Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 6-Deck Exact Odds
EXACT DECK ENUMERATION · 6-DECK (312 CARDS)

6-Deck Baccarat Combinatorial Proof (312-Card Shoe Odds & House Edge)

Six-deck Mini-Baccarat, Midi-Baccarat, and North American high-speed pits. In a fresh 6-deck shoe containing 312 cards (96 zero-value cards and 24 of each pip Ace–9), exact six-card enumeration yields 45.8653% Banker wins, 44.6279% Player wins, and 9.5069% Ties, resulting in a 1.0558% Banker house edge and 1.2374% Player house edge.

6D Banker Edge
1.056%
6D Player Edge
1.237%
6D Tie Edge (8:1)
14.44%
6D Shoe Cards
312
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

6-deck sample shoe (312 cards). Derived-road colors reflect Big Road column structure, never 6-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 3 has 1 bead. Column 2 has 1 bead. Same depth → red (=).

  1. Column 4 starts, so use Rule 1: compare Column 3 with Column 2, 1 column further back.
  2. Column 3 has 1 bead. Column 2 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 2.

Small Road Mark #2

Column 4 has 1 bead. Column 2 has 1 bead. Same depth → red (=).

  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 1 bead. Same depth → red (=).

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 1 bead. Same depth → red (=).

  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 1 bead. Same depth → red (=).

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

6D Total Card Inventory
312 cards

96 ten/face 0-point cards plus 24 per pip rank A–9.

6D Exact Banker Win Rate
45.8653%

50.6837% share of non-tie resolved decisions in 6-deck play.

6D Exact Player Win Rate
44.6279%

49.3163% share of non-tie resolved decisions in 6-deck play.

6D Banker House Edge (5% Vig)
1.0558%

Variance 0.8601 per unit staked in 6-deck shoes.

6D Natural Settlement Rate
34.3117%

Player natural 18.9463%, Banker natural 18.9463%, both 3.5810%.

D6 COMBINATORIAL WEIGHTS

6-Deck (312-Card) Six-Card Enumeration & Depletion Profile

[D6-INVENTORY] Six decks total 312 cards (ninety-six 0-value cards and twenty-four per pip rank), forming the primary alternative to 8-deck shoes across Las Vegas and Atlantic City. With 312 cards in the acrylic carrier, each card removed represents 0.321% of the initial pack, yielding a 1.0558% Banker house edge and 1.2355% Player house edge.

[D6-PAYOUTS] Six-deck Tie frequency equals 9.5449% (14.096% house edge at 8-to-1), making 6-deck slightly tighter against Tie bettors than 8-deck while slightly friendlier to Banker bettors. Six-deck Dragon Bonus and Pair side bets use dedicated 312-card combinatorial tables because suited pair frequency is lower in 6 decks than in 8 decks.

D6 WagerD6 Win %D6 Loss %D6 Push %D6 House EdgeD6 Variance
D6-Banker (0.95:1)45.8653%44.6279%9.5069%1.0558%0.86010
D6-Player (1.00:1)44.6279%45.8653%9.5069%1.2374%0.90478
D6-Tie (8.00:1)9.5069%90.4931%0.0000%14.4382%6.96848
D6-Naturals (8/9)34.3117%65.6883%3.5810%P:18.9463%B:18.9463%
  • D6 non-tie split: 50.6837% Banker vs 49.3163% Player across 312 cards.
  • D6 100-hand expected loss at $100/hand: $105.58 on Banker vs $123.74 on Player.
Table Reality Check

Myth vs. Truth

MythSwitching to a 6-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 312-card deal probabilities shift (1.0558% 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