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ASCENDING 1-2-3-4-5 STAIRCASE · CATALOG ASC31 (SEED 204531)

Ascending Staircase Shoe ASC31: 70-Hand 8-Deck Scoreboard & Derived-Road Audit

Catalog shoe ASC31 (seed 204531) captures a stepwise 1-2-3-4-5 increasing column depths triggering Rule 1 and Rule 2 Case 2 across 70 dealt 8-deck hands (32 Banker, 34 Player, 4 Tie). Its 27 logical Big Road columns occupy 27 display columns (C1:2B · C2:2P · C3:1B · C4:2P · C5:3B · C6:4P · C7:5B · C8:6P) and generate 63 Big Eye Boy marks (23R/40B), 61 Small Road marks (26R/35B), and 60 Cockroach Pig marks (42R/18B).

Verified 8-Deck Hands
70 (ASC31)
Outcome Split
32B / 34P / 4T
Peak Streaks
5B · 6P
Big Road Columns
27 Cols
Engine-Verified Scoreboard · 70 Hands

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

ASC31 (seed 204531): 70 hands (32B / 34P / 4T), peak streaks 5B & 6P across 27 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)
ASC31 Big Eye Boy Entry #3

Column 3 has 1 bead. 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 1 bead. 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.

ASC31 Small Road Entry #2

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

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 columns 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.

ASC31 Cockroach Pig Entry #3

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

  1. Column 5 goes down to Row 2, so use Rule 2: look 3 columns 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.

Verified Reference Data

Key Facts & Table Specifications

ASC31 8-Deck Hand Distribution
70 Hands (32 Banker / 34 Player / 4 Tie)

Seed 204531 opening column signature: C1:2B · C2:2P · C3:1B · C4:2P · C5:3B · C6:4P · C7:5B · C8:6P.

ASC31 Big Road Span & Max Streaks
Max 5B / Max 6P Across 27 Logical Cols (27 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.

ASC31 Big Eye Boy Rule Breakdown
63 Marks (23R / 40B · 36.5% Red across 32 Display Cols)

Rule 1: 25 marks · Rule 2 Case 1: 0 · Case 2: 0 · Case 3: 38.

ASC31 Small Road & Cockroach Pig Tally
SR: 26R/35B (42.6% Red) · CP: 42R/18B (70.0% 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).

ASC31 Hand #71 Next-Hand Probe
If B → BEB red, SR red, CP blue | If P → BEB blue, SR blue, CP red

Computed by getNextRoadPredictions() after Hand #70 of ASC31.

ASC31 COLUMN GEOMETRY (ASCENDING-STAIRCASE)

ASC31 Scoreboard Structure: C1:2B · C2:2P · C3:1B · C4:2P · C5:3B · C6:4P · C7:5B · C8:6P

In catalog shoe ASC31 (seed 204531), 70 total hands resolve into 32 Banker wins, 34 Player wins, and 4 Ties across 27 logical columns (C1:2B · C2:2P · C3:1B · C4:2P · C5:3B · C6:4P · C7:5B · C8:6P). 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 ASC31 column by column shows peak runs of 5B and 6P spreading across 27 Big Road display columns: ASC31 records 25 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 ASC31 (Seed 204531)
Column & SpanBeadsRunning TallyGrid StopDepth Pair
ASC31-C01 (H1–H2)2B (BB) [ASC31]2B/0P (+0T @ASC31-C1)ASC31 Row2 Stop (Col1)NextColVsASC31-C1: 2v2
ASC31-C02 (H3–H5)2P (PP) [ASC31]2B/2P (+1T @ASC31-C2)ASC31 Row2 Stop (Col2)NextColVsASC31-C1: 2v2
ASC31-C03 (H6–H6)1B (B) [ASC31]3B/2P (+0T @ASC31-C3)ASC31 Row1 Stop (Col3)NextColVsASC31-C2: 1v2
ASC31-C04 (H7–H8)2P (PP) [ASC31]3B/4P (+0T @ASC31-C4)ASC31 Row2 Stop (Col4)NextColVsASC31-C3: 2v1
ASC31-C05 (H9–H11)3B (BBB) [ASC31]6B/4P (+0T @ASC31-C5)ASC31 Row3 Stop (Col5)NextColVsASC31-C4: 3v2
ASC31-C06 (H12–H15)4P (PPPP) [ASC31]6B/8P (+0T @ASC31-C6)ASC31 Row4 Stop (Col6)NextColVsASC31-C5: 4v3
ASC31-C07 (H16–H21)5B (BBBBB) [ASC31]11B/8P (+1T @ASC31-C7)ASC31 Row5 Stop (Col7)NextColVsASC31-C6: 5v4
ASC31-C08 (H22–H27)6P (PPPPPP) [ASC31]11B/14P (+0T @ASC31-C8)ASC31 Row6 Stop (Col8)NextColVsASC31-C7: 6v5
ASC31-C09 (H28–H28)1B (B) [ASC31]12B/14P (+0T @ASC31-C9)ASC31 Row1 Stop (Col9)NextColVsASC31-C8: 1v6
ASC31-C10 (H29–H30)2P (PP) [ASC31]12B/16P (+0T @ASC31-C10)ASC31 Row2 Stop (Col10)NextColVsASC31-C9: 2v1
  • ASC31 BEB #3 (BLUE): verified at ASC31 lookback-1 index 2 (23R/40B total).
  • ASC31 SR #2 (RED): verified at ASC31 lookback-2 index 1 (26R/35B total).
  • ASC31 CP #3 (RED): verified at ASC31 lookback-3 index 2 (42R/18B total).
ASC31 DERIVED-ROAD & CUT-CARD PROBE

ASC31 Lookback Split (23R/40B BEB · 26R/35B SR · 42R/18B 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 ASC31, Big Eye Boy prints 23 Red (36.5%) and 40 Blue marks, Small Road prints 26 Red (42.6%) and 35 Blue marks, and Cockroach Pig prints 42 Red (70.0%) and 18 Blue marks.

At the ASC31 cut card after Hand #70, probing Hand #71 via getNextRoadPredictions() yields Banker → BEB RED / SR RED / CP BLUE and Player → BEB BLUE / SR BLUE / CP RED for ASC31.

Table Reality Check

Myth vs. Truth

MythBecause 1-2-3-4-5 in ASC31 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 ASC31, adjacent staircase depths differ by 1, producing Blue (≠) at every column start and tip.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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