Bug Fix: Geometric Series Formula Inconsistency

[phillip-simons]

Problem

The sumGeometricSeries and maxGeometricSeries functions in js/util.js are not inverses of each other, causing incorrect upgrade cost calculations.

Root cause: sumGeometricSeries uses rate ** (n + 1) instead of rate ** n, calculating one extra term than intended.

  // Current (buggy)
  return base * (1 - rate ** (n + 1)) / (1 - rate);

  // Fixed
  return base * (1 - rate ** n) / (1 - rate);

Example

For a card with levelCost: [10, 2] (base=10, rate=2):

Levels	Expected Cost	Current Cost	maxGeometricSeries
1	10	10	✓
2	30	70	Says 2 affordable with 30
3	70	150	Says 3 affordable with 70

Impact on Autobuy

This mismatch causes autobuy to fail silently, especially noticeable with low balance currencies:

1. getCardLevelMax calculates player can afford N levels
2. levelUpCard calculates cost for N levels using buggy formula (too high)
3. Affordability check fails → no purchase happens
4. Currencies appear "deleted" because expected upgrades never occur

Affected Areas

• Card level upgrades (manual & autobuy)
• Cost display in tooltips, popups, and collection UI

All costs will be lower after this fix, as players were previously being overcharged.

Addresses #41

[mzxrules]

Not sure if this PR really helps with #41.

The core issue there as I understand it is that currency is being deducted without the card level being updated at all. Like it shouldn't matter that getCardLevelCost is returning the wrong value because the affordability check should prevent currency from being deducted.

That said, this probably helps with a different bug with the auto-buyer. The auto-buyer logic incorrectly assumes that levelUpCard can never fail and increments the autobuyCount without making sure currency is deducted. So in cases where the affordability check causes levelUpCard to silently fail, you can pump up autobuyCount indefinitely without actually spending currency by spamming the auto-buy button.

[wesleyjnewcomb]

This early return is still worth keeping because it prevents pointless exponentiation.