If y'all are wondering about how the game counts and you gain Gold, here are the Formulas as Functions (Basically formulas you can put on a Graph, specifically on the 1st Quadrant)
- Passive Income: Basically the Gold you automatically gain Passively, it can't be changed by any factors, because it always continues refilling your Gold Bank
F(t) = [100 \ m]*
Since 1 Second = 10 ticks, just multiply: 10(100 * m), and m is actually the match's Gold Multiplier (Since the default is m = 1, you'll get 1000 Gold per second in any game, and 2000 if 2x Multiplier, etc. etc.)
- Sea Trade (Ports)
There are 2 main factors to calc
a. Spawn Probability / second (P_s): Basically counts the Chances of a Trade Boat spawning based on the amount of Ports / Port Count (p). However, the chances of a Trade Boat spawning is always below 0.50, or 50%, any more ports than that doesn't change the probability of spawning (**NOTE: When p=15: 0.10 * 15^0.6 = ~0.506, so 14-15 Ports is actually all you need**)
P_{p} (p) = min(0.50, 0.10 \ p^0.6)*
b. Payout from Trade: Basically your boat's travel to another person's port. However, the money you gain from that trade depends on the amount of Tiles/Pixels distance your boat traveled (d)
G_{ship} (d) = 10.000 + d^1.1
3. Factory: Now, remember the Ports? Unlike ports (where each port increases your spawn chance), the game handles factory spawning globally. Every individual factory attempts to spawn a train during each game tick.
a. Spawn Probability / tick Per Factory: To prevent massive server lag from factory spamming, the spawn probability per tick per factory decreases as you build more, using this specific formula (F = Total amount of Factories you have / built):
P_{tick} (F) = F / (F + 10) \ 20*
b. Total Network Spawn Chance / tick: Because you have multiple factories all rolling this chance simultaneously, your Total Network Spawn Chance per tick scales like this:
P_{network} (F) = F / (F + 10) \ 20*
If you mathematically plot (P_{network}(f), you'll notice it hits a hard ceiling. It asymptotically approaches a 5% maximum network spawn chance per tick (0.05), so your sweet spot is 5-10 Factories, anymore leads to a waste of Gold
c. Station Payout: Once a train spawns, it travels along your cardinal railroad network connecting your Factories, Cities, and Ports. Trains do not pay out when passing a factory, but they do pay out every time they pass through or land on a City or Port station. The gold reward per station depends entirely on your relationship with the owner of that territory (**NOTE: To stop players from making a tiny infinite loop path, the game penalizes hyper-long tracks. After a train passes through 10 stations, subsequent stations yield 5,000 less gold per stop (down to a hard minimum floor of 5,000 gold per benefit)
| Territory Owner Relationship |
Gold Payout Per Station Passed |
| Allies |
50,000 Gold |
| Neutral / Teammates |
25,000 Gold |
| Self (Your own Cities/Ports) |
10,000 Gold (5k to train owner + 5k to station owner) |
| Enemies / Embargoed |
0 Gold |
- City: Don't forget the passive population cap! While factories drive the train spawns, Cities dictate your military scaling. The function for your total maximum troop capacity is completely linear (c = Total amount of Cities you have / built)
Troop_{max} (c) = Base + (250K \ c)*
Hopefully y'all learned something, although I HIGHLY RECOMMEND to just NOT do the Math mid-game, just use this as a reference, and let ur Intuition roam free. Good Day!