Idle Clicker
An idle game with the geometric series done properly — bulk prices use the closed form, and "buy max" is the same series solved for the count.
Buy
The arithmetic underneath
- The whole genre is one geometric series. The nth building costs base times growth to the nth, so buying ten more costs base x growth^owned x (growth^10 - 1) / (growth - 1) — not ten times the current price, which at a growth of 1.15 undercharges by half.
- The closed form is used rather than a loop, and it is checked against the loop it replaces. Looping accumulates floating-point error over hundreds of purchases; the formula does not, and it is the same answer to fifteen digits when both are exact.
- The "buy as many as I can afford" figure is that series solved for the number bought. Working it out by subtracting one price at a time gives a different answer right at the boundary, which is exactly where a player notices and calls it a bug.
- Output per pound gets worse as you climb, deliberately — but not from the very start. The first upgrade is the best value in the game, because it has to feel like a reward; everything after the water wheel earns less per pound than the one below it. The tool shows that figure so the decline is visible rather than felt.
- Time away is capped at four hours. Uncapped offline earnings turn a week off into a win and make the game pointless; the cap is stated here rather than quietly applied.
How to use
- Turn the crank until you can afford something that turns it for you.
- Buy in tens or by the maximum you can afford.
- Come back later — up to four hours away still pays.
Frequently asked questions
Why do ten more cost so much more than ten times the price?
Because every copy is dearer than the last. At a growth of fifteen per cent, ten more buildings cost almost exactly twice the current price, not ten times it — the whole thing is a geometric series, and charging ten times the current price is the commonest bug in the genre.
Is "buy as many as I can afford" exact?
Yes. It is the same series solved for the number bought, rather than subtracting one price at a time until the money runs out. Those two disagree right at the boundary, which is exactly where a player notices — and holding exactly the price quoted always buys the number quoted for, which is checked over 1,500 random cases.
Does time away count?
Up to four hours of it, paid at your current rate. Uncapped offline earnings turn a week off into a win and make the game pointless, so there is a cap — stated here rather than quietly applied. A clock that has gone backwards pays nothing at all.
Which building is the best value?
The water wheel, and deliberately so — the first upgrade has to feel like a reward. From there on every building earns less per coin spent than the one below it, which is what makes a later purchase a decision rather than an obvious yes. The tool shows that figure on every row.
Is my game saved?
In this browser only, every few seconds and when you leave the page. Nothing is uploaded anywhere, so clearing your browser data ends the run — and "Start again" does it deliberately.
Why do the numbers get so big?
Because exponential costs meet exponential income, which is the shape of the entire genre. They are printed in words rather than exponents, so a quadrillion reads as a quadrillion instead of 1e15.
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