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TABLEAU CELL [B7T8] · ENGINE VERIFIED

Banker 7 vs. Player Third Card 8 (B7T8): Why Banker Always Stands

In cell B7T8, a Banker holding two-card total 7 (2+5) faces a Player fifth card valued at 8 (8). Under BANKER_TABLEAU[7][8], the Banker STANDS, resolving in 5 cards with a 40B / 20P / 0T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B7T8 Action
STAND
B7T8 Card Count
5 Cards
B7T8 60-Branch B/P/T
40/20/0
Tableau Coordinates
B=7, P3=8
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 B7T8 (Banker 7 vs Player 3rd card 8).

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 B7T8 Tableau Lookup
false (Mandatory 5-Card Stand)

Verified via bankerShouldDraw(7, 8) === false on pair 2+5.

Cell B7T8 60-Branch Matrix Split
40 Banker / 20 Player / 0 Tie

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

Cell B7T8 Resulting Player Totals
0+8=8, 1+8=9, 2+8=0, 3+8=1, 4+8=2, 5+8=3

Three-card Player totals produced when fifth card 8 (8) lands on P0..P5.

Cell B7T8 Standing Comparison
4W / 0T / 2L

How standing Banker 7 fares against the 6 Player 3-card totals for P3=8.

Cell B7T8 Sample Audition Hand
B(2+5=7) vs P3=8(8) -> STAND

Sample sixth card 10 (0) verified through resolveHand().

COMBINATORIAL PROOF · CELL B7T8

Cell B7T8 Analysis: Banker 7 (2+5) Facing Fifth-Card 8 (Value 8)

Under [B7T8], Banker holds two-card total 7 (2+5) while Player draws fifth-card 8 (point value 8) onto an initial 0–5 total. Across those six legal Player starts, [B7T8] produces three-card Player totals of P0+8->8, P1+8->9, P2+8->0, P3+8->1, P4+8->2, P5+8->3.

Because [B7T8] 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 [B7T8], standing yields 40 Banker wins, 20 Player wins, and 0 ties without wraparound risk.

Cell B7T8 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 8 (8)
B7T8 Player StartB7T8 5th CardB7T8 Banker 7 ActionB7T8 10-Card SplitB7T8 Sample Result
[B7T8:P0] 6+4=0[B7T8:5th] +8(8) -> P=8[B7T8:Pat] B=7 stands at 7[B7T8:Split] 0B/10P/0T[B7T8:Cards] 5c (P)
[B7T8:P1] 10+A=1[B7T8:5th] +8(8) -> P=9[B7T8:Pat] B=7 stands at 7[B7T8:Split] 0B/10P/0T[B7T8:Cards] 5c (P)
[B7T8:P2] 8+4=2[B7T8:5th] +8(8) -> P=0[B7T8:Pat] B=7 stands at 7[B7T8:Split] 10B/0P/0T[B7T8:Cards] 5c (B)
[B7T8:P3] 10+3=3[B7T8:5th] +8(8) -> P=1[B7T8:Pat] B=7 stands at 7[B7T8:Split] 10B/0P/0T[B7T8:Cards] 5c (B)
[B7T8:P4] A+3=4[B7T8:5th] +8(8) -> P=2[B7T8:Pat] B=7 stands at 7[B7T8:Split] 10B/0P/0T[B7T8:Cards] 5c (B)
[B7T8:P5] 2+3=5[B7T8:5th] +8(8) -> P=3[B7T8:Pat] B=7 stands at 7[B7T8:Split] 10B/0P/0T[B7T8:Cards] 5c (B)
  • [B7T8-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 7 (2+5).
  • [B7T8-Step2] Confirm Player drew fifth-card 8 (value 8) onto a 0–5 start.
  • [B7T8-Step3] Execute BANKER_TABLEAU[7][8] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B7T8

How Cell B7T8 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B7T8], 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=0 draws 8 (8).

Once [B7T8] resolves (40B/20P/0T across 60 branches), the winning side logs to the Big Road on shoe PBBBBPBPBB.

Table Reality Check

Myth vs. Truth

MythIn cell B7T8, the dealer checks the Player's 3-card sum (1) before acting on Banker 7.
TruthCell B7T8 inspects only the fifth card's face value (8 from 8), ordering Banker 7 to stands.
MythWinning cell B7T8 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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