Guessability Index (GI)

The Guessability Index is a mathematical framework for quantifying how easy or difficult it is to identify a specific NFT through binary trait queries.

The Core Formula

For NFT i with trait vector (t₁, t₂, ..., tₖ):

SI(i) = -∑ log₂(pₖ(tᵢₖ))    (self-information)

GI(i) = SI(i) / log₂(N)     (normalized guessability)

Where:

• pₖ(v) is the frequency of trait value v in category k
• N is the collection size
• GI = 1.0 means average difficulty
• GI > 1.0 means easier to identify (rare traits = more distinctive)
• GI < 1.0 means harder to identify (common traits = blends in)

Risk Tiers

Risk	GI Range	Meaning
Critical	> 1.5	Identifiable in far fewer turns than average
High	1.2 – 1.5	Noticeably easier to identify
Medium	0.8 – 1.2	Near-average difficulty
Low	< 0.8	Hard to identify — blends into the crowd

The Rarity Paradox

In traditional NFT markets: Rarity = Premium

In guessmyNFT wagering: Rarity = Liability

Rare traits make an NFT more distinctive — easier to identify in fewer questions. An opponent who knows your NFT is the only one with a Crown can confirm it in a single question.

Implication for wager strategy: Floor price NFTs (common traits, low GI) are the optimal wagering instruments. Their value splits into "collector value" (low) and "wager value" (high).

Collection Quality Score (CQS)

CQS evaluates how suitable a collection is for deduction gameplay:

CQS = 0.30 × E + 0.25 × U + 0.25 × F + 0.20 × I

Component	Measures
E — Entropy Ratio	Information capacity utilization
U — Uniqueness	Fraction of NFTs with unique trait combos
F — Flatness	How uniform the trait distributions are
I — Independence	Statistical independence between trait categories

CQS	Rating
≥ 0.85	Excellent
0.70 – 0.84	Good
0.55 – 0.69	Fair
< 0.55	Poor

SCHIZODIO BROTHERS Results

• CQS: 0.868 — Excellent
• 999 tokens, 14 trait categories, 424 questions (v3 pipeline)
• 999 unique bitmaps (v3 — 1:1 bit-to-trait-value mapping, zero coverage gaps)

Full technical paper →