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TABLEAU CELL [B6T4] · ENGINE VERIFIED

Banker 6 vs. Player Third Card 4 (B6T4): Why Banker Always Stands

In cell B6T4, a Banker holding two-card total 6 (3+3) faces a Player fifth card valued at 4 (4). Under BANKER_TABLEAU[6][4], the Banker STANDS, resolving in 5 cards with a 20B / 30P / 10T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B6T4 Action
STAND
B6T4 Card Count
5 Cards
B6T4 60-Branch B/P/T
20/30/10
Tableau Coordinates
B=6, P3=4
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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Big Road 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 B B
Big Eye Boy ≠ = = ≠ ≠ = = ≠ ≠ = ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = ≠ = = = ≠ ≠ ≠ = = = ≠
Small Road = ≠ = ≠ ≠ ≠ = ≠ = ≠ = ≠ = ≠ ≠ = ≠ ≠ ≠ = ≠ ≠ = ≠ ≠ ≠ = ≠
Cockroach Pig = ≠ ≠ ≠ ≠ = ≠ ≠ = = ≠ = = ≠ = = ≠ = ≠ ≠ = = ≠ = ≠ ≠ =

Verified scoreboard paired with tableau cell B6T4 (Banker 6 vs Player 3rd card 4).

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

  1. Column 2 goes down to Row 4, so use Rule 2: look 1 column back, at Column 1.
  2. Column 1 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 1 stopped exactly one row above this bead.

Small Road Mark #3

Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 3, 2 columns further back.
  2. Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 3.

Cockroach Pig Mark #3

This bead is at Row 2. Column 3 stopped at Row 1, one row above → blue (≠).

  1. Column 6 goes down to Row 2, so use Rule 2: look 3 columns back, at Column 3.
  2. Column 3 stopped at Row 1, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 3 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

Cell B6T4 Tableau Lookup
false (Mandatory 5-Card Stand)

Verified via bankerShouldDraw(6, 4) === false on pair 3+3.

Cell B6T4 60-Branch Matrix Split
20 Banker / 30 Player / 10 Tie

Exact resolution across 6 legal Player starts (0–5) × 10 sixth-card values (0–9).

Cell B6T4 Resulting Player Totals
0+4=4, 1+4=5, 2+4=6, 3+4=7, 4+4=8, 5+4=9

Three-card Player totals produced when fifth card 4 (4) lands on P0..P5.

Cell B6T4 Standing Comparison
2W / 1T / 3L

How standing Banker 6 fares against the 6 Player 3-card totals for P3=4.

Cell B6T4 Sample Audition Hand
B(3+3=6) vs P3=4(4) -> STAND

Sample sixth card 7 (7) verified through resolveHand().

COMBINATORIAL PROOF · CELL B6T4

Cell B6T4 Analysis: Banker 6 (3+3) Facing Fifth-Card 4 (Value 4)

Under [B6T4], Banker holds two-card total 6 (3+3) while Player draws fifth-card 4 (point value 4) onto an initial 0–5 total. Across those six legal Player starts, [B6T4] produces three-card Player totals of P0+4->4, P1+4->5, P2+4->6, P3+4->7, P4+4->8, P5+4->9.

Because [B6T4] falls outside the draw window for Banker 6, the dealer stands pat on 3+3 (6) at 5 cards: across the 60 (P0..P5 × unpulled 6th card 0..9) branches in [B6T4], standing yields 20 Banker wins, 30 Player wins, and 10 ties without wraparound risk.

Cell B6T4 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 4 (4)
B6T4 Player StartB6T4 5th CardB6T4 Banker 6 ActionB6T4 10-Card SplitB6T4 Sample Result
[B6T4:P0] 10+K=0[B6T4:5th] +4(4) -> P=4[B6T4:Pat] B=6 stands at 6[B6T4:Split] 10B/0P/0T[B6T4:Cards] 5c (B)
[B6T4:P1] 7+4=1[B6T4:5th] +4(4) -> P=5[B6T4:Pat] B=6 stands at 6[B6T4:Split] 10B/0P/0T[B6T4:Cards] 5c (B)
[B6T4:P2] 10+2=2[B6T4:5th] +4(4) -> P=6[B6T4:Pat] B=6 stands at 6[B6T4:Split] 0B/0P/10T[B6T4:Cards] 5c (T)
[B6T4:P3] 9+4=3[B6T4:5th] +4(4) -> P=7[B6T4:Pat] B=6 stands at 6[B6T4:Split] 0B/10P/0T[B6T4:Cards] 5c (P)
[B6T4:P4] 2+2=4[B6T4:5th] +4(4) -> P=8[B6T4:Pat] B=6 stands at 6[B6T4:Split] 0B/10P/0T[B6T4:Cards] 5c (P)
[B6T4:P5] A+4=5[B6T4:5th] +4(4) -> P=9[B6T4:Pat] B=6 stands at 6[B6T4:Split] 0B/10P/0T[B6T4:Cards] 5c (P)
  • [B6T4-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 6 (3+3).
  • [B6T4-Step2] Confirm Player drew fifth-card 4 (value 4) onto a 0–5 start.
  • [B6T4-Step3] Execute BANKER_TABLEAU[6][4] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B6T4

How Cell B6T4 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B6T4], Banker 6 (3+3) never takes a sixth card, so 3-card Banker Dragon 7 is impossible while Player reaches 3-card 8 (Panda 8) whenever P=4 draws 4 (4).

Once [B6T4] resolves (20B/30P/10T across 60 branches), the winning side logs to the Big Road on shoe PBBBBPBPBB.

Table Reality Check

Myth vs. Truth

MythIn cell B6T4, the dealer checks the Player's 3-card sum (7) before acting on Banker 6.
TruthCell B6T4 inspects only the fifth card's face value (4 from 4), ordering Banker 6 to stands.
MythWinning cell B6T4 guarantees a Red mark on Big Eye Boy and Small Road.
TruthOn derived roads, Red (=) means the Big Road column pattern repeated and Blue (≠) means it broke—never Banker vs Player.
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