The prestige curve that collapsed, and the arithmetic that fixed it

How the ladder is built

Prestige here works in two layers. Resetting a run converts your lifetime earnings into stars; stars are spent to move to the next region; each region is a permanent income multiplier that survives every future reset. The multiplier grows ×6 per step, so the Moon pays 46,656× what New York does.

Stars come from a square root — specifically floor(√(totalCoins ÷ threshold)). The square root is what stops a single monster run from buying the whole ladder: to earn twice the stars you need four times the money.

The bug was a constant

That last column used to read $10M all the way down. One threshold, fixed forever, written when New York was the only region in the game.

Follow what that does. In Singapore your income is multiplied by 7,776. The bar you have to clear to be allowed to prestige is still ten million — a number you now blow past in a couple of minutes. So the late game, the part that is supposed to be the long haul, turned into the fastest loop in the game. Worse, because stars scale with the square root of earnings, and earnings had gone up by orders of magnitude, each of those quick resets handed out a fat pile of stars.

The number of prestiges needed per region was falling as the player climbed. Every idle game wants that number to rise. That is the whole shape of the genre: each tier should be a longer, richer campaign than the last one. Mine was a curve that accelerated until it fell over.

It did not show up in testing for the obvious reason — nobody had played far enough. The first player to get past London found it in an afternoon.

Fixing it with one exponent

The threshold now scales with the region: 10,000,000 × 3^region. Income grows ×6 per region, the bar grows ×3, so each region is genuinely longer than the one before while the early game — region 0, still a flat ten million — is untouched. That last part mattered: I did not want a fix for hour forty to make hour one worse.

Then the star costs. They step 6 → 24 → 80 → 260 → 820 → 2,600, which is roughly ×3.3 each time. Stars earned per prestige only grow with the square root of the income-to-threshold ratio, so with income at ×6 and the bar at ×3 they grow by about ×1.4 per region. Costs climbing at 3.3 against income climbing at 1.4 is what forces the number of prestiges per region upward instead of down. The gap between those two rates is the difficulty curve; everything else is decoration.

One consequence I like: because the marginal cost of a star is (2N+1) × threshold coins, the last star before a region unlock is always the expensive one. Going from 5★ to 6★ in New York needs 110 million more lifetime coins — eleven times what the first star cost. You feel the wall before you hit it, which is a fairer kind of hard than a wall that appears without warning.

Why I do not trust my own simulation

I did not tune this by playing it — the whole problem is that the curve is weeks long. I wrote a simulator that plays the game with a simple greedy policy, buys whatever is affordable, prestiges at the threshold, and reports how long each region takes.

That simulator says the shape is right: prestiges per region now increase monotonically all the way to the Moon. It also runs roughly ten to twenty times slower than a real player, and I know exactly why. It never buys premium. It never buys character buffs. It never closes the tab and collects eight hours of offline earnings. It never pushes past the threshold to bank a better star payout — it prestiges the instant it is allowed to, which is close to the worst possible policy.

So what I have is a shape, not a schedule. The relative pacing between regions I will defend; the absolute “this takes a month” I will not, until real players have been up the ladder. Publishing that distinction is deliberate. A balance pass that claims more precision than its instrument has is how you end up shipping confident nonsense.

If you are playing rather than reading

The practical version of all of this is in the prestige and regions guide: when to reset, how much a star actually costs at your stage, and the trap of moving city the moment you can afford it. The mechanics these numbers sit on top of are covered in why nothing pays per second.