Why upgrade costs cannot be estimated linearly

An upgrade grants you a stat. The next upgrade grants you more of it. What makes the ladder interesting is that the two quantities grow at completely different speeds.

Take the ladder in +1 Wings For Eggs, which is a clean example precisely because it is unremarkable: wings raise a flight-stamina multiplier from 1× to 2.7× across 10 tiers. That is a factor of 2.7×. Real, worth having, and small.

The price of those same tiers runs from nothing to 10.0Qa of in-game Cash. The multiplier grew by a factor of 2.7. The price grew by a factor of about 3×10¹¹. Those two numbers describe the same ladder, and the gap between them is the entire decision.

This is not a quirk of one game. It is the standard design: exponential cost against roughly linear benefit is what makes an idle game last more than an afternoon. It is also what makes "save up for the best one" bad advice, and "buy the next one you can afford" subtly wrong near the top.

Comparing tier prices to each other tells you almost nothing, because the tiers are not the same size. The useful quantity is cost per point of stat gained — the marginal price of the step between two tiers, not the sticker price of either.

Here is that number for the full wings ladder, computed from the same data the planner uses:

Read the last column downward. The price of one point of stamina rises from 300K on the first paid step to 30.5Qa on the last — roughly 11 orders of magnitude, for a stat that never even doubles.

Buy the best tier you can already afford. This is true here for a structural reason, not a vibe: because each step costs more per point than the step below it, the intermediate tiers are never a cheaper route to the top. Spending on Bamboo and Bloom on the way to Armored buys the same eventual stamina for more total Cash than skipping straight to Armored. The only exception is a ladder that gates purchase order — if tier 5 requires owning tiers 1 to 4, the order is forced and the rule does not apply.

Know where the cliff is. At some point the price per point stops creeping and jumps. On this ladder the marginal cost multiplies by more than a hundred in a single step in the middle of the table. Past that point you are no longer buying stamina efficiently — you are buying the zones the stamina unlocks, and whether that is worth it depends on what those zones pay. That is a different question with a different answer, and a guide that does not separate the two is guessing.

You might reasonably ask why any of this needs a page rather than a sentence. Three reasons.

The numbers span too many orders of magnitude to hold in your head. Comparing 500,000 against 850,000,000,000,000 by eye is not a judgement call, it is an estimate of an estimate. Every unit error at that scale is a factor of a thousand, and the arithmetic is exactly where human intuition stops working.

The answer depends on your inputs, not the ladder's. The correct next purchase for a player holding 600,000 Cash is different from the correct one for a player holding 600 billion, and different again once you include how fast they earn. A written answer has to pick one and then be wrong for everyone else.

Ladders get rebalanced. A guide that hard-codes "stop after Jungle Wings" is correct until the patch that moves a price, at which point it is confidently wrong and nobody notices. The table above is not typed into this page; it is computed at render time from the same data file the planner reads. When a price is corrected in one place, the guide and the tool change together.

The method generalises to any game with a tiered upgrade shop, and it takes four steps you can do on paper.

1. Write down each tier's full price and the stat it grants. Full price, not the delta.
2. For each step between two consecutive tiers, divide the difference in price by the difference in stat. That is the marginal price of one point.
3. Find the step where that number stops creeping upward and jumps. Everything above that point is a different kind of purchase.
4. Compare your current currency against the tiers' actual prices and buy the highest one you already cover. Recompute when prices change.

That is the whole engine. The wings planner does exactly this for one ladder, with your numbers as inputs. If you want to see how the same engine handles odds rather than prices, the next guide explains why questions like this cannot be answered in a paragraph at all.

It is worth being explicit about what the arithmetic above cannot see, because a method presented as complete is worse than one presented with its edges visible.

It assumes the tiers are independent purchases. Where a game requires owning lower tiers first, the step-by-step marginal costs are still correct but the skipping strategy is not available.

It assumes the stat is the thing you want. If the real goal is a specific zone or unlock, the efficient move is the cheapest tier that reaches that gate, not the best value per point — and only you can map tiers to gates.

And it inherits the accuracy of its inputs. On the worked example above, the tier prices are community-reported rather than confirmed in game; the shape of the curve is robust to small corrections, but no individual tier should be treated as exact. The sourcing standard explains how that is labelled on the page itself.