What should you invest in next? Every option priced by the marginal formula x/(100+T) — the empty-category rule made mechanical (Algorithm A2, Theorems 2, 3 & 8).
their summed defence stack — shred is worth x/(100+THEIRS)
| Field | Example | Where it comes from |
|---|---|---|
| Attack piece (+10, T=150) | +4.0% real | attack saturates near 150 on a spender endgame stack |
| Defence node (+10, T=100) | +5.0% real | defence typically sits near 100 |
| Health universal (+10, T=35) | +7.4% real | few health sources exist, so its total stays small |
| Skill accessory (+10, T=40) | +7.1% real | its own multiplier lane (nukers only) |
| Shred (+10 vs their 150) | +4.0% real | priced against the ENEMY’s denominator (Theorem 3) |
Fed these totals the allocator picks health first — “rare, so valuable” is the arithmetic of the denominator, not scarcity pricing.
The empty-category rule, made mechanical
A point is worth the most where you hold the least: gain = x/(100+T). Shred is special — it prices against the enemy’s denominator, so the more stacked your opponent, the better it gets (Theorem 3).
| Rank | Option | Real gain |
|---|---|---|
| 1 | Attack gear pieceattack +0 | +0.0% |
| 2 | Defence tech nodedefence +0 | +0.0% |
| 3 | Health universalhealth +0 | +0.0% |
| 4 | Skill-dmg accessoryskill +0 | +0.0% |
| 5 | Shred deputy (Philip II)shred +0 | +0.0% |