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STAGE 2 · RULE 2 CASE 3 OVERHANG · S2-0854 (SEED 133456)

Rule 2 Case 3 Overhang S2-0854: 72-Hand 8-Deck Scoreboard & Derived-Road Walkthrough

Verified 8-deck shoe S2-0854 (seed 133456) documents a deep columns extending two or more rows past short lookback columns over 72 hands (34 Banker, 34 Player, 4 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 65 Big Eye Boy marks (30R/35B), 63 Small Road marks (27R/36B), and 62 Cockroach Pig marks (21R/41B).

Verified 8-Deck Hands
72 (S2-0854)
Outcome Split
34B / 34P / 4T
Longest Streaks
4B · 3P
Big Road Columns
43 Cols
Engine-Verified Scoreboard · 72 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 B P P B P P B P B P B B P P B P B P B B B P P B P B B B B P P B P B P B B B B P B P B B P P B
Big Eye Boy = = ≠ = = ≠ ≠ ≠ = = = = ≠ = ≠ ≠ ≠ ≠ ≠ ≠ = = ≠ ≠ ≠ ≠ = = = = ≠ ≠ ≠ ≠ = ≠ = ≠ = ≠ ≠ = ≠ = = ≠ = = ≠ ≠ = ≠ ≠ ≠ ≠ = = ≠ ≠ = = ≠ ≠ = =
Small Road ≠ ≠ = ≠ ≠ = ≠ = = = ≠ = ≠ = = ≠ = = = = ≠ = ≠ ≠ ≠ ≠ = = ≠ = = = ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ ≠ ≠ = = ≠ = ≠ = ≠ = ≠ ≠ ≠ ≠
Cockroach Pig ≠ ≠ ≠ ≠ = = ≠ = = ≠ = ≠ = ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ = = ≠ ≠ ≠ = = ≠ ≠ ≠ ≠ = ≠ = ≠ = ≠ ≠ = ≠ = ≠ = ≠ = ≠ = = ≠ ≠ = ≠ ≠ ≠ ≠ ≠

S2-0854 (seed 133456): 72 hands (34B / 34P / 4T), max streaks 4B & 3P 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)
S2-0854 BEB Mark #5

Column 5 has 1 bead. Column 4 has 1 bead. Same depth → red (=).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 4, 1 column further back.
  2. Column 5 has 1 bead. Column 4 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 4.

S2-0854 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.

S2-0854 CP Mark #5

Column 7 has 1 bead. Column 4 has 1 bead. Same depth → red (=).

  1. Column 8 starts, so use Rule 1: compare Column 7 with Column 4, 3 columns further back.
  2. Column 7 has 1 bead. Column 4 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 7, the one that just finished, with Column 4.

Verified Reference Data

Key Facts & Table Specifications

S2-0854 8-Deck Hand Count
72 Hands (34 Banker / 34 Player / 4 Tie)

Seed 133456 opening columns: C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B (ties at H28,H36,H52,H58).

S2-0854 Big Road Span & Max Streaks
Max 4B / Max 3P Across 43 Logical Cols (43 Display Cols)

Whenever a column's current row index is at least two rows below the reference column's bottom, Rule 2 Case 3 applies.

S2-0854 Big Eye Boy Rule Split
65 Marks (30R / 35B · 46.2% Red Across 31 Cols)

Rule 1: 41 · Rule 2 Case 1: 0 · Case 2: 0 · Case 3: 24.

S2-0854 Small Road & Cockroach Pig Split
SR: 27R/36B (42.9% Red) · CP: 21R/41B (33.9% Red)

After a single Rule 2 Case 2 Blue (≠) mark at one row past the bottom, every deeper bead in the overhang records Red (=).

S2-0854 Hand #73 Next-Hand Probe
If B -> BEB RED, SR RED, CP BLUE | If P -> BEB BLUE, SR BLUE, CP RED

Verified via getNextRoadPredictions() at Hand #72 of S2-0854.

S2-0854 SCOREBOARD STRUCTURE

S2-0854 Column Progression (C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B)

Walkthrough S2-0854 (seed 133456) examines a deep columns extending two or more rows past short lookback columns across 72 verified 8-deck hands (34B, 34P, 4T) arranged into 43 logical columns and 43 display columns (C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B). Whenever a column's current row index is at least two rows below the reference column's bottom, Rule 2 Case 3 applies.

Column depth extremes of 4B and 3P in S2-0854 (tie hands H28,H36,H52,H58) produce 41 Rule 1 entries, 0 Rule 2 Case 1 entries, 0 Case 2 entries, and 24 Case 3 entries on Big Eye Boy.

Opening 9 Big Road Columns of S2-0854 (Seed 133456)
Col SpanBeadsTallyGrid StopDepth Pair
S2-0854-C1:H1-2S2-0854:2BS2-0854:2B/0P/+0TS2-0854:R2StopS2-0854:2vs2
S2-0854-C2:H3-4S2-0854:2PS2-0854:2B/2P/+0TS2-0854:R2StopS2-0854:2vs2
S2-0854-C3:H5-5S2-0854:1BS2-0854:3B/2P/+0TS2-0854:R1StopS2-0854:1vs2
S2-0854-C4:H6-6S2-0854:1PS2-0854:3B/3P/+0TS2-0854:R1StopS2-0854:1vs1
S2-0854-C5:H7-7S2-0854:1BS2-0854:4B/3P/+0TS2-0854:R1StopS2-0854:1vs1
S2-0854-C6:H8-9S2-0854:2PS2-0854:4B/5P/+0TS2-0854:R2StopS2-0854:2vs1
S2-0854-C7:H10-10S2-0854:1BS2-0854:5B/5P/+0TS2-0854:R1StopS2-0854:1vs2
S2-0854-C8:H11-11S2-0854:1PS2-0854:5B/6P/+0TS2-0854:R1StopS2-0854:1vs1
S2-0854-C9:H12-12S2-0854:1BS2-0854:6B/6P/+0TS2-0854:R1StopS2-0854:1vs1
  • S2-0854 BEB #5 (RED): Column 5 has 1 bead. Column 4 has 1 bead. Same depth → red (=).
  • S2-0854 SR #4 (BLUE): This bead is at Row 2. Column 4 stopped at Row 1, one row above → blue (≠).
  • S2-0854 CP #5 (RED): Column 7 has 1 bead. Column 4 has 1 bead. Same depth → red (=).
S2-0854 DERIVED-ROAD & NEXT-HAND PROBE

S2-0854 Lookback Audit (30R/35B BEB · 27R/36B SR · 21R/41B CP)

Final derived-road splits in S2-0854 are BEB 30R/35B (46.2% Red), SR 27R/36B (42.9% Red), and CP 21R/41B (33.9% Red). After a single Rule 2 Case 2 Blue (≠) mark at one row past the bottom, every deeper bead in the overhang records Red (=).

Running the ?B and ?P probe at Hand #73 of S2-0854 returns BEB RED, SR RED, CP BLUE for ?B and BEB BLUE, SR BLUE, CP RED for ?P.

Table Reality Check

Myth vs. Truth

MythDropping three rows past a 1-bead column in S2-0854 keeps producing Blue break marks.
TruthOnly the first bead past the reference bottom in S2-0854 is Blue (≠); two or more rows past the bottom is always Red (=) under Rule 2 Case 3.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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