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TABLEAU CELL [B7T6] · ENGINE VERIFIED

Banker 7 vs. Player Third Card 6 (B7T6): Why Banker Always Stands

In cell B7T6, a Banker holding two-card total 7 (2+5) faces a Player fifth card valued at 6 (6). Under BANKER_TABLEAU[7][6], the Banker STANDS, resolving in 5 cards with a 30B / 20P / 10T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B7T6 Action
STAND
B7T6 Card Count
5 Cards
B7T6 60-Branch B/P/T
30/20/10
Tableau Coordinates
B=7, P3=6
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 = ≠ = ≠ ≠ = ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ = = ≠ = = ≠ ≠ ≠

Verified scoreboard paired with tableau cell B7T6 (Banker 7 vs Player 3rd card 6).

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

Cell B7T6 Tableau Lookup
false (Mandatory 5-Card Stand)

Verified via bankerShouldDraw(7, 6) === false on pair 2+5.

Cell B7T6 60-Branch Matrix Split
30 Banker / 20 Player / 10 Tie

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

Cell B7T6 Resulting Player Totals
0+6=6, 1+6=7, 2+6=8, 3+6=9, 4+6=0, 5+6=1

Three-card Player totals produced when fifth card 6 (6) lands on P0..P5.

Cell B7T6 Standing Comparison
3W / 1T / 2L

How standing Banker 7 fares against the 6 Player 3-card totals for P3=6.

Cell B7T6 Sample Audition Hand
B(2+5=7) vs P3=6(6) -> STAND

Sample sixth card 8 (8) verified through resolveHand().

COMBINATORIAL PROOF · CELL B7T6

Cell B7T6 Analysis: Banker 7 (2+5) Facing Fifth-Card 6 (Value 6)

Under [B7T6], Banker holds two-card total 7 (2+5) while Player draws fifth-card 6 (point value 6) onto an initial 0–5 total. Across those six legal Player starts, [B7T6] produces three-card Player totals of P0+6->6, P1+6->7, P2+6->8, P3+6->9, P4+6->0, P5+6->1.

Because [B7T6] falls outside the draw window for Banker 7, the dealer stands pat on 2+5 (7) at 5 cards: across the 60 (P0..P5 × unpulled 6th card 0..9) branches in [B7T6], standing yields 30 Banker wins, 20 Player wins, and 10 ties without wraparound risk.

Cell B7T6 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 6 (6)
B7T6 Player StartB7T6 5th CardB7T6 Banker 7 ActionB7T6 10-Card SplitB7T6 Sample Result
[B7T6:P0] 6+4=0[B7T6:5th] +6(6) -> P=6[B7T6:Pat] B=7 stands at 7[B7T6:Split] 10B/0P/0T[B7T6:Cards] 5c (B)
[B7T6:P1] 10+A=1[B7T6:5th] +6(6) -> P=7[B7T6:Pat] B=7 stands at 7[B7T6:Split] 0B/0P/10T[B7T6:Cards] 5c (T)
[B7T6:P2] 8+4=2[B7T6:5th] +6(6) -> P=8[B7T6:Pat] B=7 stands at 7[B7T6:Split] 0B/10P/0T[B7T6:Cards] 5c (P)
[B7T6:P3] 10+3=3[B7T6:5th] +6(6) -> P=9[B7T6:Pat] B=7 stands at 7[B7T6:Split] 0B/10P/0T[B7T6:Cards] 5c (P)
[B7T6:P4] A+3=4[B7T6:5th] +6(6) -> P=0[B7T6:Pat] B=7 stands at 7[B7T6:Split] 10B/0P/0T[B7T6:Cards] 5c (B)
[B7T6:P5] 2+3=5[B7T6:5th] +6(6) -> P=1[B7T6:Pat] B=7 stands at 7[B7T6:Split] 10B/0P/0T[B7T6:Cards] 5c (B)
  • [B7T6-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 7 (2+5).
  • [B7T6-Step2] Confirm Player drew fifth-card 6 (value 6) onto a 0–5 start.
  • [B7T6-Step3] Execute BANKER_TABLEAU[7][6] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B7T6

How Cell B7T6 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B7T6], Banker 7 (2+5) never takes a sixth card, so 3-card Banker Dragon 7 is impossible while Player reaches 3-card 8 (Panda 8) whenever P=2 draws 6 (6).

Once [B7T6] resolves (30B/20P/10T across 60 branches), the winning side logs to the Big Road on shoe BBBPPPBBBB.

Table Reality Check

Myth vs. Truth

MythIn cell B7T6, the dealer checks the Player's 3-card sum (9) before acting on Banker 7.
TruthCell B7T6 inspects only the fifth card's face value (6 from 6), ordering Banker 7 to stands.
MythWinning cell B7T6 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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