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COMBINATORIAL DEPLETION · 2D · RANK-7 · 75% DEPTH

2-Deck Seven-Pip Card Depletion at 75% Penetration (4% Audit DEP160)

Removing 7 of 8 Seven-Pip Card (Rank-7) cards at 75% penetration of a 2-deck (104-card) shoe leaves 1 Rank-7 cards inside a 26-card stub (DEP160), producing 45.8960% Banker wins, 44.5715% Player wins, 9.5325% Ties, and a 0.5113% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5113%
Player EV (1:1)
-1.3246%
Rank-7 in 26-Card Stub
1/8
Single-Hand Std Dev
0.9391
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPPBBPPBBPBTBPB) illustrating derived-road symmetry checks alongside DEP160 (2D Rank-7 at 75% 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 (DEP160)
26 / 104 Cards

75% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Rank-7 Remaining
1 of 8 Cards

7 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 2D pack.

Banker EV (4% Vig)
-0.5113%

Resolved at 45.8960% Banker win rate under 4% settlement.

Player EV (1:1)
-1.3246%

Resolved at 44.5715% Player win rate with 0.9391 unit standard deviation.

Tie Incidence (8:1)
9.5325%

Produces a 14.2074% house hold on the 8-to-1 Tie wager in state DEP160.

FINITE-SHOE ENUMERATION · DEP160

How Seven-Pip Card Depletion at 75% Depth Impacts 2D (4% Vig)

Under 4% settlement (4% Vig), combinatorial state DEP160 models a 2D carrier with 26 cards left (75% dealt) and 1/8 Seven-Pip Card cards remaining, producing a 0.5113% Banker edge versus 1.3246% on Player.

Tableau audit DEP160 confirms that player stands pat on (dep160) two-card 7, and a player (2d-75%) third-card 7 is the highest (dep160·2d-75%) card that forces banker 4, 5, and 6 to draw. Inside the 26-card 2D stub (75% depth, 1/8 Rank-7 remaining, -0.83 bps slope), standard deviation is 0.9391 under 4% Vig.

State DEP160 (2D, 75% depth, 1/8 Rank-7 left, 4% Vig)
Wager / MetricState DEP160 Value2D BaselineSettlement Note
DEP160 Banker (4% Vig)45.8960% (-0.5113% EV)45.8998%DEP160 2D 75% (1 Rank-7)
DEP160 Player (1:1)44.5715% (-1.3246% EV)44.5676%DEP160 26-card 2D stub (0.9391 SD)
DEP160 Tie (8:1)9.5325% (-14.2074% EV)9.5326%DEP160 Rank-7 (7 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP160

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP160 · 2D)

In DEP160, the 26-card 2D stub (75% penetration, 7 of 8 Rank-7 dealt) yields 45.8960% Banker, 44.5715% Player, and 9.5325% Tie outcomes with 0.9391 dispersion under 4% Vig.

  • DEP160 (2D 75%): 26/104 cards with 1/8 Rank-7 (7A).
  • DEP160 (Rank-7 split): 45.8960% Banker, 44.5715% Player, 9.5325% Tie in 26 2D cards (7B).
  • DEP160 (4% Vig EV): -0.5113% Banker, -1.3246% Player, -14.2074% Tie, 0.9391 SD at 75% (7C).
  • DEP160 (2D roads): red/blue marks log Big Road columns, never 1 Rank-7 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Seven-Pip Card cards leave a 2D shoe by 75% depth (DEP160), 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-7 stub counts (1/8 in 26 cards); Banker carries a -0.5113% expectation under 4%.
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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