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COMBINATORIAL DEPLETION · 8D · RANK-2 · 85% DEPTH

8-Deck Two-Pip (Deuce) Depletion at 85% Penetration (EZ Baccarat Audit DEP387)

Removing 31 of 32 Two-Pip (Deuce) (Rank-2) cards at 85% penetration of a 8-deck (416-card) shoe leaves 1 Rank-2 cards inside a 62-card stub (DEP387), producing 45.8625% Banker wins, 44.6218% Player wins, 9.5157% Ties, and a 1.0128% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-1.0128%
Player EV (1:1)
-1.2406%
Rank-2 in 62-Card Stub
1/32
Single-Hand Std Dev
0.9386
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBPBPBBPPBPBPBB) illustrating derived-road symmetry checks alongside DEP387 (8D Rank-2 at 85% 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 (DEP387)
62 / 416 Cards

85% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-2 Remaining
1 of 32 Cards

31 2-pip cards across all four suits removed from the 8D pack.

Banker EV (EZ Bar-7)
-1.0128%

Resolved at 45.8625% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.2406%

Resolved at 44.6218% Player win rate with 0.9386 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3586% house hold on the 8-to-1 Tie wager in state DEP387.

FINITE-SHOE ENUMERATION · DEP387

How Two-Pip (Deuce) Depletion at 85% Depth Impacts 8D (EZ Bar-7)

Across 4,998,398,275,503,360 initial 8D permutations, depletion node DEP387 narrows to a 62-card stub (85% depth) holding 1 of 32 Rank-2 cards, where Banker resolves at 45.8625% (-1.0128% EV) and Player at 44.6218% (-1.2406% EV).

Tableau audit DEP387 confirms that on banker total 4, (dep387) banker draws against player third-card (8d-85%) 2 through 7; removing 2s (dep387·8d-85%) trims low-pip player third-card triggers. Inside the 62-card 8D stub (85% depth, 1/32 Rank-2 remaining, +0.52 bps slope), standard deviation is 0.9386 under EZ Bar-7.

State DEP387 (8D, 85% depth, 1/32 Rank-2 left, EZ Bar-7)
Wager / MetricState DEP387 Value8D BaselineSettlement Note
DEP387 Banker (EZ Bar-7)45.8625% (-1.0128% EV)45.8597%DEP387 8D 85% (1 Rank-2)
DEP387 Player (1:1)44.6218% (-1.2406% EV)44.6247%DEP387 62-card 8D stub (0.9386 SD)
DEP387 Tie (8:1)9.5157% (-14.3586% EV)9.5156%DEP387 Rank-2 (31 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP387

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP387 · 8D)

In studio and floor audits of DEP387 (62 cards undealt out of 416 in 8D at 85% depth), a 0.9386 unit standard deviation accompanies the 1-card Rank-2 stub under EZ Bar-7 (45.8625% Banker vs 44.6218% Player).

  • DEP387 (8D 85%): 62/416 cards with 1/32 Rank-2 (1A).
  • DEP387 (Rank-2 split): 45.8625% Banker, 44.6218% Player, 9.5157% Tie in 62 8D cards (1B).
  • DEP387 (EZ Bar-7 EV): -1.0128% Banker, -1.2406% Player, -14.3586% Tie, 0.9386 SD at 85% (1C).
  • DEP387 (8D roads): red/blue marks log Big Road columns, never 1 Rank-2 stub count (1D).
Table Reality Check

Myth vs. Truth

MythWhen 31 Two-Pip (Deuce) cards leave a 8D shoe by 85% depth (DEP387), 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 (1/32 in 62 cards); Banker carries a -1.0128% expectation under EZ Baccarat.
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