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TABLEAU CELL [B7T3] · ENGINE VERIFIED

Banker 7 vs. Player Third Card 3 (B7T3): Why Banker Always Stands

In cell B7T3, a Banker holding two-card total 7 (3+4) faces a Player fifth card valued at 3 (3). Under BANKER_TABLEAU[7][3], the Banker STANDS, resolving in 5 cards with a 40B / 10P / 10T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B7T3 Action
STAND
B7T3 Card Count
5 Cards
B7T3 60-Branch B/P/T
40/10/10
Tableau Coordinates
B=7, P3=3
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Verified scoreboard paired with tableau cell B7T3 (Banker 7 vs Player 3rd card 3).

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 2, 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 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.

Small Road Mark #3

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

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 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.

Cockroach Pig Mark #3

Column 5 has 1 bead. Column 2 has 4 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 4 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Cell B7T3 Tableau Lookup
false (Mandatory 5-Card Stand)

Verified via bankerShouldDraw(7, 3) === false on pair 3+4.

Cell B7T3 60-Branch Matrix Split
40 Banker / 10 Player / 10 Tie

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

Cell B7T3 Resulting Player Totals
0+3=3, 1+3=4, 2+3=5, 3+3=6, 4+3=7, 5+3=8

Three-card Player totals produced when fifth card 3 (3) lands on P0..P5.

Cell B7T3 Standing Comparison
4W / 1T / 1L

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

Cell B7T3 Sample Audition Hand
B(3+4=7) vs P3=3(3) -> STAND

Sample sixth card 5 (5) verified through resolveHand().

COMBINATORIAL PROOF · CELL B7T3

Cell B7T3 Analysis: Banker 7 (3+4) Facing Fifth-Card 3 (Value 3)

Under [B7T3], Banker holds two-card total 7 (3+4) while Player draws fifth-card 3 (point value 3) onto an initial 0–5 total. Across those six legal Player starts, [B7T3] produces three-card Player totals of P0+3->3, P1+3->4, P2+3->5, P3+3->6, P4+3->7, P5+3->8.

Because [B7T3] falls outside the draw window for Banker 7, the dealer stands pat on 3+4 (7) at 5 cards: across the 60 (P0..P5 × unpulled 6th card 0..9) branches in [B7T3], standing yields 40 Banker wins, 10 Player wins, and 10 ties without wraparound risk.

Cell B7T3 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 3 (3)
B7T3 Player StartB7T3 5th CardB7T3 Banker 7 ActionB7T3 10-Card SplitB7T3 Sample Result
[B7T3:P0] 6+4=0[B7T3:5th] +3(3) -> P=3[B7T3:Pat] B=7 stands at 7[B7T3:Split] 10B/0P/0T[B7T3:Cards] 5c (B)
[B7T3:P1] 10+A=1[B7T3:5th] +3(3) -> P=4[B7T3:Pat] B=7 stands at 7[B7T3:Split] 10B/0P/0T[B7T3:Cards] 5c (B)
[B7T3:P2] 8+4=2[B7T3:5th] +3(3) -> P=5[B7T3:Pat] B=7 stands at 7[B7T3:Split] 10B/0P/0T[B7T3:Cards] 5c (B)
[B7T3:P3] 10+3=3[B7T3:5th] +3(3) -> P=6[B7T3:Pat] B=7 stands at 7[B7T3:Split] 10B/0P/0T[B7T3:Cards] 5c (B)
[B7T3:P4] A+3=4[B7T3:5th] +3(3) -> P=7[B7T3:Pat] B=7 stands at 7[B7T3:Split] 0B/0P/10T[B7T3:Cards] 5c (T)
[B7T3:P5] 2+3=5[B7T3:5th] +3(3) -> P=8[B7T3:Pat] B=7 stands at 7[B7T3:Split] 0B/10P/0T[B7T3:Cards] 5c (P)
  • [B7T3-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 7 (3+4).
  • [B7T3-Step2] Confirm Player drew fifth-card 3 (value 3) onto a 0–5 start.
  • [B7T3-Step3] Execute BANKER_TABLEAU[7][3] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B7T3

How Cell B7T3 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B7T3], Banker 7 (3+4) never takes a sixth card, so 3-card Banker Dragon 7 is impossible while Player reaches 3-card 8 (Panda 8) whenever P=5 draws 3 (3).

Once [B7T3] resolves (40B/10P/10T across 60 branches), the winning side logs to the Big Road on shoe PPBBBBPPBB.

Table Reality Check

Myth vs. Truth

MythIn cell B7T3, the dealer checks the Player's 3-card sum (6) before acting on Banker 7.
TruthCell B7T3 inspects only the fifth card's face value (3 from 3), ordering Banker 7 to stands.
MythWinning cell B7T3 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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