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PAIR SIDE-BET AUDIT · BP1D

Banker Pair (1-Deck Shoe): 11 to 1 Paytable & 29.41% House Edge

[BP1D] In a 1-deck (52-card) shoe, Banker's initial two cards share the same rank (A–K). In a 1-deck (52-card) shoe, Banker Pair (1-Deck) achieves a 5.8824% exact hit frequency at 11 to 1, producing a 29.412% house edge and 2.824u per-unit standard deviation compared to 1.0579% on standard 5%-commission Banker.

BP1D Payout
11 to 1
BP1D Hit Rate
5.8824%
BP1D House Edge
29.412%
BP1D Volatility
2.824u
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

BP1D (Banker Pair (1-Deck)) scoreboard sample. Derived-road red/blue marks track Big Road column symmetry, never BP1D side-bet triggers.

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

Column 4 has 2 beads. Column 1 has 4 beads. Different depth → blue (≠).

  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 4 beads. Different depth → blue (≠).

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

BP1D Paytable Return
11 to 1

In a 1-deck (52-card) shoe, Banker's initial two cards share the same rank (A–K).

BP1D Exact Hit Rate
5.8824%

Enumerated across 1-deck (52-card) finite deals.

BP1D House Edge
29.412%

Compared against 1.0579% Banker and 1.2351% Player main bets.

BP1D Unit Volatility (SD)
2.824u

Per-hand standard deviation for Banker Pair (1-Deck) (BP1D).

BP1D Floor Scope
1-Deck Layout

1-deck Macau, Las Vegas, UK, and live-dealer studio tables (BP1D)

BP1D ACTUARIAL PAYTABLE

Banker Pair (1-Deck) (BP1D) Combinatorial Breakdown & Jurisdiction Audit

[BP1D-RULE] Gaming-lab specification BP1D enumerates Banker Pair (1-Deck) across 52 cards: In a 1-deck (52-card) shoe, Banker's initial two cards share the same rank (A–K). After the first card is placed in a 52-card shoe, 3 rank matches and 0 identical suited matches remain among 51 unseen cards.

[BP1D-EDGE] Floor audit BP1D tracks a 5.8824% hit rate against the 11 to 1 paytable, which grades a 29.412% house hold and 2.824u volatility across 1-deck Macau, Las Vegas, UK, and live-dealer studio tables (BP1D). Because BP1D models card ranks and totals dealt from the 1-deck shoe, scoreboard trends on Big Eye Boy, Small Road, and Cockroach Pig never alter BP1D probabilities.

BP1D ParameterBP1D ValueBP1D Main Banker RefBP1D Main Player RefBP1D Audit Note
BP1D Shoe Model1 Decks (52c) [BP1D]8D 416c [BP1D]8D 416c [BP1D]BP1D finite without replacement
BP1D Paytable11 to 1 [BP1D]0.95 to 1 [BP1D]1.00 to 1 [BP1D]BP1D settled on deal completion
BP1D Hit Rate5.8824% [BP1D]45.8597% [BP1D]44.6247% [BP1D]BP1D exact six-card count
BP1D House Edge29.412% [BP1D]1.0579% [BP1D]1.2351% [BP1D]BP1D house hold per unit
BP1D Std Dev2.824u [BP1D]0.931u [BP1D]0.951u [BP1D]BP1D single-hand dispersion
  • BP1D trigger check: In a 1-deck (52-card) shoe, Banker's initial two cards share the same rank (A–K).
  • BP1D combinatorial proof: After the first card is placed in a 52-card shoe, 3 rank matches and 0 identical suited matches remain among 51 unseen cards.
  • BP1D independence verification: derived-road marks on BBBBPPPP never shift BP1D (29.412% edge).
Table Reality Check

Myth vs. Truth

MythDeck count barely affects the Banker Pair side bet because every deck has four of each rank.
TruthBecause matching the first card draws without replacement from 51 remaining cards, 1-deck Banker Pair carries a 29.41% house edge (5.8824% hit rate).
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