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EXACT DECK ENUMERATION · 4-DECK (208 CARDS)

4-Deck Baccarat Combinatorial Proof (208-Card Shoe Odds & House Edge)

Four-deck mid-tier Asian VIP rooms and compact automatic shuffler shoes. In a fresh 4-deck shoe containing 208 cards (64 zero-value cards and 16 of each pip Ace–9), exact six-card enumeration yields 45.8761% Banker wins, 44.6340% Player wins, and 9.4898% Ties, resulting in a 1.0517% Banker house edge and 1.2421% Player house edge.

4D Banker Edge
1.052%
4D Player Edge
1.242%
4D Tie Edge (8:1)
14.59%
4D Shoe Cards
208
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

4-deck sample shoe (208 cards). Derived-road colors reflect Big Road column structure, never 4-deck card depletion.

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

4D Total Card Inventory
208 cards

64 ten/face 0-point cards plus 16 per pip rank A–9.

4D Exact Banker Win Rate
45.8761%

50.6862% share of non-tie resolved decisions in 4-deck play.

4D Exact Player Win Rate
44.6340%

49.3138% share of non-tie resolved decisions in 4-deck play.

4D Banker House Edge (5% Vig)
1.0517%

Variance 0.8603 per unit staked in 4-deck shoes.

4D Natural Settlement Rate
34.3251%

Player natural 18.9521%, Banker natural 18.9521%, both 3.5790%.

D4 COMBINATORIAL WEIGHTS

4-Deck (208-Card) Six-Card Enumeration & Depletion Profile

[D4-INVENTORY] Four decks contain 208 cards (sixty-four 0-point cards and sixteen of each numeral A–9), generating over 7.67 quadrillion ordered six-card deals. At 208 cards, finite without-replacement sampling retains half the depletion sensitivity of a 2-deck shoe and twice the sensitivity of a standard 8-deck carrier.

[D4-PAYOUTS] Tie frequency advances to 9.5418%, lowering the 8-to-1 Tie house edge to 14.124% while Banker 5% commission house edge settles at 1.051%. Both-sides natural collisions occur more frequently than in single-deck play, increasing natural standoffs that return main bets untouched.

D4 WagerD4 Win %D4 Loss %D4 Push %D4 House EdgeD4 Variance
D4-Banker (0.95:1)45.8761%44.6340%9.4898%1.0517%0.86026
D4-Player (1.00:1)44.6340%45.8761%9.4898%1.2421%0.90495
D4-Tie (8.00:1)9.4898%90.5102%0.0000%14.5916%6.95729
D4-Naturals (8/9)34.3251%65.6749%3.5790%P:18.9521%B:18.9521%
  • D4 non-tie split: 50.6862% Banker vs 49.3138% Player across 208 cards.
  • D4 100-hand expected loss at $100/hand: $105.17 on Banker vs $124.21 on Player.
Table Reality Check

Myth vs. Truth

MythSwitching to a 4-deck shoe changes how derived roads (Big Eye Boy, Small Road, Cockroach Pig) are marked.
TruthDerived roads apply identical lookback rules (1, 2, and 3 columns back) on every shoe; only the underlying 208-card deal probabilities shift (1.0517% Banker edge).
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