Recovering the Designer's Ledger: Inverse Hedonic Pricing of Card Costs in a Collectible Card Game

Collectible card games (CCGs) price every card in a single integer resource, yet the rules that map card text to cost are rarely published. We cast their recovery as an inverse hedonic pricing problem and propose ZHIZHI (Zero-residual Hedonic Inversion, Zero-shot Hedonic Imputation), a two-stage framework that first inverts effect prices from anchor cards differing in a single effect, then imputes the value of any card from its text without refitting. The resulting value-to-cost ratio is reported as the AMBER score (Attribute-Matched Budget-Efficiency Ratio), with η = 1.00 as par. We apply the framework to Riftbound, Riot Games' League of Legends trading card game, using 923 cards from five sets. Stage 1 recovers prices for core effects and keywords through anchor-pair elimination, simultaneous equations, a piecewise-linear might budget and least-squares / minimax fits, and extends the linear core with three mechanism models: a mental-accounting model of hand cards (play is rent-free, stock is priced) that reconciles draw, discard and the Flow keyword; an order-statistics model of selection premia for Predict, look-N-take-1 and modal “choose one” effects; and a cost-controlled regression that separates a low-cost on-play discount (−0.63, p < 0.001) from a combat-trick discount (−0.27, p = 0.057). Stage 2 prices 497 of the 702 costed units and spells in full (70 partially; 135 deferred by pre-stated rules) and 69 of 107 gear cards. The recovered table exposes latent design regularities: a 50% rule for contingent value, zero marginal price for play-timing keywords, a 1 C same-target complementarity premium for spells that reposition and enhance one unit, and integer-rounding absorption of on-play effects and sub-1 C keywords on cheap units. Across the 497 fully priced cards the AMBER score has median 1.00 (interquartile range 0.75–1.00), and prices calibrated on one group of cards predict held-out cards (e.g. the power exchange rate solved from three spell equations matches the price of channelling a rune on two other cards). An ablation over nested models with leave-one-out cross-validation attributes nearly all error reduction to the on-play adjustments (out-of-sample RMSE 1.574 to 1.541 C); the hand-card and selection layers stay within the model's 0.3 C resolution, and at the game's 1 C cost granularity their effect on the cards they change cannot be separated from the layer below. A review of every price against its own anchors found none that should change. We discuss transfer of the framework to other CCGs and the AMBER score as a soft screen in procedural card generation. J. C. Lee and J. Chen contributed equally to this work.