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COMBINATORIAL DEPLETION · 1D · RANK-6 · 10% DEPTH

1-Deck Six-Pip Card Depletion at 10% Penetration (5% Audit DEP055)

Removing 1 of 4 Six-Pip Card (Rank-6) cards at 10% penetration of a 1-deck (52-card) shoe leaves 3 Rank-6 cards inside a 47-card stub (DEP055), producing 45.9585% Banker wins, 44.5259% Player wins, 9.5156% Ties, and a 0.8653% Banker house edge under 5%.

Banker EV (5% Vig)
-0.8653%
Player EV (1:1)
-1.4326%
Rank-6 in 47-Card Stub
3/4
Single-Hand Std Dev
0.9323
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP055 (1D Rank-6 at 10% 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

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

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

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

Small Road Mark #2

Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

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

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

Cockroach Pig Mark #2

Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP055)
47 / 52 Cards

10% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-6 Remaining
3 of 4 Cards

1 6-pip cards (standing threshold and Banker 6 trigger) removed from the 1D pack.

Banker EV (5% Vig)
-0.8653%

Resolved at 45.9585% Banker win rate under 5% settlement.

Player EV (1:1)
-1.4326%

Resolved at 44.5259% Player win rate with 0.9323 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3598% house hold on the 8-to-1 Tie wager in state DEP055.

FINITE-SHOE ENUMERATION · DEP055

How Six-Pip Card Depletion at 10% Depth Impacts 1D (5% Vig)

Shoe-stub analysis DEP055 inspects 47 remaining cards at 10% penetration of a 52-card (1D) pack after 1 Six-Pip Card cards have cleared, leaving 3 Rank-6 cards and a 0.8653% 5% Banker edge.

Mechanical draw trees in DEP055 reflect how removing 6-pip cards produces (dep055-rank-6) the strongest per-card shift toward (47c) the player side and reduces (dep055-rank-6·47c) barred banker 6 incidence. At 10% 1D depth (3 Rank-6 left of 4 in 47 cards, -1.13 bps slope), winning banker tickets pay (dep055-1d) 0.95 units per unit staked (3/4) while 90% of the initial (dep055-1d·3/4) shoe remains undealt.

State DEP055 (1D, 10% depth, 3/4 Rank-6 left, 5% Vig)
Wager / MetricState DEP055 Value1D BaselineSettlement Note
DEP055 Banker (5% Vig)45.9585% (-0.8653% EV)45.9595%DEP055 1D 10% (3 Rank-6)
DEP055 Player (1:1)44.5259% (-1.4326% EV)44.5249%DEP055 47-card 1D stub (0.9323 SD)
DEP055 Tie (8:1)9.5156% (-14.3598% EV)9.5156%DEP055 Rank-6 (1 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP055

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP055 · 1D)

While DEP055 tracks 1 removed Six-Pip Card cards across 10% of a 52-card (1D) shoe (47 remaining, 0.8653% 5% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP055 (1D 10%): 47/52 cards with 3/4 Rank-6 (7A).
  • DEP055 (Rank-6 split): 45.9585% Banker, 44.5259% Player, 9.5156% Tie in 47 1D cards (7B).
  • DEP055 (5% Vig EV): -0.8653% Banker, -1.4326% Player, -14.3598% Tie, 0.9323 SD at 10% (7C).
  • DEP055 (1D roads): red/blue marks log Big Road columns, never 3 Rank-6 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 1 Six-Pip Card cards leave a 1D shoe by 10% depth (DEP055), 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-6 stub counts (3/4 in 47 cards); Banker carries a -0.8653% expectation under 5%.
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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