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COMBINATORIAL DEPLETION · 8D · ACE-1 · 40% DEPTH

8-Deck Ace (1-Point Pip) Depletion at 40% Penetration (4% Audit DEP372)

Removing 15 of 32 Ace (1-Point Pip) (Ace-1) cards at 40% penetration of a 8-deck (416-card) shoe leaves 17 Ace-1 cards inside a 250-card stub (DEP372), producing 45.8606% Banker wins, 44.6238% Player wins, 9.5156% Ties, and a 0.5976% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5976%
Player EV (1:1)
-1.2368%
Ace-1 in 250-Card Stub
17/32
Single-Hand Std Dev
0.9338
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road P P B B P B P B P P B B P B P B P P
Big Eye Boy = = ≠ = = = ≠ ≠ = = ≠ = = = ≠
Small Road ≠ ≠ = = ≠ ≠ ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ = ≠

Reference shoe scoreboard (PPBBPBPBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP372 (8D Ace-1 at 40% 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 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #2

Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP372)
250 / 416 Cards

40% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Ace-1 Remaining
17 of 32 Cards

15 Ace cards valued at 1 modulo-10 point removed from the 8D pack.

Banker EV (4% Vig)
-0.5976%

Resolved at 45.8606% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2368%

Resolved at 44.6238% Player win rate with 0.9338 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3594% house hold on the 8-to-1 Tie wager in state DEP372.

FINITE-SHOE ENUMERATION · DEP372

How Ace (1-Point Pip) Depletion at 40% Depth Impacts 8D (4% Vig)

Within eight-deck Macau, Las Vegas Strip, and Singapore standard shoes, profile DEP372 examines 40% shoe depletion (250 of 416 cards remaining) after 15 Ace-1 cards exit, leaving 17 Ace (1-Point Pip) cards and a 0.5976% Banker house hold under 4%.

For DEP372 (8-deck shoe, 40% dealt), removing aces slightly favors (dep372) banker because banker stands on (8d-40%) 6 against player third-card ace (dep372·8d-40%) while player must draw on 0–5. Holding 17 of 32 Ace-1 cards in a 250-card stub with +0.44 bps rank slope yields 45.8606% Banker, 44.6238% Player, and 9.5156% Tie.

State DEP372 (8D, 40% depth, 17/32 Ace-1 left, 4% Vig)
Wager / MetricState DEP372 Value8D BaselineSettlement Note
DEP372 Banker (4% Vig)45.8606% (-0.5976% EV)45.8597%DEP372 8D 40% (17 Ace-1)
DEP372 Player (1:1)44.6238% (-1.2368% EV)44.6247%DEP372 250-card 8D stub (0.9338 SD)
DEP372 Tie (8:1)9.5156% (-14.3594% EV)9.5156%DEP372 Ace-1 (15 out, 17 in)
TABLEAU & SCOREBOARD SEPARATION · DEP372

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP372 · 8D)

In studio and floor audits of DEP372 (250 cards undealt out of 416 in 8D at 40% depth), a 0.9338 unit standard deviation accompanies the 17-card Ace-1 stub under 4% Vig (45.8606% Banker vs 44.6238% Player).

  • DEP372 (8D 40%): 250/416 cards with 17/32 Ace-1 (3A).
  • DEP372 (Ace-1 split): 45.8606% Banker, 44.6238% Player, 9.5156% Tie in 250 8D cards (3B).
  • DEP372 (4% Vig EV): -0.5976% Banker, -1.2368% Player, -14.3594% Tie, 0.9338 SD at 40% (3C).
  • DEP372 (8D roads): red/blue marks log Big Road columns, never 17 Ace-1 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 15 Ace (1-Point Pip) cards leave a 8D shoe by 40% depth (DEP372), 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 Ace-1 stub counts (17/32 in 250 cards); Banker carries a -0.5976% expectation under 4%.
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