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DECISION CELL [B=4, P3=7] · ENGINE VERIFIED

Banker 4 vs. Player Third Card 7: Why Banker Always Draws

When the Banker holds a two-card total of 4 and the Player draws a third card with a point value of 7 (a 7), the official Punto Banco tableau mandates that the Banker DRAWS. Every such hand resolves in exactly 6 cards (3 Player, 3 Banker).

Banker 4 Action vs P3=7
DRAW
Exact Hand Card Count
6 Cards
Banker 2-Card Total
4
Player 3rd Card Point Value
7
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Engine-verified scoreboard accompanying the Banker 4 vs. Player third-card 7 (DRAW) cell.

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 #3

This bead is at Row 3. Column 2 stopped at Row 1, more than one row above → red (=).

  1. Column 3 goes down to Row 3, so use Rule 2: look 1 column back, at Column 2.
  2. Column 2 stopped at Row 1, more than one row above → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

Small Road Mark #3

This bead is at Row 4. Column 1 stopped at Row 2, more than one row above → red (=).

  1. Column 3 goes down to Row 4, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 stopped at Row 2, more than one row above → 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 #3

Column 6 has 1 bead. Column 3 has 4 beads. Different depth → blue (≠).

  1. Column 7 starts, so use Rule 1: compare Column 6 with Column 3, 3 columns further back.
  2. Column 6 has 1 bead. Column 3 has 4 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 6, the one that just finished, with Column 3.

Verified Reference Data

Key Facts & Table Specifications

Tableau Lookup BANKER_TABLEAU[4][7]
true (Banker Draws 6th Card)

Verified directly against packages/core/lib/baccarat/handResolution.ts.

Total Cards Dealt in [B=4, P3=7]
6 Cards (Big Hand)

Player holds 3 cards and Banker holds 3 cards.

Possible Player 3-Card Totals When P3=7
7, 8, 9, 0, 1, 2

Resulting modulo-10 Player totals when adding 7 to legal drawing totals 0–5.

Standing Banker 4 vs Player Totals (P3=7)
3 Wins / 0 Ties / 3 Losses

How a standing Banker 4 compares against the 6 possible Player 3-card totals when P3=7.

Sample Verified Deal ([B=4, P3=7])
P: 10+A+7 vs B: A+3+5

Confirmed via resolveHand() with sample sixth card 5 (5B/0P/1T across the 6 Player starts).

COMBINATORIAL PROOF FOR [B=4, P3=7]

Why the Tableau Orders Banker 4 to Draw Against a Player Third-Card 7

Player third-card 7 is the upper boundary of the Banker 4 draw window (2–7): the Banker MUST DRAW a third card.

When the Player pulls a 7 onto an initial 0, 1, or 2, the Player lands on 7, 8, or 9—crushing a standing Banker 4. Drawing onto 4 is mandatory to stay competitive against those high three-card Player totals.

For Banker 4 facing Player's third card 7 (7), combining 7 with the 6 legal Player starts (0..5) yields the specific Player 3-card sequence [0+7→7; 1+7→8; 2+7→9; 3+7→0; 4+7→1; 5+7→2], against which Banker 4 (A+3) tallies 3 standing wins, 0 pushes, and 3 deficits.

All 6 Real Player Starting Totals (0–5) When Player Draws 7 Against Banker 4
Player 2-Card StartPlayer Draws 7 (Value 7)Banker 4 Tableau RuleHand SizeSample Outcome (Banker Draw = 5)
Player starts at 0 (10+K)Draws 7 (val 7) → Player 3-card total 7Banker 4 DRAWS (e.g. +5 → 9)6 cards dealtBanker wins (9 vs 7)
Player starts at 1 (10+A)Draws 7 (val 7) → Player 3-card total 8Banker 4 DRAWS (e.g. +5 → 9)6 cards dealtBanker wins (9 vs 8)
Player starts at 2 (A+A)Draws 7 (val 7) → Player 3-card total 9Banker 4 DRAWS (e.g. +5 → 9)6 cards dealtTie at 9
Player starts at 3 (A+2)Draws 7 (val 7) → Player 3-card total 0Banker 4 DRAWS (e.g. +5 → 9)6 cards dealtBanker wins (9 vs 0)
Player starts at 4 (2+2)Draws 7 (val 7) → Player 3-card total 1Banker 4 DRAWS (e.g. +5 → 9)6 cards dealtBanker wins (9 vs 1)
Player starts at 5 (2+3)Draws 7 (val 7) → Player 3-card total 2Banker 4 DRAWS (e.g. +5 → 9)6 cards dealtBanker wins (9 vs 2)
  • [4 vs 7] Check A: No Natural 8/9 appeared on the initial 4 cards (10+A vs A+3).
  • [4 vs 7] Check B: Player drew 7 (value 7) as the 5th card of the hand.
  • [4 vs 7] Check C: BANKER_TABLEAU[4][7] = true → Banker 4 draws 6th card (5).
DEALER EXECUTION & SIDE-BET IMPACT [B=4, P3=7]

How [Banker 4, Player 3rd Card 7] Affects Side Bets and Road Tracking

In the [4 vs 7] draw branch (A+3 drawing against Player's 7), a 6th card is dealt from the shoe: catching a 3 forms a 3-card Banker 7 (Dragon 7), whereas catching a 2 forms a 3-card Banker 6 (Super 6).

Testing [4 vs 7] with sixth-card 5 across all 6 Player starts yields 5B / 0P / 1T on shoe BBPBBBBPBPBB…

Table Reality Check

Myth vs. Truth

MythWhen Player draws a 7 to reach a three-card total of 9, the Banker looks at 9 to decide whether to draw on 4.
TruthThe dealer and the tableau never use the Player's three-card total (9)—the Banker 4 rule keys strictly off the third card's own value (7), which always triggers a draw.
MythA 6-card hand caused by Banker 4 vs Player third-card 7 changes the probabilities of the next hand's road pattern.
TruthDerived roads record whether Big Road column lengths repeat (Red =) or break (Blue ≠); they do not track whether a hand used 4, 5, or 6 cards and never predict the next hand.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

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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
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