Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 6D Rank-5 Depletion at 70% Depth (5% Vig)
COMBINATORIAL DEPLETION · 6D · RANK-5 · 70% DEPTH

6-Deck Five-Pip Card Depletion at 70% Penetration (5% Audit DEP321)

Removing 19 of 24 Five-Pip Card (Rank-5) cards at 70% penetration of a 6-deck (312-card) shoe leaves 5 Rank-5 cards inside a 94-card stub (DEP321), producing 45.8614% Banker wins, 44.5937% Player wins, 9.5448% Ties, and a 1.0254% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0254%
Player EV (1:1)
-1.2677%
Rank-5 in 94-Card Stub
5/24
Single-Hand Std Dev
0.9380
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 DEP321 (6D Rank-5 at 70% 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 (DEP321)
94 / 312 Cards

70% penetration depth in 6D (six-deck Mini-Baccarat and Midi-Baccarat North American floors).

Rank-5 Remaining
5 of 24 Cards

19 5-pip cards (final mandatory Player draw threshold) removed from the 6D pack.

Banker EV (5% Vig)
-1.0254%

Resolved at 45.8614% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2677%

Resolved at 44.5937% Player win rate with 0.9380 unit standard deviation.

Tie Incidence (8:1)
9.5448%

Produces a 14.0966% house hold on the 8-to-1 Tie wager in state DEP321.

FINITE-SHOE ENUMERATION · DEP321

How Five-Pip Card Depletion at 70% Depth Impacts 6D (5% Vig)

Shoe-stub analysis DEP321 inspects 94 remaining cards at 70% penetration of a 312-card (6D) pack after 19 Five-Pip Card cards have cleared, leaving 5 Rank-5 cards and a 1.0254% 5% Banker edge.

In six-card resolution tree DEP321 (6D at 70% depth, 94 cards left), fewer 5s in the (dep321-rank-5) stub reduce banker third-card improvements (94c) from 3 to 8 and (dep321-rank-5·94c) from 4 to 9; removing 19 of 24 Rank-5 cards (-0.84 bps weight) leaves Banker at -1.0254% EV under 5%.

State DEP321 (6D, 70% depth, 5/24 Rank-5 left, 5% Vig)
Wager / MetricState DEP321 Value6D BaselineSettlement Note
DEP321 Banker (5% Vig)45.8614% (-1.0254% EV)45.8648%DEP321 6D 70% (5 Rank-5)
DEP321 Player (1:1)44.5937% (-1.2677% EV)44.5903%DEP321 94-card 6D stub (0.9380 SD)
DEP321 Tie (8:1)9.5448% (-14.0966% EV)9.5449%DEP321 Rank-5 (19 out, 5 in)
TABLEAU & SCOREBOARD SEPARATION · DEP321

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP321 · 6D)

Statistical verification of DEP321 (6D, 70% penetration, 5 Five-Pip Card cards in 94 stub cards) demonstrates why single-rank depletion (19 Rank-5 dealt) shifts edges by basis points around -1.0254% (5% Vig).

  • DEP321 (6D 70%): 94/312 cards with 5/24 Rank-5 (7A).
  • DEP321 (Rank-5 split): 45.8614% Banker, 44.5937% Player, 9.5448% Tie in 94 6D cards (7B).
  • DEP321 (5% Vig EV): -1.0254% Banker, -1.2677% Player, -14.0966% Tie, 0.9380 SD at 70% (7C).
  • DEP321 (6D roads): red/blue marks log Big Road columns, never 5 Rank-5 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 19 Five-Pip Card cards leave a 6D shoe by 70% depth (DEP321), 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-5 stub counts (5/24 in 94 cards); Banker carries a -1.0254% 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