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

2-Deck Two-Pip (Deuce) Depletion at 80% Penetration (Super 6 Audit DEP116)

Removing 7 of 8 Two-Pip (Deuce) (Rank-2) cards at 80% penetration of a 2-deck (104-card) shoe leaves 1 Rank-2 cards inside a 21-card stub (DEP116), producing 45.9022% Banker wins, 44.5651% Player wins, 9.5327% Ties, and a 1.3559% Banker house edge under Super 6.

Banker EV (Super 6)
-1.3559%
Player EV (1:1)
-1.3371%
Rank-2 in 21-Card Stub
1/8
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 B P P B B P B P B P P
Big Eye Boy = = ≠ = = = ≠ ≠ = = ≠ = = = ≠
Small Road ≠ ≠ = = ≠ ≠ ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ = ≠

Reference shoe scoreboard (PPBBPBPBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP116 (2D 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

Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #2

Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP116)
21 / 104 Cards

80% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Rank-2 Remaining
1 of 8 Cards

7 2-pip cards across all four suits removed from the 2D pack.

Banker EV (Super 6)
-1.3559%

Resolved at 45.9022% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.3371%

Resolved at 44.5651% Player win rate with 0.9381 unit standard deviation.

Tie Incidence (8:1)
9.5327%

Produces a 14.2058% house hold on the 8-to-1 Tie wager in state DEP116.

FINITE-SHOE ENUMERATION · DEP116

How Two-Pip (Deuce) Depletion at 80% Depth Impacts 2D (Super 6)

Finite-shoe specification DEP116 tracks Rank-2 removal at 80% depth in 2-deck play: with 1 of 8 Two-Pip (Deuce) cards left in the 21-card stub, Tie incidence is 9.5327% and Banker expectation settles at -1.3559% (Super 6).

In six-card resolution tree DEP116 (2D at 80% depth, 21 cards left), depleting 2s shifts the (dep116-rank-2) probability of banker converting a (21c) two-card 4 or 5 into (dep116-rank-2·21c) a winning three-card 6 or 7; removing 7 of 8 Rank-2 cards (+0.52 bps weight) leaves Banker at -1.3559% EV under Super 6.

State DEP116 (2D, 80% depth, 1/8 Rank-2 left, Super 6)
Wager / MetricState DEP116 Value2D BaselineSettlement Note
DEP116 Banker (Super 6)45.9022% (-1.3559% EV)45.8998%DEP116 2D 80% (1 Rank-2)
DEP116 Player (1:1)44.5651% (-1.3371% EV)44.5676%DEP116 21-card 2D stub (0.9381 SD)
DEP116 Tie (8:1)9.5327% (-14.2058% EV)9.5326%DEP116 Rank-2 (7 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP116

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP116 · 2D)

While DEP116 tracks 7 removed Two-Pip (Deuce) cards across 80% of a 104-card (2D) shoe (21 remaining, 1.3559% Super 6 edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP116 (2D 80%): 21/104 cards with 1/8 Rank-2 (4A).
  • DEP116 (Rank-2 split): 45.9022% Banker, 44.5651% Player, 9.5327% Tie in 21 2D cards (4B).
  • DEP116 (Super 6 EV): -1.3559% Banker, -1.3371% Player, -14.2058% Tie, 0.9381 SD at 80% (4C).
  • DEP116 (2D roads): red/blue marks log Big Road columns, never 1 Rank-2 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Two-Pip (Deuce) cards leave a 2D shoe by 80% depth (DEP116), 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 (1/8 in 21 cards); Banker carries a -1.3559% 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