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COMBINATORIAL DEPLETION · 1D · RANK-2 · 80% DEPTH

1-Deck Two-Pip (Deuce) Depletion at 80% Penetration (Super 6 Audit DEP026)

Removing 3 of 4 Two-Pip (Deuce) (Rank-2) cards at 80% penetration of a 1-deck (52-card) shoe leaves 1 Rank-2 cards inside a 10-card stub (DEP026), producing 45.9616% Banker wins, 44.5227% Player wins, 9.5157% Ties, and a 1.2542% Banker house edge under Super 6.

Banker EV (Super 6)
-1.2542%
Player EV (1:1)
-1.4388%
Rank-2 in 10-Card Stub
1/4
Single-Hand Std Dev
0.9381
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPBTBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP026 (1D Rank-2 at 80% 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

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.

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 (DEP026)
10 / 52 Cards

80% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-2 Remaining
1 of 4 Cards

3 2-pip cards across all four suits removed from the 1D pack.

Banker EV (Super 6)
-1.2542%

Resolved at 45.9616% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.4388%

Resolved at 44.5227% Player win rate with 0.9381 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3589% house hold on the 8-to-1 Tie wager in state DEP026.

FINITE-SHOE ENUMERATION · DEP026

How Two-Pip (Deuce) Depletion at 80% Depth Impacts 1D (Super 6)

Exact conditional enumeration DEP026 for a 1D shoe at 80% depth (10/52 cards undealt) with 1 remaining Rank-2 cards confirms a 1.2542% Banker edge (Super 6), 1.4388% Player edge, and 14.3589% Tie edge.

On Banker total 4, (DEP026) Banker draws against Player third-card (1D-80%) 2 through 7; removing 2s (DEP026·1D-80%) trims low-pip Player third-card triggers. In state DEP026 (1D, 80% depth), each removed Rank-2 card applies a +0.52 bps baseline directional pressure before scaling to the 10-card remainder (1 Rank-2 left), while Only 20% of the (DEP026-1D) initial shoe remains undealt while (1/4) winning Banker 6 hands forfeit (DEP026-1D·1/4) half their payout.

State DEP026 (1D, 80% depth, 1/4 Rank-2 left, Super 6)
Wager / MetricState DEP026 Value1D BaselineSettlement Note
DEP026 Banker (Super 6)45.9616% (-1.2542% EV)45.9595%DEP026 1D 80% (1 Rank-2)
DEP026 Player (1:1)44.5227% (-1.4388% EV)44.5249%DEP026 10-card 1D stub (0.9381 SD)
DEP026 Tie (8:1)9.5157% (-14.3589% EV)9.5156%DEP026 Rank-2 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP026

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP026 · 1D)

Statistical verification of DEP026 (1D, 80% penetration, 1 Two-Pip (Deuce) cards in 10 stub cards) demonstrates why single-rank depletion (3 Rank-2 dealt) shifts edges by basis points around -1.2542% (Super 6).

  • DEP026 (1D 80%): 10/52 cards with 1/4 Rank-2 (2A).
  • DEP026 (Rank-2 split): 45.9616% Banker, 44.5227% Player, 9.5157% Tie in 10 1D cards (2B).
  • DEP026 (Super 6 EV): -1.2542% Banker, -1.4388% Player, -14.3589% Tie, 0.9381 SD at 80% (2C).
  • DEP026 (1D roads): red/blue marks log Big Road columns, never 1 Rank-2 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Two-Pip (Deuce) cards leave a 1D shoe by 80% depth (DEP026), 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-2 stub counts (1/4 in 10 cards); Banker carries a -1.2542% 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
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