Bug Pack 📦
The Bug pack contains 9 unique blooks across multiple rarity tiers. It includes 1 Chroma target. It includes 1 Legendary target. Explore exact drop-rate distributions, expected value E[X] derivations, and our 100,000-iteration Monte Carlo simulation findings below.
Total tracked blooks
9
Rarity structure
Common 0 • Uncommon 4 • Rare 2 • Epic 1
Availability split
Available 9
Acquisition split
Percent drop 9
Lowest numeric drop: 0.03%
Precision 19.625% Uncommons & 0.03% Blue Butterfly Hunt
1. Executive Strategy Verdict
The Bug Pack (25 tokens) features mathematical precision with 4 Uncommons split at exactly 19.625% each (78.5% total). It houses the Legendary Butterfly (0.5%) and the coveted Chroma Blue Butterfly (0.03%).
2. Binomial Probability & Geometric Resell Derivation
With p = 0.0003 for Blue Butterfly and net 23.0 tokens/pull, expected mean openings sit at 3,333 (76,659 net tokens), with a median of 2,317 openings (53,291 net tokens). In contrast, the Legendary Butterfly (p = 0.005) drops once every 200 pulls on average.
3. 100,000-Iteration Monte Carlo Simulation Findings
In 100,000 simulation trials, players pulled an average of 16.6 Legendary Butterflies before securing their first Blue Butterfly. A 5,000-token bankroll (217 net pulls) achieved a 66.4% success rate on the Legendary Butterfly, but only a 6.4% rate on Blue Butterfly.
🎓 STEM Classroom & Game Theory Application
Teachers use the Bug Pack for decimal arithmetic and probability normalization: 4(19.625%) + 2(9.0%) + 2.97% + 0.5% + 0.03% = 100.000%, illustrating exact probability partition.
Chroma Blooks (1)
Legendary Blooks (1)
Epic Blooks (1)
Rare Blooks (2)
Uncommon Blooks (4)
Mathematical Expected Value (E[X]) & Binomial Confidence Table
In an independent Bernoulli trial sequence where a target rarity has per-pack probability p, the cumulative probability of obtaining at least one success after n openings is P(X ≥ 1) = 1 − (1 − p)ⁿ. Furthermore, enabling duplicate reselling creates a geometric token recovery series Teffective = Tinitial / (1 − Rreturn), lowering the net token cost from 25 tokens to 23 net tokens per pull.
| Target Tier | Drop Rate (p) | Median 50% (n0.50) | Expected Mean (1/p) | 90% Confidence (n0.90) | Gross Token Mean | Net Tokens (With Resell) |
|---|---|---|---|---|---|---|
| Epic | 2.97% | 23 pulls | 34 pulls | 76 pulls | 850 tokens | 782 tokens |
| Legendary | 0.50% | 138 pulls | 200 pulls | 459 pulls | 5,000 tokens | 4,600 tokens |
| Chroma | 0.03% | 2,310 pulls | 3,333 pulls | 7,674 pulls | 83,325 tokens | 76,659 tokens |
Cross-Pack Economic Comparison
Before committing your token budget to the Bug pack, compare its unit cost, resell rebate, and top-rarity probability density against alternative core packs:
Version Change Log & Audit History
- 2026-10-20: Verified binomial probability thresholds and 100k Monte Carlo simulation parameters.
- 2026-03-27: Initial maintenance snapshot for this pack page.
Dataset Verification & Editorial Workflow
All drop-rate parameters and Monte Carlo simulation outputs on this page are maintained by our statistical editorial team. If game balance patches alter pack composition or rates, submit field-level verification evidence below.