Clean Sweep

CLEAN SWEEP — Official Rules & Gameplay Guide

1. EQUIPMENT & SETUP

1:1. Equipment: Six (6) standard six-sided dice (d6) (6 x 6).

1:2. Players: 2 to 4 players.

1:3. Objective: Score points by assembling qualifying matching sets (3-of-a-kind or higher), managing risk ceilings during tactical re-rolls, or triggering special turn-resetting events (Perfect Straight, High Ball, Lowball, or Clean Sweep).

1:4. Rounds: Players each get their full turn (which may include multiple re-rolls) and after all players present have concluded their turns, a Round is completed.

1:5. Game End & Ties: Multiple rounds are played until a player meets or exceeds a predetermined end of game score. A round must be fully completed with all players having the exact same number of turns. If 2 players exceed the score, the highest total wins. In the rare event of a tie, an additional round shall be played between the tied players.

2. TURN STRUCTURE

2:1. Master Roll & Line-Up: Active player rolls all six (6) dice simultaneously. All dice are immediately arranged in descending numerical order (highest to lowest) to establish the Line-up.

2:2. Establishing the Anchor: The highest face value in the Line-up is designated as the Anchor. An anchor of 6 is permanently locked and cannot be re-rolled. An anchor of less than 6 cannot be re-rolled alone, but is eligible for a re-roll if it is a pair or greater.

3. RE-ROLLING QUALIFYING SETS

3:1. Sets Only: Only matching sets (pairs, 3, 4, or 5-of-a-kinds) are eligible for re-rolls. Singletons cannot be re-rolled.

3:3. Dynamic Ceilings: Re-rolled dice cannot exceed a strict Ceiling number based on numbers present in the Line-up:

• Pair (2-of-a-kind): Cannot exceed 1st higher distinct number.
• 3-of-a-Kind: Skips 1 number → Cannot exceed 2nd higher distinct number.
• 4-of-a-Kind: Skips 2 numbers → Cannot exceed 3rd higher distinct number.
• 5-of-a-Kind: Skips 3 numbers → Cannot exceed 4th higher distinct number.
• No limiting criteria once ceiling reaches 6.

3:4. Elimination: Any re-rolled die exceeding the Ceiling is permanently eliminated for the remainder of the turn.

3:6. Tag-Along Rule: Lower-ranking qualifying sets may tag along if directly contiguous in the Line-up with no intervening singletons. All obey the Ceiling of the highest set.

4. CLEAN SWEEPS & SPECIAL BONUSES (Requires All 6 Active Dice)

4:1. Clean Sweep (+20 Pts & Turn Reset): Triggered when every active die lower than an Anchored 6 qualifies to be picked up simultaneously, or when every die in the Line-up qualifies to be picked up (anchor < 6 is a pair or greater).

4:1.D. 6-of-a-Kind: Awards 100 points + 20-point Clean Sweep bonus (120 pts total) & fresh Master Roll.

4:2.A. Perfect Straight [6, 5, 4, 3, 2, 1]: Awards 35 points + 20-point Clean Sweep bonus (55 pts total) & fresh Master Roll.

4:2.B. High Ball (≥ 31 Total Sum): Awards exact total sum + 20-point Clean Sweep bonus & fresh Master Roll.

4:2.C. Lowball Roll (All dice ≤ 2): Awards 30 points + 20-point Clean Sweep bonus (50 pts total) & fresh Master Roll.

5. END OF TURN & PASS SCORING

• 3-of-a-Kind: 1× Face Value
• 4-of-a-Kind: 2× Face Value
• 5-of-a-Kind: 4× Face Value

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Design & Algorithm Narrative

The Triad of Algorithmic Play

Within the Melee Quest game engine ecosystem, Clean Sweep serves as the probabilistic and dynamic risk counterpart to its sister games:

• Head of the Line: Focuses on deterministic grid traversal and topological queue algorithms.
• Get Off My Lawn: Explores spatial perimeter containment, territory graph expansion, and boundary exclusion mechanics.
• Clean Sweep: Formulates a discrete state-machine optimizer governing stochastic risk ceilings, cascading subset eliminations, and mathematical reset thresholds.

1. Dynamic Ceiling & Set-Skipping Formula

The core computational engine utilizes dynamic combinatorial filtering. For a selected subset of matching dice $S$ with highest value $v_{max}$ and count $k$, the upper numeric threshold $C$ is computed across the ordered distinct set of active table dice $D_{active}$:

jumpIndex = max(0, k - 2);
higherDistincts = { d ∈ D_{active} | d > v_{max} } (sorted ascending);
Ceiling C = higherDistincts[jumpIndex] || 6;

2. Algorithmic Architecture & System Properties

• Bounded Stochastic Optimization: Models sequential multi-agent decision-making under uncertainty, where risk exposure dynamically expands or contracts based on existing resource depth.
• Cascading State Elimination: Enforces deterministic boundary failure—exceeding a calculated tolerance boundary results in isolated node pruning (die elimination) without terminating the active operational pipeline.
• Contiguous Dependency Cascades: Lower-tier subsets inherit the ceiling boundary of contiguous lead subsets, demonstrating grouped risk aggregation.

3. Real-World Applications in Controlled Risk Systems

While implemented as a digital table game, the underlying state architecture demonstrates structural parallels to production-grade algorithms:

• Dynamic Portfolio Risk & Volatility Collars (Quantitative Finance): Higher-order sets scale risk ceilings similarly to how capital depth unlocks wider Value-at-Risk (VaR) bands. Exceeding the dynamic ceiling models automated limit-order liquidation or tripwires, preventing systemic failure.
• Adaptive Backoff & Throughput Optimization (Network Routing): Contiguous tag-along mechanics mirror packet burst aggregation in congestion avoidance protocols (e.g., dynamic window sizing in TCP/Ethernet), where bundled payloads inherit the bounded retry window of the lead cluster.
• Multi-Agent Failsafe Systems (Robotics & Distributed Computing): The interplay between anchored constants (locked 6s) and variable subordinate nodes models multi-sensor fusion architectures, isolating compromised threads while preserving overall state continuity.

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