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DECISION CELL [B=4, P3=2] · ENGINE VERIFIED

Banker 4 vs. Player Third Card 2: 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 2 (a 2), 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=2
DRAW
Exact Hand Card Count
6 Cards
Banker 2-Card Total
4
Player 3rd Card Point Value
2
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Engine-verified scoreboard accompanying the Banker 4 vs. Player third-card 2 (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

Column 2 has 3 beads. Column 1 has 3 beads. Same depth → red (=).

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

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

Small Road Mark #3

This bead is at Row 4. Column 1 stopped at Row 3, one row above → blue (≠).

  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 3, one row above → blue (≠).

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

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 5 goes down to Row 2, so use Rule 2: look 3 columns back, at Column 2.
  2. Column 2 has a bead at Row 2 too → 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.

Verified Reference Data

Key Facts & Table Specifications

Tableau Lookup BANKER_TABLEAU[4][2]
true (Banker Draws 6th Card)

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

Total Cards Dealt in [B=4, P3=2]
6 Cards (Big Hand)

Player holds 3 cards and Banker holds 3 cards.

Possible Player 3-Card Totals When P3=2
2, 3, 4, 5, 6, 7

Resulting modulo-10 Player totals when adding 2 to legal drawing totals 0–5.

Standing Banker 4 vs Player Totals (P3=2)
2 Wins / 1 Ties / 3 Losses

How a standing Banker 4 compares against the 6 possible Player 3-card totals when P3=2.

Sample Verified Deal ([B=4, P3=2])
P: A+2+2 vs B: 10+4+4

Confirmed via resolveHand() with sample sixth card 4 (6B/0P/0T across the 6 Player starts).

COMBINATORIAL PROOF FOR [B=4, P3=2]

Why the Tableau Orders Banker 4 to Draw Against a Player Third-Card 2

Player third-card 2 is the exact lower threshold where a Banker holding 4 switches from standing to DRAWING a third card.

Once the Player draws a 2 onto an initial 0–5, three of the six possible Player starting totals (3+2=5, 4+2=6, 5+2=7) overtake a standing Banker 4. Drawing gives the Banker five winning improvement ranks (Ace through 5 make 5 through 9).

For Banker 4 facing Player's third card 2 (2), combining 2 with the 6 legal Player starts (0..5) yields the specific Player 3-card sequence [0+2→2; 1+2→3; 2+2→4; 3+2→5; 4+2→6; 5+2→7], against which Banker 4 (10+4) tallies 2 standing wins, 1 pushes, and 3 deficits.

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

How [Banker 4, Player 3rd Card 2] Affects Side Bets and Road Tracking

In the [4 vs 2] draw branch (10+4 drawing against Player's 2), 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 2] with sixth-card 4 across all 6 Player starts yields 6B / 0P / 0T on shoe BBBPPPBBBBPP…

Table Reality Check

Myth vs. Truth

MythWhen Player draws a 2 to reach a three-card total of 4, the Banker looks at 4 to decide whether to draw on 4.
TruthThe dealer and the tableau never use the Player's three-card total (4)—the Banker 4 rule keys strictly off the third card's own value (2), which always triggers a draw.
MythA 6-card hand caused by Banker 4 vs Player third-card 2 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

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