In an incremental game nearly everything can be bought again, and each one
costs more than the last. How fast that price climbs, the cost curve, sets
the pace of the whole game: when it flies, and when it stalls. Here are the
first 100 purchases of the same thing, priced six ways.
Prices that addLinearEach one costs 5 more than the last: the 100th costs 505.
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Prices that addPolynomialThe price follows the square of the count: the 100th costs 100K.
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Prices that multiplyExponential, ×1.07Each one costs 7% more than the last: the 100th costs 8.11K.
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Prices that multiplyExponential, ×1.15Each one costs 15% more than the last: the 100th costs 10.2M.
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Prices that multiplySteppedTen at one price, then ten times more: the 100th costs 10B.
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Faster than multiplyingSuper-exponentialThe multiplier itself keeps growing: the 100th costs 40.3T.
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Each picture shows the price of purchases 1 to 100. Every faint line is ten
times the one below, so a price that keeps multiplying by the same amount
climbs in a straight line.
Prices that add
Each price is the last one plus some amount. In proportion, the rises shrink as the price grows: 10 to 15 is half again, but 500 to 505 is just 1%.
Linear
Also called arithmetic, flat step
Every purchase costs the same amount more than the last. The income from what you've bought grows just as fast, so a game priced this way keeps a steady pace and never slows down.
Price
10 + 5 × owned
100th costs
505
×1,000 by
The 1,999th purchase
Good for
Things bought a handful of times, and levels that should never stall
Polynomial
Also called power curve, quadratic, cubic
The price follows a power of the count, here its square. It climbs much faster than linear early on, but its steps shrink in proportion, so in the long run any multiplying price overtakes it.
Price
10 × (owned + 1)²
100th costs
100K
×1,000 by
The 32nd purchase
Good for
RPG levels and stat upgrades bought a few dozen times
Prices that multiply
Prices multiply: by a little each purchase, or by a lot every ten. Gentle at first, they eventually outrun any price that adds, and most idle games price their generators this way.
Exponential, ×1.07
Also called geometric, compound
Each purchase costs 7% more than the last, so the price doubles about every ten. Here it starts out cheaper than the linear curve, passes it around the 50th purchase, and then pulls away for good.
Price
10 × 1.07^owned
100th costs
8.11K
×1,000 by
The 104th purchase
Good for
Generators bought hundreds of times, in a game with a long first run
Exponential, ×1.15
Also called geometric, compound
Each purchase costs 15% more, doubling the price about every five. Each new generator matters for a while and then gives way to the next tier, which is why the shop keeps growing.
Price
10 × 1.15^owned
100th costs
10.2M
×1,000 by
The 51st purchase
Good for
A shop with many tiers, where the newest one should take over
Stepped
Also called bought in tens, tiered price
The price holds for ten purchases, then jumps ten times higher. On average it multiplies like an exponential, but players buy in sets and aim for the next step.
Price
10 × 10^⌊owned ÷ 10⌋
100th costs
10B
×1,000 by
The 31st purchase
Good for
Pairing with a reward for each full set, like a ×2 per ten
Faster than multiplying
The multiplier itself grows, so the climb gets steeper with every purchase.
Super-exponential
Also called cost scaling, accelerating price
Each price is ×1.05 the last, and that multiplier grows 0.5% with every purchase. It works as a ceiling without a hard limit: past a point no realistic income keeps up, so the player turns to something else.
Price
10 × 1.05^owned × 1.005^(owned × (owned − 1) ÷ 2)
100th costs
40.3T
×1,000 by
The 46th purchase
Good for
Capping an upgrade softly instead of with a hard limit
Side by side
The same purchases on each curve, all starting at 10 coins.