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COMBINATORIAL DEPLETION · 1D · RANK-9 · 50% DEPTH

1-Deck Nine-Pip Card Depletion at 50% Penetration (Super 6 Audit DEP085)

Removing 2 of 4 Nine-Pip Card (Rank-9) cards at 50% penetration of a 1-deck (52-card) shoe leaves 2 Rank-9 cards inside a 26-card stub (DEP085), producing 45.9590% Banker wins, 44.5254% Player wins, 9.5156% Ties, and a 1.2595% Banker house edge under Super 6.

Banker EV (Super 6)
-1.2595%
Player EV (1:1)
-1.4335%
Rank-9 in 26-Card Stub
2/4
Single-Hand Std Dev
0.9372
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P P B B B P P B B P B B P
Big Eye Boy = ≠ ≠ = = = = ≠ ≠ = = = ≠ ≠
Small Road = ≠ ≠ = ≠ ≠ ≠ = = ≠ ≠
Cockroach Pig = = ≠ ≠ ≠ = ≠ ≠

Reference shoe scoreboard (BBPPPBBBPPBPTBPBBP) illustrating derived-road symmetry checks alongside DEP085 (1D Rank-9 at 50% depth).

Big Road B is Banker, P is Player Roads under it Red (=): repeating Blue (≠): breaking
Step-by-Step Mark Proofs (Rule 1 & Rule 2)
Big Eye Boy Mark #2

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

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

Small Road Mark #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.

Cockroach Pig Mark #2

Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP085)
26 / 52 Cards

50% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-9 Remaining
2 of 4 Cards

2 9-pip cards (top Natural 9 generator) removed from the 1D pack.

Banker EV (Super 6)
-1.2595%

Resolved at 45.9590% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.4335%

Resolved at 44.5254% Player win rate with 0.9372 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3598% house hold on the 8-to-1 Tie wager in state DEP085.

FINITE-SHOE ENUMERATION · DEP085

How Nine-Pip Card Depletion at 50% Depth Impacts 1D (Super 6)

Audit DEP085 evaluates a 1-deck (52-card) shoe at 50% penetration where 2 of 4 Nine-Pip Card cards have exited, leaving 2 Rank-9 cards inside the 26-card stub with Banker EV at -1.2595% under Super 6.

Why does Rank-9 carry a -0.23 bps per-card effect in DEP085? Rank 9 paired with (DEP085) any ten or face card (1D-50%) creates an unbeatable two-card Natural (DEP085·1D-50%) 9 that halts all third-card drawing on both sides, and at 50% penetration (2 Nine-Pip Card cards left in 26 1D cards), banker wins on totals (dep085-1d) 1–5 and 7–9 pay 1:1 (2/4) while any winning 2-card or (dep085-1d·2/4) 3-card banker 6 pays 50 cents on the dollar.

State DEP085 (1D, 50% depth, 2/4 Rank-9 left, Super 6)
Wager / MetricState DEP085 Value1D BaselineSettlement Note
DEP085 Banker (Super 6)45.9590% (-1.2595% EV)45.9595%DEP085 1D 50% (2 Rank-9)
DEP085 Player (1:1)44.5254% (-1.4335% EV)44.5249%DEP085 26-card 1D stub (0.9372 SD)
DEP085 Tie (8:1)9.5156% (-14.3598% EV)9.5156%DEP085 Rank-9 (2 out, 2 in)
TABLEAU & SCOREBOARD SEPARATION · DEP085

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP085 · 1D)

In DEP085, the 26-card 1D stub (50% penetration, 2 of 4 Rank-9 dealt) yields 45.9590% Banker, 44.5254% Player, and 9.5156% Tie outcomes with 0.9372 dispersion under Super 6.

  • DEP085 (1D 50%): 26/52 cards with 2/4 Rank-9 (3A).
  • DEP085 (Rank-9 split): 45.9590% Banker, 44.5254% Player, 9.5156% Tie in 26 1D cards (3B).
  • DEP085 (Super 6 EV): -1.2595% Banker, -1.4335% Player, -14.3598% Tie, 0.9372 SD at 50% (3C).
  • DEP085 (1D roads): red/blue marks log Big Road columns, never 2 Rank-9 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 2 Nine-Pip Card cards leave a 1D shoe by 50% depth (DEP085), Big Eye Boy red or blue marks show whether Banker or Player will win next.
TruthDerived-road red and blue marks only compare Big Road column lengths and never track Rank-9 stub counts (2/4 in 26 cards); Banker carries a -1.2595% expectation under Super 6.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android