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STAGE 2 · RULE 2 CASE 3 OVERHANG · S2-0851 (SEED 105928)

Rule 2 Case 3 Overhang S2-0851: 81-Hand 8-Deck Scoreboard & Derived-Road Walkthrough

Verified 8-deck shoe S2-0851 (seed 105928) documents a deep columns extending two or more rows past short lookback columns over 81 hands (38 Banker, 39 Player, 4 Tie). Its 44 logical columns span 44 display columns (C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B) and produce 74 Big Eye Boy marks (32R/42B), 72 Small Road marks (29R/43B), and 71 Cockroach Pig marks (33R/38B).

Verified 8-Deck Hands
81 (S2-0851)
Outcome Split
38B / 39P / 4T
Longest Streaks
4B · 4P
Big Road Columns
44 Cols
Engine-Verified Scoreboard · 81 Hands

Read the Board at Table Speed

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

S2-0851 (seed 105928): 81 hands (38B / 39P / 4T), max streaks 4B & 4P across 44 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)
S2-0851 BEB Mark #2

Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 3 starts, so use Rule 1: compare Column 2 with Column 1, 1 column further back.
  2. Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

S2-0851 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.

S2-0851 CP Mark #2

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

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

S2-0851 8-Deck Hand Count
81 Hands (38 Banker / 39 Player / 4 Tie)

Seed 105928 opening columns: C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B (ties at H35,H54,H56,H77).

S2-0851 Big Road Span & Max Streaks
Max 4B / Max 4P Across 44 Logical Cols (44 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.

S2-0851 Big Eye Boy Rule Split
74 Marks (32R / 42B · 43.2% Red Across 38 Cols)

Rule 1: 42 · Rule 2 Case 1: 0 · Case 2: 0 · Case 3: 32.

S2-0851 Small Road & Cockroach Pig Split
SR: 29R/43B (40.3% Red) · CP: 33R/38B (46.5% Red)

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

S2-0851 Hand #82 Next-Hand Probe
If B -> BEB BLUE, SR BLUE, CP BLUE | If P -> BEB RED, SR RED, CP RED

Verified via getNextRoadPredictions() at Hand #81 of S2-0851.

S2-0851 SCOREBOARD STRUCTURE

S2-0851 Column Progression (C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B)

In 8-deck record S2-0851 (seed 105928), 44 logical columns (44 display columns, C1:2B C2:2P C3:1B C4:1P C5:1B C6:2P C7:1B) organize 81 hands (38B, 39P, 4T) around a deep columns extending two or more rows past short lookback columns. Whenever a column's current row index is at least two rows below the reference column's bottom, Rule 2 Case 3 applies.

Scoreboard metrics on S2-0851 list 4B and 4P max runs (ties H35,H54,H56,H77) with 42 Rule 1, 0 Case 1, 0 Case 2, and 32 Case 3 Lookback-1 outcomes.

Opening 9 Big Road Columns of S2-0851 (Seed 105928)
Col SpanBeadsTallyGrid StopDepth Pair
S2-0851-C1:H1-2S2-0851:2BS2-0851:2B/0P/+0TS2-0851:R2StopS2-0851:2vs2
S2-0851-C2:H3-4S2-0851:2PS2-0851:2B/2P/+0TS2-0851:R2StopS2-0851:2vs2
S2-0851-C3:H5-5S2-0851:1BS2-0851:3B/2P/+0TS2-0851:R1StopS2-0851:1vs2
S2-0851-C4:H6-6S2-0851:1PS2-0851:3B/3P/+0TS2-0851:R1StopS2-0851:1vs1
S2-0851-C5:H7-7S2-0851:1BS2-0851:4B/3P/+0TS2-0851:R1StopS2-0851:1vs1
S2-0851-C6:H8-9S2-0851:2PS2-0851:4B/5P/+0TS2-0851:R2StopS2-0851:2vs1
S2-0851-C7:H10-10S2-0851:1BS2-0851:5B/5P/+0TS2-0851:R1StopS2-0851:1vs2
S2-0851-C8:H11-14S2-0851:4PS2-0851:5B/9P/+0TS2-0851:R4StopS2-0851:4vs1
S2-0851-C9:H15-16S2-0851:2BS2-0851:7B/9P/+0TS2-0851:R2StopS2-0851:2vs4
  • S2-0851 BEB #2 (RED): Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
  • S2-0851 SR #4 (BLUE): This bead is at Row 2. Column 4 stopped at Row 1, one row above → blue (≠).
  • S2-0851 CP #2 (BLUE): Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).
S2-0851 DERIVED-ROAD & NEXT-HAND PROBE

S2-0851 Lookback Audit (32R/42B BEB · 29R/43B SR · 33R/38B CP)

Across all three derived grids in S2-0851, Lookback 1 posts 32R/42B (43.2% Red), Lookback 2 posts 29R/43B (40.3% Red), and Lookback 3 posts 33R/38B (46.5% Red). After a single Rule 2 Case 2 Blue (≠) mark at one row past the bottom, every deeper bead in the overhang records Red (=).

For hypothetical Hand #82 in S2-0851, Banker produces BEB BLUE, SR BLUE, and CP BLUE while Player produces BEB RED, SR RED, and CP RED, reflecting opposite Rule 1 and Rule 2 branches.

Table Reality Check

Myth vs. Truth

MythDropping three rows past a 1-bead column in S2-0851 keeps producing Blue break marks.
TruthOnly the first bead past the reference bottom in S2-0851 is Blue (≠); two or more rows past the bottom is always Red (=) under Rule 2 Case 3.
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