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DESCENDING 5-4-3-2-1 CASCADE · CATALOG DSC39 (SEED 204639)

Descending Cascade Shoe DSC39: 81-Hand 8-Deck Scoreboard & Derived-Road Audit

Catalog shoe DSC39 (seed 204639) captures a tapering 5-4-3-2-1 column depths where every continuing row is covered by a taller reference column across 81 dealt 8-deck hands (39 Banker, 37 Player, 5 Tie). Its 35 logical Big Road columns occupy 35 display columns (C1:1B · C2:1P · C3:5B · C4:4P · C5:3B · C6:2P · C7:1B · C8:1P) and generate 74 Big Eye Boy marks (27R/47B), 73 Small Road marks (27R/46B), and 68 Cockroach Pig marks (45R/23B).

Verified 8-Deck Hands
81 (DSC39)
Outcome Split
39B / 37P / 5T
Peak Streaks
5B · 4P
Big Road Columns
35 Cols
Engine-Verified Scoreboard · 81 Hands

Read the Board at Table Speed

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

DSC39 (seed 204639): 81 hands (39B / 37P / 5T), peak streaks 5B & 4P across 35 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)
DSC39 Big Eye Boy Entry #5

This bead is at Row 5. Column 2 stopped at Row 1, more than one row above → red (=).

  1. Column 3 goes down to Row 5, so use Rule 2: look 1 column back, at Column 2.
  2. Column 2 stopped at Row 1, more than one row above → 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.

DSC39 Small Road Entry #5

Column 3 has 5 beads. Column 1 has 1 bead. 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 5 beads. Column 1 has 1 bead. Different depth → blue (≠).

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

DSC39 Cockroach Pig Entry #3

This bead is at Row 4. Column 1 stopped at Row 1, 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 1, 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

DSC39 8-Deck Hand Distribution
81 Hands (39 Banker / 37 Player / 5 Tie)

Seed 204639 opening column signature: C1:1B · C2:1P · C3:5B · C4:4P · C5:3B · C6:2P · C7:1B · C8:1P.

DSC39 Big Road Span & Max Streaks
Max 5B / Max 4P Across 35 Logical Cols (35 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.

DSC39 Big Eye Boy Rule Breakdown
74 Marks (27R / 47B · 36.5% Red across 44 Display Cols)

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

DSC39 Small Road & Cockroach Pig Tally
SR: 27R/46B (37.0% Red) · CP: 45R/23B (66.2% 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.

DSC39 Hand #82 Next-Hand Probe
If B → BEB red, SR blue, CP red | If P → BEB blue, SR red, CP blue

Computed by getNextRoadPredictions() after Hand #81 of DSC39.

DSC39 COLUMN GEOMETRY (DESCENDING-CASCADE)

DSC39 Scoreboard Structure: C1:1B · C2:1P · C3:5B · C4:4P · C5:3B · C6:2P · C7:1B · C8:1P

In catalog shoe DSC39 (seed 204639), 81 total hands resolve into 39 Banker wins, 37 Player wins, and 5 Ties across 35 logical columns (C1:1B · C2:1P · C3:5B · C4:4P · C5:3B · C6:2P · C7:1B · 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 DSC39 column by column shows peak runs of 5B and 4P spreading across 35 Big Road display columns: DSC39 records 33 Rule 1 new-column checks, 0 Rule 2 Case 1 covered-row checks, 0 Rule 2 Case 2 one-past-bottom breaks, and 41 Rule 2 Case 3 deep-tail checks.

Opening 10 Big Road Columns of DSC39 (Seed 204639)
Column & SpanBeadsRunning TallyGrid StopDepth Pair
DSC39-C01 (H1–H1)1B (B) [DSC39]1B/0P (+0T @DSC39-C1)DSC39 Row1 Stop (Col1)NextColVsDSC39-C1: 1v1
DSC39-C02 (H2–H3)1P (P) [DSC39]1B/1P (+1T @DSC39-C2)DSC39 Row1 Stop (Col2)NextColVsDSC39-C1: 1v1
DSC39-C03 (H4–H8)5B (BBBBB) [DSC39]6B/1P (+0T @DSC39-C3)DSC39 Row5 Stop (Col3)NextColVsDSC39-C2: 5v1
DSC39-C04 (H9–H12)4P (PPPP) [DSC39]6B/5P (+0T @DSC39-C4)DSC39 Row4 Stop (Col4)NextColVsDSC39-C3: 4v5
DSC39-C05 (H13–H16)3B (BBB) [DSC39]9B/5P (+1T @DSC39-C5)DSC39 Row3 Stop (Col5)NextColVsDSC39-C4: 3v4
DSC39-C06 (H17–H18)2P (PP) [DSC39]9B/7P (+0T @DSC39-C6)DSC39 Row2 Stop (Col6)NextColVsDSC39-C5: 2v3
DSC39-C07 (H19–H19)1B (B) [DSC39]10B/7P (+0T @DSC39-C7)DSC39 Row1 Stop (Col7)NextColVsDSC39-C6: 1v2
DSC39-C08 (H20–H20)1P (P) [DSC39]10B/8P (+0T @DSC39-C8)DSC39 Row1 Stop (Col8)NextColVsDSC39-C7: 1v1
DSC39-C09 (H21–H22)2B (BB) [DSC39]12B/8P (+0T @DSC39-C9)DSC39 Row2 Stop (Col9)NextColVsDSC39-C8: 2v1
DSC39-C10 (H23–H25)3P (PPP) [DSC39]12B/11P (+0T @DSC39-C10)DSC39 Row3 Stop (Col10)NextColVsDSC39-C9: 3v2
  • DSC39 BEB #5 (RED): verified at DSC39 lookback-1 index 4 (27R/47B total).
  • DSC39 SR #5 (BLUE): verified at DSC39 lookback-2 index 4 (27R/46B total).
  • DSC39 CP #3 (RED): verified at DSC39 lookback-3 index 2 (45R/23B total).
DSC39 DERIVED-ROAD & CUT-CARD PROBE

DSC39 Lookback Split (27R/47B BEB · 27R/46B SR · 45R/23B 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 DSC39, Big Eye Boy prints 27 Red (36.5%) and 47 Blue marks, Small Road prints 27 Red (37.0%) and 46 Blue marks, and Cockroach Pig prints 45 Red (66.2%) and 23 Blue marks.

At the DSC39 cut card after Hand #81, probing Hand #82 via getNextRoadPredictions() yields Banker → BEB RED / SR BLUE / CP RED and Player → BEB BLUE / SR RED / CP BLUE for DSC39.

Table Reality Check

Myth vs. Truth

MythTapering columns in DSC39 mark Blue on the way down because each streak is shorter than the last.
TruthWhile moving down a shorter column in DSC39, 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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