Cost scaling in idle games (general)

Pecorella calls idle games a seesaw between production and costs, typically with exponential costs ( ${cost}_{base} \times {({rate}_{growth})}^{owned}$ ) against linear or polynomial production. cost-scaling/pecorella-seesaw

T2 primary statementThe Math of Idle Games, Part IThis is typically accomplished by having costs grow exponentially while production grows at a linear or polynomial rate.The Math of Idle Games, Part I$cost_{next} = cost_{base} \times (rate_{growth})^{owned}$Checked by claude, 2026-10-20 — read the 2017-07-20 Wayback capture of the post

Cited by: Exponential cost scaling

In Pecorella's account, production first outruns costs, multipliers keep it close, and a prohibitive wait for the next generator marks the time to prestige. cost-scaling/pecorella-wait

T2 primary statementThe Math of Idle Games, Part IBut eventually the costs become overwhelming, and the time you would have to wait to be able to afford the next generator gets prohibitively long.Checked by claude, 2026-10-20 — read the 2017-07-20 Wayback capture of the post

Cited by: Exponential cost scaling

For a plain exponential (base $b$ , rate $r$ , and $k$ owned), Pecorella gives the most you can buy with $c$ currency as $⌊ \log_{r} (c (r - 1) / (b \cdot r^{k}) + 1) ⌋$ . cost-scaling/pecorella-max-affordable

About: Bulk buying

T2 primary statementThe Math of Idle Games, Part I · “BONUS CONTENT!”$max = floor(log_r(\frac{c(r-1)}{b(r^k)}+1))$Checked by claude, 2026-10-20 — read the 2017-07-20 Wayback capture of the post

Cited by: Exponential cost scaling

A price that grows by a factor of $r$ per purchase doubles every $\ln 2 / \ln r$ purchases. cost-scaling/doubling-purchases

Value

{
 "1.07": 10.24,
 "1.15": 4.96,
 "1.25": 3.11
}

T4 reproducedCookie Clicker web version, main.js (v2.058) · main.js#L7972 — the r = 1.15 caseGame.priceIncrease=1.15;The Math of Idle Games, Part I — the price rule$cost_{next} = cost_{base} \times (rate_{growth})^{owned}$Checked by claude, 2026-10-20 — ran the probe; it computes ln 2 / ln r for r = 1.07, 1.15, and 1.25 and checks each by stepping r^n in steps of 0.01 until it reaches 2Probe: probes/idle-costs/growth-math.mjs

Arithmetic on the price rule, not a measurement of a game. The rates are Cookie Clicker's 1.15, the Lemonade Stand's 1.07 (adventure-capitalist/lemonade-stand), and a steeper 1.25 for comparison.

Cited by: Exponential cost scaling

With income linear in the count, waits shrink until $n = 1 / (r - 1)$ owned, then each is about $r$ times the last. cost-scaling/wait-turn

Value

{
 "1.07": 14.29,
 "1.15": 6.67,
 "1.25": 4
}

T4 reproducedCookie Clicker web version, main.js (v2.058) · main.js#L5276-L5285 — income linear in the count, before upgradesme.storedTotalCps=me.amount*me.storedCps;Cookie Clicker web version, main.js (v2.058) · main.js#L7972 — the r = 1.15 caseGame.priceIncrease=1.15;Checked by claude, 2026-10-20 — ran the probe; for each r it finds the n with the shortest wait rⁿ/n by brute force, compares it with 1/(r − 1), and checks that wait(n + 1) / wait(n) = r·n/(n + 1) nears r by n = 10,000Probe: probes/idle-costs/growth-math.mjs

With $n$ owned, each earning $p$ per second, $wait (n) = b \cdot r^{n} / (p \cdot n)$ , so $wait (n + 1) / wait (n) = r \cdot n / (n + 1)$ . The shortest wait comes at the first whole $n$ from $1 / (r - 1)$ : 15 owned at $r = 1.07$ , 7 at 1.15, and 4 at 1.25 (where 4 and 5 tie). Arithmetic, not a measurement of a game.

Cited by: Exponential cost scaling

A long bulk purchase whose price grows by a factor of $r$ per item costs about $r / (r - 1)$ times its last price. cost-scaling/bulk-sum-limit

About: Bulk buying

Value

{
 "1000": 1.001,
 "1.15": 7.67
}

T4 reproducedCookie Clicker web version, main.js (v2.058) · main.js#L8096-L8105 — Cookie Clicker's bulk sumprice+=this.basePrice*Math.pow(Game.priceIncrease,Math.max(0,i-this.free));Antimatter Dimensions source code · src/core/math.js#L387-L429 — Antimatter Dimensions charges the last price onlyNOTE! this assumes you only have to pay for the most expensive thing you get when you buy in bulk.Checked by claude, 2026-10-20 — ran the probe; it sums r^i for i = 0..k − 1, divides by r^(k − 1), and compares the result at k = 200 with r/(r − 1) for r = 1.15 and 1,000Probe: probes/idle-costs/growth-math.mjs

The sum of $b \cdot r^{i}$ over $k$ items, divided by the last term, tends to $r / (r - 1)$ as $k$ grows. Antimatter Dimensions prices sets of 10, so its $r$ is the ×1,000 per set of tier 1. Arithmetic, not a measurement of a game.

Cited by: Exponential cost scaling