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COMBINATORIAL DEPLETION · 6D · RANK-0 · 10% DEPTH

6-Deck 0-Value Tens & Faces Depletion at 10% Penetration (5% Audit DEP271)

Removing 11 of 96 0-Value Tens & Faces (Rank-0) cards at 10% penetration of a 6-deck (312-card) shoe leaves 85 Rank-0 cards inside a 281-card stub (DEP271), producing 45.8651% Banker wins, 44.5900% Player wins, 9.5449% Ties, and a 1.0182% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0182%
Player EV (1:1)
-1.2751%
Rank-0 in 281-Card Stub
85/96
Single-Hand Std Dev
0.9305
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 P B B P B
Big Eye Boy = = = = = = ≠ = = = = = = =
Small Road = = = = = = ≠ ≠ = = = =
Cockroach Pig = = = = = = ≠ ≠ ≠ =

Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP271 (6D Rank-0 at 10% 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 (DEP271)
281 / 312 Cards

10% penetration depth in 6D (six-deck Mini-Baccarat and Midi-Baccarat North American floors).

Rank-0 Remaining
85 of 96 Cards

11 10, Jack, Queen, and King (zero-point cards) removed from the 6D pack.

Banker EV (5% Vig)
-1.0182%

Resolved at 45.8651% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2751%

Resolved at 44.5900% Player win rate with 0.9305 unit standard deviation.

Tie Incidence (8:1)
9.5449%

Produces a 14.0958% house hold on the 8-to-1 Tie wager in state DEP271.

FINITE-SHOE ENUMERATION · DEP271

How 0-Value Tens & Faces Depletion at 10% Depth Impacts 6D (5% Vig)

At 10% penetration of a 312-card (6D) shoe, state DEP271 isolates 11 dealt Rank-0 cards (85 remaining inside 281 stub cards), yielding 45.8651% Banker wins, 44.5900% Player wins, and 0.9305 per-hand standard deviation under 5%.

Tableau audit DEP271 confirms that depleting zero-point cards reduces (dep271) modulo-10 standoffs and alters two-card (6d-10%) natural combinations paired with 8s (dep271·6d-10%) and 9s. Inside the 281-card 6D stub (10% depth, 85/96 Rank-0 remaining, +0.18 bps slope), standard deviation is 0.9305 under 5% Vig.

State DEP271 (6D, 10% depth, 85/96 Rank-0 left, 5% Vig)
Wager / MetricState DEP271 Value6D BaselineSettlement Note
DEP271 Banker (5% Vig)45.8651% (-1.0182% EV)45.8648%DEP271 6D 10% (85 Rank-0)
DEP271 Player (1:1)44.5900% (-1.2751% EV)44.5903%DEP271 281-card 6D stub (0.9305 SD)
DEP271 Tie (8:1)9.5449% (-14.0958% EV)9.5449%DEP271 Rank-0 (11 out, 85 in)
TABLEAU & SCOREBOARD SEPARATION · DEP271

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP271 · 6D)

Cut-card protocol at 10% depth in DEP271 (6D, 281 stub cards containing 85 Rank-0 cards) ensures the shoe reshuffles long before 5% house hold (1.0182% Banker / 1.2751% Player) is overturned.

  • DEP271 (6D 10%): 281/312 cards with 85/96 Rank-0 (2A).
  • DEP271 (Rank-0 split): 45.8651% Banker, 44.5900% Player, 9.5449% Tie in 281 6D cards (2B).
  • DEP271 (5% Vig EV): -1.0182% Banker, -1.2751% Player, -14.0958% Tie, 0.9305 SD at 10% (2C).
  • DEP271 (6D roads): red/blue marks log Big Road columns, never 85 Rank-0 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 11 0-Value Tens & Faces cards leave a 6D shoe by 10% depth (DEP271), 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-0 stub counts (85/96 in 281 cards); Banker carries a -1.0182% expectation under 5%.
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