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EXACT DECK ENUMERATION · 7-DECK (364 CARDS)

7-Deck Baccarat Combinatorial Proof (364-Card Shoe Odds & House Edge)

Seven-deck custom shoe audits and finite-to-infinite limit interpolation. In a fresh 7-deck shoe containing 364 cards (112 zero-value cards and 28 of each pip Ace–9), exact six-card enumeration yields 45.8621% Banker wins, 44.6260% Player wins, and 9.5118% Ties, resulting in a 1.0570% Banker house edge and 1.2361% Player house edge.

7D Banker Edge
1.057%
7D Player Edge
1.236%
7D Tie Edge (8:1)
14.39%
7D Shoe Cards
364
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

7-deck sample shoe (364 cards). Derived-road colors reflect Big Road column structure, never 7-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

7D Total Card Inventory
364 cards

112 ten/face 0-point cards plus 28 per pip rank A–9.

7D Exact Banker Win Rate
45.8621%

50.6830% share of non-tie resolved decisions in 7-deck play.

7D Exact Player Win Rate
44.6260%

49.3170% share of non-tie resolved decisions in 7-deck play.

7D Banker House Edge (5% Vig)
1.0570%

Variance 0.8601 per unit staked in 7-deck shoes.

7D Natural Settlement Rate
34.3078%

Player natural 18.9447%, Banker natural 18.9447%, both 3.5816%.

D7 COMBINATORIAL WEIGHTS

7-Deck (364-Card) Six-Card Enumeration & Depletion Profile

[D7-INVENTORY] Seven decks hold 364 cards (112 zero-point cards and 28 of each pip value A–9), sitting one deck shy of the global 416-card tournament standard. At 364 cards, each dealt rank changes subsequent draw weights by 0.275%, placing Banker house edge at 1.0570% and Player house edge at 1.2353%.

[D7-PAYOUTS] Seven-deck Tie probability reaches 9.5458%, reducing the 8-to-1 Tie house edge to 14.088% as duplicate card combinations expand. Third-card draw frequencies on Banker 3, 4, 5, and 6 differ from 8-deck values only in the fifth decimal place.

D7 WagerD7 Win %D7 Loss %D7 Push %D7 House EdgeD7 Variance
D7-Banker (0.95:1)45.8621%44.6260%9.5118%1.0570%0.86005
D7-Player (1.00:1)44.6260%45.8621%9.5118%1.2361%0.90473
D7-Tie (8.00:1)9.5118%90.4882%-0.0000%14.3934%6.97174
D7-Naturals (8/9)34.3078%65.6922%3.5816%P:18.9447%B:18.9447%
  • D7 non-tie split: 50.6830% Banker vs 49.3170% Player across 364 cards.
  • D7 100-hand expected loss at $100/hand: $105.70 on Banker vs $123.61 on Player.
Table Reality Check

Myth vs. Truth

MythSwitching to a 7-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 364-card deal probabilities shift (1.0570% 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