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STAGE 2 · TRIPLE BLOCK SYMMETRY · S2-0305 (SEED 41791)

Triple Block Symmetry S2-0305: 84-Hand 8-Deck Scoreboard & Derived-Road Walkthrough

Verified 8-deck shoe S2-0305 (seed 41791) documents a three-deep BBB-PPP column blocks testing Lookback-2 parity over 84 hands (44 Banker, 33 Player, 7 Tie). Its 43 logical columns span 43 display columns (C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B) and produce 74 Big Eye Boy marks (34R/40B), 72 Small Road marks (35R/37B), and 71 Cockroach Pig marks (36R/35B).

Verified 8-Deck Hands
84 (S2-0305)
Outcome Split
44B / 33P / 7T
Longest Streaks
7B · 4P
Big Road Columns
43 Cols
Engine-Verified Scoreboard · 84 Hands

Read the Board at Table Speed

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Big Road B B P P B P B P P B P B P B P P P P B P B B B P B P B P P B B B B B P B B P P P P B P B B P B P B B P P B B B B B B P B B B P B B B B P B P
Big Eye Boy = = ≠ = = ≠ ≠ ≠ = = = = ≠ = ≠ ≠ ≠ ≠ ≠ = ≠ = ≠ ≠ = = = ≠ ≠ = ≠ = = ≠ ≠ ≠ ≠ = ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ = ≠ ≠ = ≠ ≠ = = = ≠ = = = = ≠ ≠ ≠ = ≠ ≠ ≠ = = ≠ ≠ = =
Small Road ≠ ≠ = ≠ ≠ = ≠ = = = ≠ = ≠ = = ≠ = ≠ ≠ = ≠ = ≠ = = ≠ ≠ ≠ = = = ≠ ≠ = ≠ ≠ = = ≠ ≠ = ≠ ≠ = ≠ = = ≠ ≠ ≠ ≠ ≠ ≠ = ≠ = = = = ≠ ≠ = = ≠ = = = ≠ ≠ = ≠ =
Cockroach Pig ≠ ≠ ≠ ≠ = = ≠ = = ≠ = ≠ = ≠ ≠ ≠ = = ≠ ≠ = = ≠ = ≠ ≠ ≠ = = = ≠ = = = = = = ≠ = = = = = ≠ ≠ ≠ ≠ ≠ = = ≠ ≠ ≠ = = = = = ≠ ≠ = ≠ ≠ ≠ ≠ = = ≠ ≠ = ≠

S2-0305 (seed 41791): 84 hands (44B / 33P / 7T), max streaks 7B & 4P across 43 columns.

Big Road B is Banker, P is Player Roads under it Red (=): repeating Blue (≠): breaking
Step-by-Step Mark Proofs (Rule 1 & Rule 2)
S2-0305 BEB Mark #7

Column 6 has 2 beads. Column 5 has 1 bead. Different depth → blue (≠).

  1. Column 7 starts, so use Rule 1: compare Column 6 with Column 5, 1 column further back.
  2. Column 6 has 2 beads. Column 5 has 1 bead. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 6, the one that just finished, with Column 5.

S2-0305 SR Mark #4

This bead is at Row 2. Column 4 stopped at Row 1, one row above → blue (≠).

  1. Column 6 goes down to Row 2, so use Rule 2: look 2 columns back, at Column 4.
  2. Column 4 stopped at Row 1, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 4 stopped exactly one row above this bead.

S2-0305 CP Mark #1

Column 4 has 1 bead. Column 1 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. Column 4 has 1 bead. Column 1 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

S2-0305 8-Deck Hand Count
84 Hands (44 Banker / 33 Player / 7 Tie)

Seed 41791 opening columns: C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B (ties at H19,H21,H48,H51).

S2-0305 Big Road Span & Max Streaks
Max 7B / Max 4P Across 43 Logical Cols (43 Display Cols)

Three-row blocks test one Rule 1 new-column comparison and two consecutive Rule 2 Case 1 downward checks per column.

S2-0305 Big Eye Boy Rule Split
74 Marks (34R / 40B · 45.9% Red Across 37 Cols)

Rule 1: 41 · Rule 2 Case 1: 0 · Case 2: 0 · Case 3: 33.

S2-0305 Small Road & Cockroach Pig Split
SR: 35R/37B (48.6% Red) · CP: 36R/35B (50.7% Red)

Small Road compares each 3-deep column against the column two steps back, locking into Red (=) whenever 3-bead depth repeats.

S2-0305 Hand #85 Next-Hand Probe
If B -> BEB BLUE, SR BLUE, CP BLUE | If P -> BEB RED, SR RED, CP RED

Verified via getNextRoadPredictions() at Hand #84 of S2-0305.

S2-0305 SCOREBOARD STRUCTURE

S2-0305 Column Progression (C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B)

Recording 44 Banker wins, 33 Player wins, and 7 Ties over 84 hands, catalog entry S2-0305 (seed 41791) maps 43 logical columns onto 43 display columns (C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B) as a three-deep BBB-PPP column blocks testing Lookback-2 parity. Three-row blocks test one Rule 1 new-column comparison and two consecutive Rule 2 Case 1 downward checks per column.

Auditing S2-0305 shows maximum runs of 7B and 4P (ties at H19,H21,H48,H51) alongside 41 Rule 1 checks, 0 Case 1 checks, 0 Case 2 checks, and 33 Case 3 checks.

Opening 9 Big Road Columns of S2-0305 (Seed 41791)
Col SpanBeadsTallyGrid StopDepth Pair
S2-0305-C1:H1-2S2-0305:2BS2-0305:2B/0P/+0TS2-0305:R2StopS2-0305:2vs2
S2-0305-C2:H3-4S2-0305:2PS2-0305:2B/2P/+0TS2-0305:R2StopS2-0305:2vs2
S2-0305-C3:H5-5S2-0305:1BS2-0305:3B/2P/+0TS2-0305:R1StopS2-0305:1vs2
S2-0305-C4:H6-6S2-0305:1PS2-0305:3B/3P/+0TS2-0305:R1StopS2-0305:1vs1
S2-0305-C5:H7-7S2-0305:1BS2-0305:4B/3P/+0TS2-0305:R1StopS2-0305:1vs1
S2-0305-C6:H8-9S2-0305:2PS2-0305:4B/5P/+0TS2-0305:R2StopS2-0305:2vs1
S2-0305-C7:H10-10S2-0305:1BS2-0305:5B/5P/+0TS2-0305:R1StopS2-0305:1vs2
S2-0305-C8:H11-11S2-0305:1PS2-0305:5B/6P/+0TS2-0305:R1StopS2-0305:1vs1
S2-0305-C9:H12-12S2-0305:1BS2-0305:6B/6P/+0TS2-0305:R1StopS2-0305:1vs1
  • S2-0305 BEB #7 (BLUE): Column 6 has 2 beads. Column 5 has 1 bead. Different depth → blue (≠).
  • S2-0305 SR #4 (BLUE): This bead is at Row 2. Column 4 stopped at Row 1, one row above → blue (≠).
  • S2-0305 CP #1 (BLUE): Column 4 has 1 bead. Column 1 has 2 beads. Different depth → blue (≠).
S2-0305 DERIVED-ROAD & NEXT-HAND PROBE

S2-0305 Lookback Audit (34R/40B BEB · 35R/37B SR · 36R/35B CP)

On the lower boards of S2-0305, Big Eye Boy marks 34R/40B (45.9% Red), Small Road marks 35R/37B (48.6% Red), and Cockroach Pig marks 36R/35B (50.7% Red). Small Road compares each 3-deep column against the column two steps back, locking into Red (=) whenever 3-bead depth repeats.

Hand #85 projection table for S2-0305: Banker triggers BEB BLUE, SR BLUE, CP BLUE; Player triggers BEB RED, SR RED, CP RED.

Table Reality Check

Myth vs. Truth

MythStopping a 3-deep block at 2 beads in S2-0305 causes a Blue mark on Row 2.
TruthRow 2 in S2-0305 is still covered by the 3-bead reference column (Red =); the depth mismatch registers on the next column's Row 1 bead.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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