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TABLEAU CELL [B7T7] · ENGINE VERIFIED

Banker 7 vs. Player Third Card 7 (B7T7): Why Banker Always Stands

In cell B7T7, a Banker holding two-card total 7 (3+4) faces a Player fifth card valued at 7 (7). Under BANKER_TABLEAU[7][7], the Banker STANDS, resolving in 5 cards with a 30B / 20P / 10T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B7T7 Action
STAND
B7T7 Card Count
5 Cards
B7T7 60-Branch B/P/T
30/20/10
Tableau Coordinates
B=7, P3=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 P B P P P B B B P B B P P B B B B P B P B B P P P B
Big Eye Boy ≠ ≠ = = ≠ = ≠ ≠ ≠ = ≠ = = = ≠ ≠ ≠ = = = ≠ = ≠ ≠ = = ≠ ≠ = ≠ ≠
Small Road = ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ ≠ = ≠ ≠ = ≠ ≠ ≠ = ≠ = ≠ ≠ ≠ = ≠ ≠ ≠ = ≠
Cockroach Pig = = = = = ≠ = ≠ ≠ = = ≠ = ≠ ≠ = = ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠

Verified scoreboard paired with tableau cell B7T7 (Banker 7 vs Player 3rd card 7).

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 5 has 1 bead. Column 2 has 1 bead. Same depth → red (=).

  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 1 bead. Same depth → red (=).

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 B7T7 Tableau Lookup
false (Mandatory 5-Card Stand)

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

Cell B7T7 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 B7T7 Resulting Player Totals
0+7=7, 1+7=8, 2+7=9, 3+7=0, 4+7=1, 5+7=2

Three-card Player totals produced when fifth card 7 (7) lands on P0..P5.

Cell B7T7 Standing Comparison
3W / 1T / 2L

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

Cell B7T7 Sample Audition Hand
B(3+4=7) vs P3=7(7) -> STAND

Sample sixth card 9 (9) verified through resolveHand().

COMBINATORIAL PROOF · CELL B7T7

Cell B7T7 Analysis: Banker 7 (3+4) Facing Fifth-Card 7 (Value 7)

Under [B7T7], Banker holds two-card total 7 (3+4) while Player draws fifth-card 7 (point value 7) onto an initial 0–5 total. Across those six legal Player starts, [B7T7] produces three-card Player totals of P0+7->7, P1+7->8, P2+7->9, P3+7->0, P4+7->1, P5+7->2.

Because [B7T7] 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 [B7T7], standing yields 30 Banker wins, 20 Player wins, and 10 ties without wraparound risk.

Cell B7T7 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 7 (7)
B7T7 Player StartB7T7 5th CardB7T7 Banker 7 ActionB7T7 10-Card SplitB7T7 Sample Result
[B7T7:P0] 6+4=0[B7T7:5th] +7(7) -> P=7[B7T7:Pat] B=7 stands at 7[B7T7:Split] 0B/0P/10T[B7T7:Cards] 5c (T)
[B7T7:P1] 10+A=1[B7T7:5th] +7(7) -> P=8[B7T7:Pat] B=7 stands at 7[B7T7:Split] 0B/10P/0T[B7T7:Cards] 5c (P)
[B7T7:P2] 8+4=2[B7T7:5th] +7(7) -> P=9[B7T7:Pat] B=7 stands at 7[B7T7:Split] 0B/10P/0T[B7T7:Cards] 5c (P)
[B7T7:P3] 10+3=3[B7T7:5th] +7(7) -> P=0[B7T7:Pat] B=7 stands at 7[B7T7:Split] 10B/0P/0T[B7T7:Cards] 5c (B)
[B7T7:P4] A+3=4[B7T7:5th] +7(7) -> P=1[B7T7:Pat] B=7 stands at 7[B7T7:Split] 10B/0P/0T[B7T7:Cards] 5c (B)
[B7T7:P5] 2+3=5[B7T7:5th] +7(7) -> P=2[B7T7:Pat] B=7 stands at 7[B7T7:Split] 10B/0P/0T[B7T7:Cards] 5c (B)
  • [B7T7-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 7 (3+4).
  • [B7T7-Step2] Confirm Player drew fifth-card 7 (value 7) onto a 0–5 start.
  • [B7T7-Step3] Execute BANKER_TABLEAU[7][7] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B7T7

How Cell B7T7 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B7T7], 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=1 draws 7 (7).

Once [B7T7] resolves (30B/20P/10T across 60 branches), the winning side logs to the Big Road on shoe BBPBBBBPPB.

Table Reality Check

Myth vs. Truth

MythIn cell B7T7, the dealer checks the Player's 3-card sum (0) before acting on Banker 7.
TruthCell B7T7 inspects only the fifth card's face value (7 from 7), ordering Banker 7 to stands.
MythWinning cell B7T7 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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