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COMBINATORIAL DEPLETION · 1D · RANK-5 · 25% DEPTH

1-Deck Five-Pip Card Depletion at 25% Penetration (5% Audit DEP047)

Removing 1 of 4 Five-Pip Card (Rank-5) cards at 25% penetration of a 1-deck (52-card) shoe leaves 3 Rank-5 cards inside a 39-card stub (DEP047), producing 45.9587% Banker wins, 44.5257% Player wins, 9.5156% Ties, and a 0.8650% Banker house edge under 5%.

Banker EV (5% Vig)
-0.8650%
Player EV (1:1)
-1.4330%
Rank-5 in 39-Card Stub
3/4
Single-Hand Std Dev
0.9335
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 P B B P P B B P B
Big Eye Boy = = = = = = ≠ = = = = = = =
Small Road = = = = = = ≠ ≠ = = = =
Cockroach Pig = = = = = = ≠ ≠ ≠ =

Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP047 (1D Rank-5 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

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 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 (DEP047)
39 / 52 Cards

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

Rank-5 Remaining
3 of 4 Cards

1 5-pip cards (final mandatory Player draw threshold) removed from the 1D pack.

Banker EV (5% Vig)
-0.8650%

Resolved at 45.9587% Banker win rate under 5% settlement.

Player EV (1:1)
-1.4330%

Resolved at 44.5257% Player win rate with 0.9335 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3598% house hold on the 8-to-1 Tie wager in state DEP047.

FINITE-SHOE ENUMERATION · DEP047

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

At 25% penetration of a 52-card (1D) shoe, state DEP047 isolates 1 dealt Rank-5 cards (3 remaining inside 39 stub cards), yielding 45.9587% Banker wins, 44.5257% Player wins, and 0.9335 per-hand standard deviation under 5%.

In six-card resolution tree DEP047 (1D at 25% depth, 39 cards left), fewer 5s in the (dep047-rank-5) stub reduce banker third-card improvements (39c) from 3 to 8 and (dep047-rank-5·39c) from 4 to 9; removing 1 of 4 Rank-5 cards (-0.84 bps weight) leaves Banker at -0.8650% EV under 5%.

State DEP047 (1D, 25% depth, 3/4 Rank-5 left, 5% Vig)
Wager / MetricState DEP047 Value1D BaselineSettlement Note
DEP047 Banker (5% Vig)45.9587% (-0.8650% EV)45.9595%DEP047 1D 25% (3 Rank-5)
DEP047 Player (1:1)44.5257% (-1.4330% EV)44.5249%DEP047 39-card 1D stub (0.9335 SD)
DEP047 Tie (8:1)9.5156% (-14.3598% EV)9.5156%DEP047 Rank-5 (1 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP047

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP047 · 1D)

In studio and floor audits of DEP047 (39 cards undealt out of 52 in 1D at 25% depth), a 0.9335 unit standard deviation accompanies the 3-card Rank-5 stub under 5% Vig (45.9587% Banker vs 44.5257% Player).

  • DEP047 (1D 25%): 39/52 cards with 3/4 Rank-5 (2A).
  • DEP047 (Rank-5 split): 45.9587% Banker, 44.5257% Player, 9.5156% Tie in 39 1D cards (2B).
  • DEP047 (5% Vig EV): -0.8650% Banker, -1.4330% Player, -14.3598% Tie, 0.9335 SD at 25% (2C).
  • DEP047 (1D roads): red/blue marks log Big Road columns, never 3 Rank-5 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 1 Five-Pip Card cards leave a 1D shoe by 25% depth (DEP047), 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-5 stub counts (3/4 in 39 cards); Banker carries a -0.8650% expectation under 5%.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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