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COMBINATORIAL DEPLETION · 2D · RANK-7 · 80% DEPTH

2-Deck Seven-Pip Card Depletion at 80% Penetration (Super 6 Audit DEP161)

Removing 7 of 8 Seven-Pip Card (Rank-7) cards at 80% penetration of a 2-deck (104-card) shoe leaves 1 Rank-7 cards inside a 21-card stub (DEP161), producing 45.8959% Banker wins, 44.5716% Player wins, 9.5325% Ties, and a 1.3686% Banker house edge under Super 6.

Banker EV (Super 6)
-1.3686%
Player EV (1:1)
-1.3244%
Rank-7 in 21-Card Stub
1/8
Single-Hand Std Dev
0.9396
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 B B P B P
Big Eye Boy = = = = = = ≠ = = = ≠ ≠ ≠ =
Small Road = = = = ≠ ≠ = = ≠ ≠ = ≠
Cockroach Pig = = ≠ ≠ ≠ = ≠ ≠ = =

Reference shoe scoreboard (BBPPBBPPBPTBPBBPBP) illustrating derived-road symmetry checks alongside DEP161 (2D Rank-7 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

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 (DEP161)
21 / 104 Cards

80% 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 (Super 6)
-1.3686%

Resolved at 45.8959% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.3244%

Resolved at 44.5716% Player win rate with 0.9396 unit standard deviation.

Tie Incidence (8:1)
9.5325%

Produces a 14.2074% house hold on the 8-to-1 Tie wager in state DEP161.

FINITE-SHOE ENUMERATION · DEP161

How Seven-Pip Card Depletion at 80% Depth Impacts 2D (Super 6)

Card-removal benchmark DEP161 measures Seven-Pip Card (Rank-7) scarcity at 80% depth in a 2-deck shoe: 7 removed ranks leave 1 in the 21-card remainder, shifting Banker win share to 45.8959% (1.3686% edge, Super 6).

Because depleting 7s lowers the (dep161-rank-7) rate of winning three-card banker (21c) 7 hands (the barred push (dep161-rank-7·21c) total on ez baccarat tables), state DEP161 (80% 2D depth, 7 Rank-7 removed, 1 in 21 cards) registers a -0.83 bps rank derivative and 1.3686% Banker house edge (Super 6).

State DEP161 (2D, 80% depth, 1/8 Rank-7 left, Super 6)
Wager / MetricState DEP161 Value2D BaselineSettlement Note
DEP161 Banker (Super 6)45.8959% (-1.3686% EV)45.8998%DEP161 2D 80% (1 Rank-7)
DEP161 Player (1:1)44.5716% (-1.3244% EV)44.5676%DEP161 21-card 2D stub (0.9396 SD)
DEP161 Tie (8:1)9.5325% (-14.2074% EV)9.5326%DEP161 Rank-7 (7 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP161

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP161 · 2D)

While DEP161 tracks 7 removed Seven-Pip Card cards across 80% of a 104-card (2D) shoe (21 remaining, 1.3686% Super 6 edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP161 (2D 80%): 21/104 cards with 1/8 Rank-7 (5A).
  • DEP161 (Rank-7 split): 45.8959% Banker, 44.5716% Player, 9.5325% Tie in 21 2D cards (5B).
  • DEP161 (Super 6 EV): -1.3686% Banker, -1.3244% Player, -14.2074% Tie, 0.9396 SD at 80% (5C).
  • DEP161 (2D roads): red/blue marks log Big Road columns, never 1 Rank-7 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Seven-Pip Card cards leave a 2D shoe by 80% depth (DEP161), 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 21 cards); Banker carries a -1.3686% expectation under Super 6.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

Read Every Derived Road at Table Speed

Every reference guide, glossary definition, and road calculator on Baccarat Smart is open for everyone. When you want all 6 modules and 36 lessons (about 5.5 hours of lessons) organized in structured step-by-step order with 74 hands-on boards, 94 quiz checks along the way, and Cloud Shoe Log sync across web, iPhone, and Android, start Module 1 (10 lessons, about 64 minutes of lessons) free or unlock full membership for $25 a month.

  • 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