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ASCENDING 1-2-3-4-5 STAIRCASE · CATALOG ASC21 (SEED 204521)

Ascending Staircase Shoe ASC21: 74-Hand 8-Deck Scoreboard & Derived-Road Audit

Catalog shoe ASC21 (seed 204521) captures a stepwise 1-2-3-4-5 increasing column depths triggering Rule 1 and Rule 2 Case 2 across 74 dealt 8-deck hands (37 Banker, 33 Player, 4 Tie). Its 29 logical Big Road columns occupy 29 display columns (C1:1B · C2:2P · C3:3B · C4:4P · C5:5B · C6:4P · C7:1B · C8:3P) and generate 68 Big Eye Boy marks (25R/43B), 66 Small Road marks (27R/39B), and 63 Cockroach Pig marks (44R/19B).

Verified 8-Deck Hands
74 (ASC21)
Outcome Split
37B / 33P / 4T
Peak Streaks
5B · 4P
Big Road Columns
29 Cols
Engine-Verified Scoreboard · 74 Hands

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

ASC21 (seed 204521): 74 hands (37B / 33P / 4T), peak streaks 5B & 4P 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)
ASC21 Big Eye Boy Entry #5

Column 3 has 3 beads. Column 2 has 2 beads. Different depth → blue (≠).

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

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 2.

ASC21 Small Road Entry #2

This bead is at Row 3. Column 1 stopped at Row 1, more than one row above → red (=).

  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 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.

ASC21 Cockroach Pig Entry #1

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

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

Verified Reference Data

Key Facts & Table Specifications

ASC21 8-Deck Hand Distribution
74 Hands (37 Banker / 33 Player / 4 Tie)

Seed 204521 opening column signature: C1:1B · C2:2P · C3:3B · C4:4P · C5:5B · C6:4P · C7:1B · C8:3P.

ASC21 Big Road Span & Max Streaks
Max 5B / Max 4P Across 29 Logical Cols (29 Display Cols)

Because each staircase column is exactly one bead deeper than its predecessor, every column tip lands on Row (priorDepth + 1) while every new column compares unequal depths.

ASC21 Big Eye Boy Rule Breakdown
68 Marks (25R / 43B · 36.8% Red across 40 Display Cols)

Rule 1: 27 marks · Rule 2 Case 1: 0 · Case 2: 0 · Case 3: 41.

ASC21 Small Road & Cockroach Pig Tally
SR: 27R/39B (40.9% Red) · CP: 44R/19B (69.8% Red)

On Big Eye Boy (lookback 1), an ascending 1-2-3-4-5 sequence marks Blue (≠) at Row 1 of every new column (Rule 1) and Blue (≠) on the final bead of every column (Rule 2 Case 2).

ASC21 Hand #75 Next-Hand Probe
If B → BEB red, SR red, CP red | If P → BEB blue, SR blue, CP blue

Computed by getNextRoadPredictions() after Hand #74 of ASC21.

ASC21 COLUMN GEOMETRY (ASCENDING-STAIRCASE)

ASC21 Scoreboard Structure: C1:1B · C2:2P · C3:3B · C4:4P · C5:5B · C6:4P · C7:1B · C8:3P

In catalog shoe ASC21 (seed 204521), 74 total hands resolve into 37 Banker wins, 33 Player wins, and 4 Ties across 29 logical columns (C1:1B · C2:2P · C3:3B · C4:4P · C5:5B · C6:4P · C7:1B · C8:3P). Because each staircase column is exactly one bead deeper than its predecessor, every column tip lands on Row (priorDepth + 1) while every new column compares unequal depths.

Tracking ASC21 column by column shows peak runs of 5B and 4P spreading across 29 Big Road display columns: ASC21 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 41 Rule 2 Case 3 deep-tail checks.

Opening 10 Big Road Columns of ASC21 (Seed 204521)
Column & SpanBeadsRunning TallyGrid StopDepth Pair
ASC21-C01 (H1–H1)1B (B) [ASC21]1B/0P (+0T @ASC21-C1)ASC21 Row1 Stop (Col1)NextColVsASC21-C1: 1v1
ASC21-C02 (H2–H3)2P (PP) [ASC21]1B/2P (+0T @ASC21-C2)ASC21 Row2 Stop (Col2)NextColVsASC21-C1: 2v1
ASC21-C03 (H4–H7)3B (BBB) [ASC21]4B/2P (+1T @ASC21-C3)ASC21 Row3 Stop (Col3)NextColVsASC21-C2: 3v2
ASC21-C04 (H8–H11)4P (PPPP) [ASC21]4B/6P (+0T @ASC21-C4)ASC21 Row4 Stop (Col4)NextColVsASC21-C3: 4v3
ASC21-C05 (H12–H16)5B (BBBBB) [ASC21]9B/6P (+0T @ASC21-C5)ASC21 Row5 Stop (Col5)NextColVsASC21-C4: 5v4
ASC21-C06 (H17–H20)4P (PPPP) [ASC21]9B/10P (+0T @ASC21-C6)ASC21 Row4 Stop (Col6)NextColVsASC21-C5: 4v5
ASC21-C07 (H21–H22)1B (B) [ASC21]10B/10P (+1T @ASC21-C7)ASC21 Row1 Stop (Col7)NextColVsASC21-C6: 1v4
ASC21-C08 (H23–H25)3P (PPP) [ASC21]10B/13P (+0T @ASC21-C8)ASC21 Row3 Stop (Col8)NextColVsASC21-C7: 3v1
ASC21-C09 (H26–H27)2B (BB) [ASC21]12B/13P (+0T @ASC21-C9)ASC21 Row2 Stop (Col9)NextColVsASC21-C8: 2v3
ASC21-C10 (H28–H28)1P (P) [ASC21]12B/14P (+0T @ASC21-C10)ASC21 Row1 Stop (Col10)NextColVsASC21-C9: 1v2
  • ASC21 BEB #5 (BLUE): verified at ASC21 lookback-1 index 4 (25R/43B total).
  • ASC21 SR #2 (RED): verified at ASC21 lookback-2 index 1 (27R/39B total).
  • ASC21 CP #1 (BLUE): verified at ASC21 lookback-3 index 0 (44R/19B total).
ASC21 DERIVED-ROAD & CUT-CARD PROBE

ASC21 Lookback Split (25R/43B BEB · 27R/39B SR · 44R/19B CP)

On Big Eye Boy (lookback 1), an ascending 1-2-3-4-5 sequence marks Blue (≠) at Row 1 of every new column (Rule 1) and Blue (≠) on the final bead of every column (Rule 2 Case 2). Across ASC21, Big Eye Boy prints 25 Red (36.8%) and 43 Blue marks, Small Road prints 27 Red (40.9%) and 39 Blue marks, and Cockroach Pig prints 44 Red (69.8%) and 19 Blue marks.

At the ASC21 cut card after Hand #74, probing Hand #75 via getNextRoadPredictions() yields Banker → BEB RED / SR RED / CP RED and Player → BEB BLUE / SR BLUE / CP BLUE for ASC21.

Table Reality Check

Myth vs. Truth

MythBecause 1-2-3-4-5 in ASC21 is a neat visual staircase, Big Eye Boy marks solid Red from start to finish.
TruthBig Eye Boy tests depth equality, not arithmetic progression; in ASC21, adjacent staircase depths differ by 1, producing Blue (≠) at every column start and tip.
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