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COMBINATORIAL DEPLETION · 1D · RANK-4 · 25% DEPTH

1-Deck Four-Pip Card Depletion at 25% Penetration (5% Audit DEP038)

Removing 1 of 4 Four-Pip Card (Rank-4) cards at 25% penetration of a 1-deck (52-card) shoe leaves 3 Rank-4 cards inside a 39-card stub (DEP038), producing 45.9607% Banker wins, 44.5237% Player wins, 9.5156% Ties, and a 0.8611% Banker house edge under 5%.

Banker EV (5% Vig)
-0.8611%
Player EV (1:1)
-1.4369%
Rank-4 in 39-Card Stub
3/4
Single-Hand Std Dev
0.9332
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBBPPPBBPBTBPBPP) illustrating derived-road symmetry checks alongside DEP038 (1D Rank-4 at 25% 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 (DEP038)
39 / 52 Cards

25% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-4 Remaining
3 of 4 Cards

1 4-pip cards (strongest pro-Banker removal sensitivity) removed from the 1D pack.

Banker EV (5% Vig)
-0.8611%

Resolved at 45.9607% Banker win rate under 5% settlement.

Player EV (1:1)
-1.4369%

Resolved at 44.5237% Player win rate with 0.9332 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3594% house hold on the 8-to-1 Tie wager in state DEP038.

FINITE-SHOE ENUMERATION · DEP038

How Four-Pip Card Depletion at 25% Depth Impacts 1D (5% Vig)

Depletion matrix entry DEP038 pairs 1D (52 cards) at 25% penetration with 1 removed Four-Pip Card cards (3 left in 39 cards), fixing per-hand volatility at 0.9332 and Banker house hold at 0.8611% (5% Vig).

Removing 4s produces the (DEP038-Rank-4) single largest per-card shift toward (39c) Banker (and away from Player) (DEP038-Rank-4·39c) of any rank in the shoe. Because 1 of 4 Four-Pip Card cards are absent in DEP038 at 25% 1D penetration (39 cards left), per-card sensitivity (+1.19 bps) interacts directly with quarter-shoe 25% penetration depth (DEP038) under standard 5% Banker commission (Rank-4) (0.95:1 payout).

State DEP038 (1D, 25% depth, 3/4 Rank-4 left, 5% Vig)
Wager / MetricState DEP038 Value1D BaselineSettlement Note
DEP038 Banker (5% Vig)45.9607% (-0.8611% EV)45.9595%DEP038 1D 25% (3 Rank-4)
DEP038 Player (1:1)44.5237% (-1.4369% EV)44.5249%DEP038 39-card 1D stub (0.9332 SD)
DEP038 Tie (8:1)9.5156% (-14.3594% EV)9.5156%DEP038 Rank-4 (1 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP038

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP038 · 1D)

Whether DEP038 is observed in single-deck laboratory benchmarks and historical pitch audits at 25% depth (39/52 cards left, 3 Rank-4 remaining), 5% Vig settlement locks Banker EV at -0.8611% and Player EV at -1.4369% with 9.5156% Ties.

  • DEP038 (1D 25%): 39/52 cards with 3/4 Rank-4 (6A).
  • DEP038 (Rank-4 split): 45.9607% Banker, 44.5237% Player, 9.5156% Tie in 39 1D cards (6B).
  • DEP038 (5% Vig EV): -0.8611% Banker, -1.4369% Player, -14.3594% Tie, 0.9332 SD at 25% (6C).
  • DEP038 (1D roads): red/blue marks log Big Road columns, never 3 Rank-4 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 1 Four-Pip Card cards leave a 1D shoe by 25% depth (DEP038), 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-4 stub counts (3/4 in 39 cards); Banker carries a -0.8611% 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