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DESCENDING 5-4-3-2-1 CASCADE · CATALOG DSC31 (SEED 204631)

Descending Cascade Shoe DSC31: 77-Hand 8-Deck Scoreboard & Derived-Road Audit

Catalog shoe DSC31 (seed 204631) captures a tapering 5-4-3-2-1 column depths where every continuing row is covered by a taller reference column across 77 dealt 8-deck hands (39 Banker, 31 Player, 7 Tie). Its 29 logical Big Road columns occupy 29 display columns (C1:2B · C2:2P · C3:6B · C4:5P · C5:4B · C6:3P · C7:2B · C8:1P) and generate 67 Big Eye Boy marks (29R/38B), 65 Small Road marks (30R/35B), and 59 Cockroach Pig marks (38R/21B).

Verified 8-Deck Hands
77 (DSC31)
Outcome Split
39B / 31P / 7T
Peak Streaks
6B · 5P
Big Road Columns
29 Cols
Engine-Verified Scoreboard · 77 Hands

Read the Board at Table Speed

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

DSC31 (seed 204631): 77 hands (39B / 31P / 7T), peak streaks 6B & 5P across 29 logical 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)
DSC31 Big Eye Boy Entry #3

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 3 goes down to Row 2, so use Rule 2: look 1 column back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

DSC31 Small Road Entry #2

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 3 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

DSC31 Cockroach Pig Entry #3

This bead is at Row 4. Column 1 stopped at Row 2, more than one row above → red (=).

  1. Column 4 goes down to Row 4, so use Rule 2: look 3 columns back, at Column 1.
  2. Column 1 stopped at Row 2, more than one row above → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

DSC31 8-Deck Hand Distribution
77 Hands (39 Banker / 31 Player / 7 Tie)

Seed 204631 opening column signature: C1:2B · C2:2P · C3:6B · C4:5P · C5:4B · C6:3P · C7:2B · C8:1P.

DSC31 Big Road Span & Max Streaks
Max 6B / Max 5P Across 29 Logical Cols (29 Display Cols)

When columns shrink by one bead each time, every downward step (Row 2 and below) sits beside an existing bead in the taller reference column to the left.

DSC31 Big Eye Boy Rule Breakdown
67 Marks (29R / 38B · 43.3% Red across 37 Display Cols)

Rule 1: 27 marks · Rule 2 Case 1: 0 · Case 2: 0 · Case 3: 40.

DSC31 Small Road & Cockroach Pig Tally
SR: 30R/35B (46.2% Red) · CP: 38R/21B (64.4% Red)

Throughout the 5-4-3-2-1 cascade, 100% of Rule 2 marks are Red (=) under Case 1, whereas every Rule 1 mark at Row 1 of a new column is Blue (≠) due to unequal finished depths.

DSC31 Hand #78 Next-Hand Probe
If B → BEB blue, SR red, CP red | If P → BEB red, SR blue, CP blue

Computed by getNextRoadPredictions() after Hand #77 of DSC31.

DSC31 COLUMN GEOMETRY (DESCENDING-CASCADE)

DSC31 Scoreboard Structure: C1:2B · C2:2P · C3:6B · C4:5P · C5:4B · C6:3P · C7:2B · C8:1P

In catalog shoe DSC31 (seed 204631), 77 total hands resolve into 39 Banker wins, 31 Player wins, and 7 Ties across 29 logical columns (C1:2B · C2:2P · C3:6B · C4:5P · C5:4B · C6:3P · C7:2B · C8:1P). When columns shrink by one bead each time, every downward step (Row 2 and below) sits beside an existing bead in the taller reference column to the left.

Tracking DSC31 column by column shows peak runs of 6B and 5P spreading across 29 Big Road display columns: DSC31 records 27 Rule 1 new-column checks, 0 Rule 2 Case 1 covered-row checks, 0 Rule 2 Case 2 one-past-bottom breaks, and 40 Rule 2 Case 3 deep-tail checks.

Opening 10 Big Road Columns of DSC31 (Seed 204631)
Column & SpanBeadsRunning TallyGrid StopDepth Pair
DSC31-C01 (H1–H2)2B (BB) [DSC31]2B/0P (+0T @DSC31-C1)DSC31 Row2 Stop (Col1)NextColVsDSC31-C1: 2v2
DSC31-C02 (H3–H4)2P (PP) [DSC31]2B/2P (+0T @DSC31-C2)DSC31 Row2 Stop (Col2)NextColVsDSC31-C1: 2v2
DSC31-C03 (H5–H11)6B (BBBBBB) [DSC31]8B/2P (+1T @DSC31-C3)DSC31 Row6 Stop (Col3)NextColVsDSC31-C2: 6v2
DSC31-C04 (H12–H17)5P (PPPPP) [DSC31]8B/7P (+1T @DSC31-C4)DSC31 Row5 Stop (Col4)NextColVsDSC31-C3: 5v6
DSC31-C05 (H18–H21)4B (BBBB) [DSC31]12B/7P (+0T @DSC31-C5)DSC31 Row4 Stop (Col5)NextColVsDSC31-C4: 4v5
DSC31-C06 (H22–H25)3P (PPP) [DSC31]12B/10P (+1T @DSC31-C6)DSC31 Row3 Stop (Col6)NextColVsDSC31-C5: 3v4
DSC31-C07 (H26–H27)2B (BB) [DSC31]14B/10P (+0T @DSC31-C7)DSC31 Row2 Stop (Col7)NextColVsDSC31-C6: 2v3
DSC31-C08 (H28–H28)1P (P) [DSC31]14B/11P (+0T @DSC31-C8)DSC31 Row1 Stop (Col8)NextColVsDSC31-C7: 1v2
DSC31-C09 (H29–H30)2B (BB) [DSC31]16B/11P (+0T @DSC31-C9)DSC31 Row2 Stop (Col9)NextColVsDSC31-C8: 2v1
DSC31-C10 (H31–H31)1P (P) [DSC31]16B/12P (+0T @DSC31-C10)DSC31 Row1 Stop (Col10)NextColVsDSC31-C9: 1v2
  • DSC31 BEB #3 (RED): verified at DSC31 lookback-1 index 2 (29R/38B total).
  • DSC31 SR #2 (BLUE): verified at DSC31 lookback-2 index 1 (30R/35B total).
  • DSC31 CP #3 (RED): verified at DSC31 lookback-3 index 2 (38R/21B total).
DSC31 DERIVED-ROAD & CUT-CARD PROBE

DSC31 Lookback Split (29R/38B BEB · 30R/35B SR · 38R/21B CP)

Throughout the 5-4-3-2-1 cascade, 100% of Rule 2 marks are Red (=) under Case 1, whereas every Rule 1 mark at Row 1 of a new column is Blue (≠) due to unequal finished depths. Across DSC31, Big Eye Boy prints 29 Red (43.3%) and 38 Blue marks, Small Road prints 30 Red (46.2%) and 35 Blue marks, and Cockroach Pig prints 38 Red (64.4%) and 21 Blue marks.

At the DSC31 cut card after Hand #77, probing Hand #78 via getNextRoadPredictions() yields Banker → BEB BLUE / SR RED / CP RED and Player → BEB RED / SR BLUE / CP BLUE for DSC31.

Table Reality Check

Myth vs. Truth

MythTapering columns in DSC31 mark Blue on the way down because each streak is shorter than the last.
TruthWhile moving down a shorter column in DSC31, the taller reference column still has a bead at every row visited (Rule 2 Case 1 Red =); only the Row 1 new-column check marks Blue (≠).
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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