Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 1D Rank-0 Depletion at 10% Depth (5% Vig)
COMBINATORIAL DEPLETION · 1D · RANK-0 · 10% DEPTH

1-Deck 0-Value Tens & Faces Depletion at 10% Penetration (5% Audit DEP001)

Removing 2 of 16 0-Value Tens & Faces (Rank-0) cards at 10% penetration of a 1-deck (52-card) shoe leaves 14 Rank-0 cards inside a 47-card stub (DEP001), producing 45.9598% Banker wins, 44.5246% Player wins, 9.5156% Ties, and a 0.8627% Banker house edge under 5%.

Banker EV (5% Vig)
-0.8627%
Player EV (1:1)
-1.4352%
Rank-0 in 47-Card Stub
14/16
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 B B P B P
Big Eye Boy = = = = = = ≠ = = = ≠ ≠ ≠ =
Small Road = = = = ≠ ≠ = = ≠ ≠ = ≠
Cockroach Pig = = ≠ ≠ ≠ = ≠ ≠ = =

Reference shoe scoreboard (BBPPBBPPBPTBPBBPBP) illustrating derived-road symmetry checks alongside DEP001 (1D 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 (DEP001)
47 / 52 Cards

10% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-0 Remaining
14 of 16 Cards

2 10, Jack, Queen, and King (zero-point cards) removed from the 1D pack.

Banker EV (5% Vig)
-0.8627%

Resolved at 45.9598% Banker win rate under 5% settlement.

Player EV (1:1)
-1.4352%

Resolved at 44.5246% Player win rate with 0.9305 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3594% house hold on the 8-to-1 Tie wager in state DEP001.

FINITE-SHOE ENUMERATION · DEP001

How 0-Value Tens & Faces Depletion at 10% Depth Impacts 1D (5% Vig)

Audit DEP001 evaluates a 1-deck (52-card) shoe at 10% penetration where 2 of 16 0-Value Tens & Faces cards have exited, leaving 14 Rank-0 cards inside the 47-card stub with Banker EV at -0.8627% under 5%.

Depleting zero-point cards reduces (DEP001) modulo-10 standoffs and alters two-card (1D-10%) natural combinations paired with 8s (DEP001·1D-10%) and 9s. In state DEP001 (1D, 10% depth), each removed Rank-0 card applies a +0.18 bps baseline directional pressure before scaling to the 47-card remainder (14 Rank-0 left), while Winning Banker tickets pay (DEP001-1D) 0.95 units per unit staked (14/16) while 90% of the initial (DEP001-1D·14/16) shoe remains undealt.

State DEP001 (1D, 10% depth, 14/16 Rank-0 left, 5% Vig)
Wager / MetricState DEP001 Value1D BaselineSettlement Note
DEP001 Banker (5% Vig)45.9598% (-0.8627% EV)45.9595%DEP001 1D 10% (14 Rank-0)
DEP001 Player (1:1)44.5246% (-1.4352% EV)44.5249%DEP001 47-card 1D stub (0.9305 SD)
DEP001 Tie (8:1)9.5156% (-14.3594% EV)9.5156%DEP001 Rank-0 (2 out, 14 in)
TABLEAU & SCOREBOARD SEPARATION · DEP001

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP001 · 1D)

On the electronic scoreboard for DEP001 (1D, 10% depth, 47 cards left), Bead Plate and Big Road circles record Banker (45.9598%) and Player (44.5246%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Rank-0 card counts (14/16).

  • DEP001 (1D 10%): 47/52 cards with 14/16 Rank-0 (3A).
  • DEP001 (Rank-0 split): 45.9598% Banker, 44.5246% Player, 9.5156% Tie in 47 1D cards (3B).
  • DEP001 (5% Vig EV): -0.8627% Banker, -1.4352% Player, -14.3594% Tie, 0.9305 SD at 10% (3C).
  • DEP001 (1D roads): red/blue marks log Big Road columns, never 14 Rank-0 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 2 0-Value Tens & Faces cards leave a 1D shoe by 10% depth (DEP001), 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 (14/16 in 47 cards); Banker carries a -0.8627% 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