floor( (75,000 / (1 + exp(-0.03 × (dist - 300))) + 50 × dist) × goldMultiplier )
- Trade ship spawn
- spawnRate = floor((100 × 1/(rejections+1)) / (1 - sigmoid(numShips, ln(2)/50, 400)))
- Trade ship scaling
- v32 sigmoid midpoint: 400 active ships; spawning becomes progressively slower
Base Gold
Humans receive 100 Gold per tick before modifiers. It is reliable and cannot be embargoed, so waiting with a purpose is valid. Hoarding without a trigger is not: decide whether the reserve answers cap, defense, trade, trains, or a nuclear threat.
Trade Ships
Longer safe routes pay more, but fleet-wide spawn suppression rises around the v32 midpoint of 400 active trade ships. A protected long route and reliable partner are better than several exposed Ports. Rejecting ships triggers a pity mechanic that changes later spawn timing, so an embargo is a strategic cost, not a free toggle.
Trains
Trains need a Factory, City stations, and usable rail links. Visits pay 35k for an ally, 25k for a teammate or other player, and 10k for your own City before distance penalties and modifiers. Build the network where the stations can survive; a theoretically rich route that crosses the battle line is a donation to the opponent.
Decision table: buy for the current constraint
| Signal | Best next action | Common losing move |
|---|---|---|
| Below 30% with a hostile border | Stop optional attacks, stabilize the shortest front, rebuild | Buying an exposed Port or City because the Gold button is available |
| 35–50%, quiet border, cheap neutral land | Expand efficiently while preserving one recovery route | Holding a full bar and wasting growth headroom |
| Above 80%, safe and cap-limited | Use troops for value or add protected City cap | Staying full with no planned attack or cap increase |
| Safe coast and reliable distant partner | Invest in a Port route | Counting Ports instead of route safety, distance, and capture risk |
| Protected cluster of City stations | Add a Factory and train loop when the lobby supports it | Building rails through a contested frontier |
| Enemy nuclear capability is credible | Keep enough liquid Gold for spacing, SAM, or recovery | Locking every resource into slow income infrastructure |
Common failures and opponent counterplay
- Full-bar fallacy: a large stored army looks strong, but above 80% its natural growth is heavily throttled. Opponents can outgrow you if they spend efficiently and keep a reserve.
- Blind City timing: cap does not solve an exposed border. Pressure a player immediately after they spend Gold on a City they cannot protect.
- Port spam: more Ports add capture targets and do not remove global trade-ship suppression. Embargo, threaten the partner, or attack the coastal cluster.
- Growth-band greed: a player sitting near 42% is optimized for generation, not for absorbing a surprise. Betrayal or concentrated pressure forces them into a slower reserve band.
- Gold without a trigger: saved Gold preserves options only when the player knows what condition releases it. Take decisive land while a passive hoarder waits for a perfect purchase.
Sources and next reading
Verify the current population cap and troop-growth code, then use the formula reference for the compact data view.
- Economy Fundamentals — choose between protected cap, trade, trains, defense, and nuclear spending.
- FFA Opening — apply the reserve bands during the first expansion.
- Trade System — inspect route income and embargo behavior in more detail.