Pecorella 2016 · Frame Advance

Cite as: Pecorella 2016
Original: https://blog.kongregate.com/the-math-of-idle-games-part-i/
Archived: https://web.archive.org/web/20170720203630/http://blog.kongregate.com/the-math-of-idle-games-part-i/
Accessed: 2026-10-20
Credit: Anthony Pecorella (Kongregate; producer of AdVenture Capitalist mobile, per the author bio). Part I of a three-part series based on his talk on idle-game math.
Notes: The live URL now returns 404, so this was read from the 2017-07-20 Wayback capture. Its AdVenture Capitalist numbers are credited in the post to the AdCap wiki.

Cited on

Claims (10)

Pecorella, crediting the AdCap wiki, gives AdVenture Capitalist's Lemonade Stand growth 1.07, base cost 4, and 1.67/s each; with the first free, the price is $3.738 \times {1.07}^{owned}$ .		T2
Initial costs are $3.738 for the Lemonade Stand and $60 for the Newspaper Delivery; each later business costs 12 times the one before, up to $25,798,901,760 for the Oil Company.		T1
Each business's coefficient, the factor on its price per one owned, falls by 0.01 per business from the Newspaper Delivery's 1.15 to the Oil Company's 1.07; the Lemonade Stand's is also 1.07.		T1
Revenue per second before upgrades, revenue per cycle ÷ cycle time, runs from the Lemonade Stand's $1.67 ($1 every 0.6 s) to the Oil Company's $804,816 ($29,668,737,024 every 36,864 s).		T1
A business's next price is its initial cost times its coefficient raised to the number owned, with a fixed coefficient for each business.		T1
The shown bulk price (`getSumPrice`) is the geometric sum $b \cdot r^{a} \cdot (r^{k} - 1) / (r - 1)$ , discounted and rounded up once: 20.30× the next single price for 10, and 7.83 million× for 100.	`“BONUS CONTENT!”`	T4
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.		T2
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.		T2
For a plain exponential (base $b$ , rate $r$ , and $k$ owned), Pecorella gives the most you can buy with $c$ currency as $⌊ \log_{r} (c (r - 1) / (b \cdot r^{k}) + 1) ⌋$ .	`“BONUS CONTENT!”`	T2
A price that grows by a factor of $r$ per purchase doubles every $\ln 2 / \ln r$ purchases.		T4