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EXACT DECK ENUMERATION · 1-DECK (52 CARDS)

1-Deck Baccarat Combinatorial Proof (52-Card Shoe Odds & House Edge)

Single-deck studio tables and Macau historical audit benchmarks. In a fresh 1-deck shoe containing 52 cards (16 zero-value cards and 4 of each pip Ace–9), exact six-card enumeration yields 45.9624% Banker wins, 44.6760% Player wins, and 9.3615% Ties, resulting in a 1.0117% Banker house edge and 1.2864% Player house edge.

1D Banker Edge
1.012%
1D Player Edge
1.286%
1D Tie Edge (8:1)
15.75%
1D Shoe Cards
52
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

1-deck sample shoe (52 cards). Derived-road colors reflect Big Road column structure, never 1-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

This bead is at Row 3. Column 1 has a bead at Row 3 too → red (=).

  1. Column 2 goes down to Row 3, so use Rule 2: look 1 column back, at Column 1.
  2. Column 1 has a bead at Row 3 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Small Road Mark #2

This bead is at Row 3. Column 1 has a bead at Row 3 too → red (=).

  1. Column 3 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 has a bead at Row 3 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Cockroach Pig Mark #2

This bead is at Row 3. Column 1 has a bead at Row 3 too → red (=).

  1. Column 4 goes down to Row 3, so use Rule 2: look 3 columns back, at Column 1.
  2. Column 1 has a bead at Row 3 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

1D Total Card Inventory
52 cards

16 ten/face 0-point cards plus 4 per pip rank A–9.

1D Exact Banker Win Rate
45.9624%

50.7096% share of non-tie resolved decisions in 1-deck play.

1D Exact Player Win Rate
44.6760%

49.2904% share of non-tie resolved decisions in 1-deck play.

1D Banker House Edge (5% Vig)
1.0117%

Variance 0.8615 per unit staked in 1-deck shoes.

1D Natural Settlement Rate
34.4411%

Player natural 19.0045%, Banker natural 19.0045%, both 3.5680%.

D1 COMBINATORIAL WEIGHTS

1-Deck (52-Card) Six-Card Enumeration & Depletion Profile

[D1-INVENTORY] With only 52 cards (sixteen zero-value tens/faces and four of each pip A through 9), pulling a single card alters remaining rank density by 1.923% immediately. Drawing a first-card 8 or 9 sharply reduces the chance of an opposing natural on the same deal, compressing Tie frequency to its lowest finite-shoe level.

[D1-PAYOUTS] A 1-deck shoe produces a 9.5156% Tie rate and a 15.748% house edge on the 8-to-1 Tie wager, punishing Tie tickets more severely than multi-deck shoes. Single-deck play yields the highest Banker theoretical advantage (1.011% house edge under 5% commission) because third-card asymmetry interacts strongly with card depletion.

D1 WagerD1 Win %D1 Loss %D1 Push %D1 House EdgeD1 Variance
D1-Banker (0.95:1)45.9624%44.6760%9.3615%1.0117%0.86147
D1-Player (1.00:1)44.6760%45.9624%9.3615%1.2864%0.90622
D1-Tie (8.00:1)9.3615%90.6385%0.0000%15.7461%6.87298
D1-Naturals (8/9)34.4411%65.5589%3.5680%P:19.0045%B:19.0045%
  • D1 non-tie split: 50.7096% Banker vs 49.2904% Player across 52 cards.
  • D1 100-hand expected loss at $100/hand: $101.17 on Banker vs $128.64 on Player.
Table Reality Check

Myth vs. Truth

MythSwitching to a 1-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 52-card deal probabilities shift (1.0117% 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