Data Density Analysis — Sylvester Longitudinal Study

Total Cards (N)

Nonland Cards

Unique Nonland

Lands

Information Theory

Concentration & Entropy Metrics

We model the deck as a discrete probability distribution where p_i = c_i / Σc for each unique card. This enables information-theoretic analysis of how concentrated or distributed the deck's resources are:

0.0698

Herfindahl-Hirschman Index

HHI = Σ p_i²

Low HHI (0.07 vs. max 1.0) indicates moderate dispersion — no single card dominates. In antitrust economics, this would classify as an "unconcentrated market."

14.33

Effective Card Count

1/HHI

Of 22 unique cards, the deck behaves as if it has 14.3 equally-weighted cards. The difference (22 - 14.3 = 7.7) measures the "concentration penalty."

4.135

Shannon Entropy (bits)

H = -Σ p_i log₂(p_i)

Normalized entropy: 0.927 (93% of maximum). The deck is highly entropic — nearly as diverse as theoretically possible while maintaining strategic focus.

0.348

Gini Coefficient

Inequality of Distribution

Moderate inequality — the deck intentionally concentrates copies on key cards (Kutzil at 6) while maintaining breadth. In economics, this is comparable to a Nordic country's income distribution.

Quantity Histogram

Distribution of copy counts across 22 unique cards:

1-of

2-of

4-of

6-of

59.1% of unique cards are singletons (13/22), but they represent only 30.2% of total copies (13/43). The four 4-of playsets and one 6-of create the draw-reliability backbone.

Combinatorial Probability

Hypergeometric Draw Reliability

The hypergeometric distribution models sampling without replacement from a finite population — exactly how a Magic deck operates. For key cards and card classes, we compute draw probabilities at critical sample sizes (n = cards seen by that turn):

X ~ Hypergeometric(N, K, n)
P(X ≥ 1) = 1 - C(N-K, n) / C(N, n)
P(X ≥ k) = Σ_j=k^min(K,n) C(K,j) · C(N-K, n-j) / C(N, n)
E[X] = nK/N

Key Card Draw Probabilities (N=69)

Probability of drawing at least one copy by turn/sample size. Includes full deck (69 cards with lands).

n (cards seen)	P(Mercy ≥ 1)	P(Paladin ≥ 1)	P(Drizzt ≥ 1)	P(Mercy ≥ 2)	E[Mercy]
7 (opening)	0.355	0.355	0.194	0.048	0.406
8 (T1 draw)	0.396	0.396	0.220	0.063	0.464
9 (T2 play)	0.436	0.436	0.246	0.080	0.522
10 (T3 play)	0.474	0.474	0.271	0.097	0.580
11	0.509	0.509	0.295	0.117	0.638
13	0.575	0.575	0.344	0.158	0.754
15	0.634	0.634	0.390	0.204	0.870

Behavioral Mass Draw Probabilities (N=43, nonland only)

Probability of drawing at least one card from each behavioral archetype, modeled on the 43-card nonland pool.

n	P(PREDATOR ≥ 1)	P(DIVINE ≥ 1)	P(RELIC ≥ 1)	P(PACK ≥ 1)	E[PREDATOR]	E[DIVINE]
7	0.937	0.896	0.681	0.608	2.116	1.791
9	0.975	0.950	0.779	0.711	2.721	2.302
11	0.991	0.978	0.851	0.791	3.326	2.814
15	0.999	0.996	0.938	0.898	4.535	3.837

Key insight: PREDATOR behavioral mass reaches 93.7% probability in the opening hand — the deck is engineered so that aggressive creatures appear with near-certainty from turn 1. By turn 3 (n=9), you have a 97.5% chance of at least one predatory threat on board.

Mana Calculus

Neutral Basic-Land Optimization

With 26 lands in a 69-card deck (37.7% land ratio), we optimize the Plains/Forest split to maximize the probability of casting the deck's key early plays — specifically, double-white for Paladin Class and green-white for Drizzt Do'Urden:

Optimized Split: 13 Plains / 13 Forest

Metric	Value
P(WW by T3)	49.6%
P(Drizzt on-curve T3)	14.1%
P(Paladin T1)	26.4%

Equal split is optimal because the deck's mana requirements are symmetric — both colors needed equally by turn 3. Any skew toward Plains improves WW but degrades Drizzt below baseline.

Combinatorial Formula

P(WW by T3) = Σ_{k_pl,k_for}
  [k_pl+k_for ≥ 3 AND k_pl ≥ 2]
  × C(Plains,k_pl) · C(Forest,k_for)
  × C(Other, 9-k_pl-k_for)
  / C(N, 9)

On the play, no mulligans: 9 cards seen by turn 3. The triple constraint (enough total lands, enough of the right color, room for spells) is a multivariate hypergeometric optimization.

"Hypergeometric draw reliability is sampling without replacement from a finite population. Every SRE availability calculation, every load test capacity model, every security coverage metric uses the same mathematics." — ArchDaemon™ · Quality Engineering Framework

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ArchDaemon™ (US Serial 98940257) · GoldHat™ (US Serial 98925168) · All analyses are original IP of David Leo Sylvester.