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DESCENDING 5-4-3-2-1 CASCADE · CATALOG DSC13 (SEED 204613)

Descending Cascade Shoe DSC13: 77-Hand 8-Deck Scoreboard & Derived-Road Audit

Catalog shoe DSC13 (seed 204613) 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 (38 Banker, 35 Player, 4 Tie). Its 30 logical Big Road columns occupy 30 display columns (C1:6B · C2:5P · C3:4B · C4:3P · C5:2B · C6:1P · C7:3B · C8:1P) and generate 66 Big Eye Boy marks (25R/41B), 61 Small Road marks (25R/36B), and 57 Cockroach Pig marks (37R/20B).

Verified 8-Deck Hands
77 (DSC13)
Outcome Split
38B / 35P / 4T
Peak Streaks
6B · 5P
Big Road Columns
30 Cols
Engine-Verified Scoreboard · 77 Hands

Read the Board at Table Speed

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

DSC13 (seed 204613): 77 hands (38B / 35P / 4T), peak streaks 6B & 5P across 30 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)
DSC13 Big Eye Boy Entry #3

This bead is at Row 4. Column 1 has a bead at Row 4 too → red (=).

  1. Column 2 goes down to Row 4, so use Rule 2: look 1 column back, at Column 1.
  2. Column 1 has a bead at Row 4 too → 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.

DSC13 Small Road Entry #4

Column 3 has 4 beads. Column 1 has 6 beads. Different depth → blue (≠).

  1. Column 4 starts, so use Rule 1: compare Column 3 with Column 1, 2 columns further back.
  2. Column 3 has 4 beads. Column 1 has 6 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.

DSC13 Cockroach Pig Entry #1

This bead is at Row 2. Column 1 has a bead at Row 2 too → red (=).

  1. Column 4 goes down to Row 2, so use Rule 2: look 3 columns back, at Column 1.
  2. Column 1 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 1 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

DSC13 8-Deck Hand Distribution
77 Hands (38 Banker / 35 Player / 4 Tie)

Seed 204613 opening column signature: C1:6B · C2:5P · C3:4B · C4:3P · C5:2B · C6:1P · C7:3B · C8:1P.

DSC13 Big Road Span & Max Streaks
Max 6B / Max 5P Across 30 Logical Cols (30 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.

DSC13 Big Eye Boy Rule Breakdown
66 Marks (25R / 41B · 37.9% Red across 38 Display Cols)

Rule 1: 28 marks · Rule 2 Case 1: 0 · Case 2: 0 · Case 3: 38.

DSC13 Small Road & Cockroach Pig Tally
SR: 25R/36B (41.0% Red) · CP: 37R/20B (64.9% 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.

DSC13 Hand #78 Next-Hand Probe
If B → BEB blue, SR blue, CP red | If P → BEB red, SR red, CP blue

Computed by getNextRoadPredictions() after Hand #77 of DSC13.

DSC13 COLUMN GEOMETRY (DESCENDING-CASCADE)

DSC13 Scoreboard Structure: C1:6B · C2:5P · C3:4B · C4:3P · C5:2B · C6:1P · C7:3B · C8:1P

In catalog shoe DSC13 (seed 204613), 77 total hands resolve into 38 Banker wins, 35 Player wins, and 4 Ties across 30 logical columns (C1:6B · C2:5P · C3:4B · C4:3P · C5:2B · C6:1P · C7:3B · 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 DSC13 column by column shows peak runs of 6B and 5P spreading across 30 Big Road display columns: DSC13 records 28 Rule 1 new-column checks, 0 Rule 2 Case 1 covered-row checks, 0 Rule 2 Case 2 one-past-bottom breaks, and 38 Rule 2 Case 3 deep-tail checks.

Opening 10 Big Road Columns of DSC13 (Seed 204613)
Column & SpanBeadsRunning TallyGrid StopDepth Pair
DSC13-C01 (H1–H6)6B (BBBBBB) [DSC13]6B/0P (+0T @DSC13-C1)DSC13 Row6 Stop (Col1)NextColVsDSC13-C1: 6v6
DSC13-C02 (H7–H11)5P (PPPPP) [DSC13]6B/5P (+0T @DSC13-C2)DSC13 Row5 Stop (Col2)NextColVsDSC13-C1: 5v6
DSC13-C03 (H12–H16)4B (BBBB) [DSC13]10B/5P (+1T @DSC13-C3)DSC13 Row4 Stop (Col3)NextColVsDSC13-C2: 4v5
DSC13-C04 (H17–H19)3P (PPP) [DSC13]10B/8P (+0T @DSC13-C4)DSC13 Row3 Stop (Col4)NextColVsDSC13-C3: 3v4
DSC13-C05 (H20–H21)2B (BB) [DSC13]12B/8P (+0T @DSC13-C5)DSC13 Row2 Stop (Col5)NextColVsDSC13-C4: 2v3
DSC13-C06 (H22–H22)1P (P) [DSC13]12B/9P (+0T @DSC13-C6)DSC13 Row1 Stop (Col6)NextColVsDSC13-C5: 1v2
DSC13-C07 (H23–H25)3B (BBB) [DSC13]15B/9P (+0T @DSC13-C7)DSC13 Row3 Stop (Col7)NextColVsDSC13-C6: 3v1
DSC13-C08 (H26–H26)1P (P) [DSC13]15B/10P (+0T @DSC13-C8)DSC13 Row1 Stop (Col8)NextColVsDSC13-C7: 1v3
DSC13-C09 (H27–H29)2B (BB) [DSC13]17B/10P (+1T @DSC13-C9)DSC13 Row2 Stop (Col9)NextColVsDSC13-C8: 2v1
DSC13-C10 (H30–H33)4P (PPPP) [DSC13]17B/14P (+0T @DSC13-C10)DSC13 Row4 Stop (Col10)NextColVsDSC13-C9: 4v2
  • DSC13 BEB #3 (RED): verified at DSC13 lookback-1 index 2 (25R/41B total).
  • DSC13 SR #4 (BLUE): verified at DSC13 lookback-2 index 3 (25R/36B total).
  • DSC13 CP #1 (RED): verified at DSC13 lookback-3 index 0 (37R/20B total).
DSC13 DERIVED-ROAD & CUT-CARD PROBE

DSC13 Lookback Split (25R/41B BEB · 25R/36B SR · 37R/20B 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 DSC13, Big Eye Boy prints 25 Red (37.9%) and 41 Blue marks, Small Road prints 25 Red (41.0%) and 36 Blue marks, and Cockroach Pig prints 37 Red (64.9%) and 20 Blue marks.

At the DSC13 cut card after Hand #77, probing Hand #78 via getNextRoadPredictions() yields Banker → BEB BLUE / SR BLUE / CP RED and Player → BEB RED / SR RED / CP BLUE for DSC13.

Table Reality Check

Myth vs. Truth

MythTapering columns in DSC13 mark Blue on the way down because each streak is shorter than the last.
TruthWhile moving down a shorter column in DSC13, 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 (≠).
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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