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COMBINATORIAL DEPLETION · 6D · RANK-2 · 25% DEPTH

6-Deck Two-Pip (Deuce) Depletion at 25% Penetration (5% Audit DEP290)

Removing 7 of 24 Two-Pip (Deuce) (Rank-2) cards at 25% penetration of a 6-deck (312-card) shoe leaves 17 Rank-2 cards inside a 234-card stub (DEP290), producing 45.8654% Banker wins, 44.5897% Player wins, 9.5449% Ties, and a 1.0176% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0176%
Player EV (1:1)
-1.2757%
Rank-2 in 234-Card Stub
17/24
Single-Hand Std Dev
0.9326
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 B P
Big Eye Boy = = = = = = ≠ = = = = ≠ ≠ = =
Small Road = = = = = = ≠ ≠ = = = ≠ ≠
Cockroach Pig = = = = = = ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (PPBBPPBBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP290 (6D Rank-2 at 25% 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 (DEP290)
234 / 312 Cards

25% penetration depth in 6D (six-deck Mini-Baccarat and Midi-Baccarat North American floors).

Rank-2 Remaining
17 of 24 Cards

7 2-pip cards across all four suits removed from the 6D pack.

Banker EV (5% Vig)
-1.0176%

Resolved at 45.8654% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2757%

Resolved at 44.5897% Player win rate with 0.9326 unit standard deviation.

Tie Incidence (8:1)
9.5449%

Produces a 14.0957% house hold on the 8-to-1 Tie wager in state DEP290.

FINITE-SHOE ENUMERATION · DEP290

How Two-Pip (Deuce) Depletion at 25% Depth Impacts 6D (5% Vig)

Depletion matrix entry DEP290 pairs 6D (312 cards) at 25% penetration with 7 removed Two-Pip (Deuce) cards (17 left in 234 cards), fixing per-hand volatility at 0.9326 and Banker house hold at 1.0176% (5% Vig).

Why does Rank-2 carry a +0.52 bps per-card effect in DEP290? On Banker total 4, (DEP290) Banker draws against Player third-card (6D-25%) 2 through 7; removing 2s (DEP290·6D-25%) trims low-pip Player third-card triggers, and at 25% penetration (17 Two-Pip (Deuce) cards left in 234 6D cards), one-quarter of the shoe (dep290-6d) has exited the carrier and (17/24) winning banker wagers pay 0.95 (dep290-6d·17/24) to 1 after 5% house tax.

State DEP290 (6D, 25% depth, 17/24 Rank-2 left, 5% Vig)
Wager / MetricState DEP290 Value6D BaselineSettlement Note
DEP290 Banker (5% Vig)45.8654% (-1.0176% EV)45.8648%DEP290 6D 25% (17 Rank-2)
DEP290 Player (1:1)44.5897% (-1.2757% EV)44.5903%DEP290 234-card 6D stub (0.9326 SD)
DEP290 Tie (8:1)9.5449% (-14.0957% EV)9.5449%DEP290 Rank-2 (7 out, 17 in)
TABLEAU & SCOREBOARD SEPARATION · DEP290

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP290 · 6D)

While DEP290 tracks 7 removed Two-Pip (Deuce) cards across 25% of a 312-card (6D) shoe (234 remaining, 1.0176% 5% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP290 (6D 25%): 234/312 cards with 17/24 Rank-2 (6A).
  • DEP290 (Rank-2 split): 45.8654% Banker, 44.5897% Player, 9.5449% Tie in 234 6D cards (6B).
  • DEP290 (5% Vig EV): -1.0176% Banker, -1.2757% Player, -14.0957% Tie, 0.9326 SD at 25% (6C).
  • DEP290 (6D roads): red/blue marks log Big Road columns, never 17 Rank-2 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Two-Pip (Deuce) cards leave a 6D shoe by 25% depth (DEP290), 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 (17/24 in 234 cards); Banker carries a -1.0176% 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