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COMBINATORIAL DEPLETION · 8D · ACE-1 · 25% DEPTH

8-Deck Ace (1-Point Pip) Depletion at 25% Penetration (5% Audit DEP371)

Removing 9 of 32 Ace (1-Point Pip) (Ace-1) cards at 25% penetration of a 8-deck (416-card) shoe leaves 23 Ace-1 cards inside a 312-card stub (DEP371), producing 45.8602% Banker wins, 44.6242% Player wins, 9.5156% Ties, and a 1.0570% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0570%
Player EV (1:1)
-1.2360%
Ace-1 in 312-Card Stub
23/32
Single-Hand Std Dev
0.9323
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBPBPBBPPBPBPBB) illustrating derived-road symmetry checks alongside DEP371 (8D Ace-1 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 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 (DEP371)
312 / 416 Cards

25% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Ace-1 Remaining
23 of 32 Cards

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

Banker EV (5% Vig)
-1.0570%

Resolved at 45.8602% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2360%

Resolved at 44.6242% Player win rate with 0.9323 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3595% house hold on the 8-to-1 Tie wager in state DEP371.

FINITE-SHOE ENUMERATION · DEP371

How Ace (1-Point Pip) Depletion at 25% Depth Impacts 8D (5% Vig)

Card-removal benchmark DEP371 measures Ace (1-Point Pip) (Ace-1) scarcity at 25% depth in a 8-deck shoe: 9 removed ranks leave 23 in the 312-card remainder, shifting Banker win share to 45.8602% (1.0570% edge, 5% Vig).

Tracking DEP371 across 312 remaining 8D cards (25% depth) shows that when fewer aces remain, (dep371-ace-1) player 7 and 8 third-card (312c) transitions from 6 and 7 (dep371-ace-1·312c) occur less often during six-card resolutions. With 9 Ace-1 cards gone (+0.44 bps unit sensitivity), Banker expectation is -1.0570% (5% Vig) vs -1.2360% on Player.

State DEP371 (8D, 25% depth, 23/32 Ace-1 left, 5% Vig)
Wager / MetricState DEP371 Value8D BaselineSettlement Note
DEP371 Banker (5% Vig)45.8602% (-1.0570% EV)45.8597%DEP371 8D 25% (23 Ace-1)
DEP371 Player (1:1)44.6242% (-1.2360% EV)44.6247%DEP371 312-card 8D stub (0.9323 SD)
DEP371 Tie (8:1)9.5156% (-14.3595% EV)9.5156%DEP371 Ace-1 (9 out, 23 in)
TABLEAU & SCOREBOARD SEPARATION · DEP371

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP371 · 8D)

On the electronic scoreboard for DEP371 (8D, 25% depth, 312 cards left), Bead Plate and Big Road circles record Banker (45.8602%) and Player (44.6242%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Ace-1 card counts (23/32).

  • DEP371 (8D 25%): 312/416 cards with 23/32 Ace-1 (5A).
  • DEP371 (Ace-1 split): 45.8602% Banker, 44.6242% Player, 9.5156% Tie in 312 8D cards (5B).
  • DEP371 (5% Vig EV): -1.0570% Banker, -1.2360% Player, -14.3595% Tie, 0.9323 SD at 25% (5C).
  • DEP371 (8D roads): red/blue marks log Big Road columns, never 23 Ace-1 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 9 Ace (1-Point Pip) cards leave a 8D shoe by 25% depth (DEP371), 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 (23/32 in 312 cards); Banker carries a -1.0570% 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