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COMBINATORIAL DEPLETION · 6D · RANK-9 · 25% DEPTH

6-Deck Nine-Pip Card Depletion at 25% Penetration (5% Audit DEP353)

Removing 7 of 24 Nine-Pip Card (Rank-9) cards at 25% penetration of a 6-deck (312-card) shoe leaves 17 Rank-9 cards inside a 234-card stub (DEP353), producing 45.8645% Banker wins, 44.5906% Player wins, 9.5449% Ties, and a 1.0193% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0193%
Player EV (1:1)
-1.2740%
Rank-9 in 234-Card Stub
17/24
Single-Hand Std Dev
0.9347
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 DEP353 (6D Rank-9 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 (DEP353)
234 / 312 Cards

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

Rank-9 Remaining
17 of 24 Cards

7 9-pip cards (top Natural 9 generator) removed from the 6D pack.

Banker EV (5% Vig)
-1.0193%

Resolved at 45.8645% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2740%

Resolved at 44.5906% Player win rate with 0.9347 unit standard deviation.

Tie Incidence (8:1)
9.5449%

Produces a 14.0960% house hold on the 8-to-1 Tie wager in state DEP353.

FINITE-SHOE ENUMERATION · DEP353

How Nine-Pip Card Depletion at 25% Depth Impacts 6D (5% Vig)

When a 6D shoe reaches 25% cut-card depth (234 of 312 cards undealt, state DEP353) with 7 Nine-Pip Card cards removed and 17 remaining, Player wins 44.5906% (1.2740% edge) while Banker wins 45.8645% (1.0193% edge under 5%).

Comparing initial 312-card 6D weights against stub DEP353 (234 cards, 25% depth, 17 Rank-9 left) illustrates how rank 9 paired with (dep353) any ten or face card (6d-25%) creates an unbeatable two-card natural (dep353·6d-25%) 9 that halts all third-card drawing on both sides (-0.23 bps slope, 1.0193% 5% Vig edge).

State DEP353 (6D, 25% depth, 17/24 Rank-9 left, 5% Vig)
Wager / MetricState DEP353 Value6D BaselineSettlement Note
DEP353 Banker (5% Vig)45.8645% (-1.0193% EV)45.8648%DEP353 6D 25% (17 Rank-9)
DEP353 Player (1:1)44.5906% (-1.2740% EV)44.5903%DEP353 234-card 6D stub (0.9347 SD)
DEP353 Tie (8:1)9.5449% (-14.0960% EV)9.5449%DEP353 Rank-9 (7 out, 17 in)
TABLEAU & SCOREBOARD SEPARATION · DEP353

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP353 · 6D)

Synthesizing DEP353 (6D at 25% depth, 17 Nine-Pip Card cards left inside 234 stub cards): 5% rules produce a 1.0193% Banker edge, 1.2740% Player edge, 14.0960% Tie edge, and 0.9347 unit volatility.

  • DEP353 (6D 25%): 234/312 cards with 17/24 Rank-9 (6A).
  • DEP353 (Rank-9 split): 45.8645% Banker, 44.5906% Player, 9.5449% Tie in 234 6D cards (6B).
  • DEP353 (5% Vig EV): -1.0193% Banker, -1.2740% Player, -14.0960% Tie, 0.9347 SD at 25% (6C).
  • DEP353 (6D roads): red/blue marks log Big Road columns, never 17 Rank-9 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Nine-Pip Card cards leave a 6D shoe by 25% depth (DEP353), 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-9 stub counts (17/24 in 234 cards); Banker carries a -1.0193% 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