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TABLEAU CELL [B7T2] · ENGINE VERIFIED

Banker 7 vs. Player Third Card 2 (B7T2): Why Banker Always Stands

In cell B7T2, a Banker holding two-card total 7 (2+5) faces a Player fifth card valued at 2 (2). Under BANKER_TABLEAU[7][2], the Banker STANDS, resolving in 5 cards with a 50B / 0P / 10T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B7T2 Action
STAND
B7T2 Card Count
5 Cards
B7T2 60-Branch B/P/T
50/0/10
Tableau Coordinates
B=7, P3=2
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Verified scoreboard paired with tableau cell B7T2 (Banker 7 vs Player 3rd card 2).

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

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

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 2.

Small Road Mark #3

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

  1. Column 4 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 2.
  2. Column 2 stopped at Row 2, one row above → blue (≠).

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 4 has 3 beads. Column 1 has 6 beads. Different depth → blue (≠).

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

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

Cell B7T2 Tableau Lookup
false (Mandatory 5-Card Stand)

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

Cell B7T2 60-Branch Matrix Split
50 Banker / 0 Player / 10 Tie

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

Cell B7T2 Resulting Player Totals
0+2=2, 1+2=3, 2+2=4, 3+2=5, 4+2=6, 5+2=7

Three-card Player totals produced when fifth card 2 (2) lands on P0..P5.

Cell B7T2 Standing Comparison
5W / 1T / 0L

How standing Banker 7 fares against the 6 Player 3-card totals for P3=2.

Cell B7T2 Sample Audition Hand
B(2+5=7) vs P3=2(2) -> STAND

Sample sixth card 4 (4) verified through resolveHand().

COMBINATORIAL PROOF · CELL B7T2

Cell B7T2 Analysis: Banker 7 (2+5) Facing Fifth-Card 2 (Value 2)

Under [B7T2], Banker holds two-card total 7 (2+5) while Player draws fifth-card 2 (point value 2) onto an initial 0–5 total. Across those six legal Player starts, [B7T2] produces three-card Player totals of P0+2->2, P1+2->3, P2+2->4, P3+2->5, P4+2->6, P5+2->7.

Because [B7T2] 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 [B7T2], standing yields 50 Banker wins, 0 Player wins, and 10 ties without wraparound risk.

Cell B7T2 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 2 (2)
B7T2 Player StartB7T2 5th CardB7T2 Banker 7 ActionB7T2 10-Card SplitB7T2 Sample Result
[B7T2:P0] 6+4=0[B7T2:5th] +2(2) -> P=2[B7T2:Pat] B=7 stands at 7[B7T2:Split] 10B/0P/0T[B7T2:Cards] 5c (B)
[B7T2:P1] 10+A=1[B7T2:5th] +2(2) -> P=3[B7T2:Pat] B=7 stands at 7[B7T2:Split] 10B/0P/0T[B7T2:Cards] 5c (B)
[B7T2:P2] 8+4=2[B7T2:5th] +2(2) -> P=4[B7T2:Pat] B=7 stands at 7[B7T2:Split] 10B/0P/0T[B7T2:Cards] 5c (B)
[B7T2:P3] 10+3=3[B7T2:5th] +2(2) -> P=5[B7T2:Pat] B=7 stands at 7[B7T2:Split] 10B/0P/0T[B7T2:Cards] 5c (B)
[B7T2:P4] A+3=4[B7T2:5th] +2(2) -> P=6[B7T2:Pat] B=7 stands at 7[B7T2:Split] 10B/0P/0T[B7T2:Cards] 5c (B)
[B7T2:P5] 2+3=5[B7T2:5th] +2(2) -> P=7[B7T2:Pat] B=7 stands at 7[B7T2:Split] 0B/0P/10T[B7T2:Cards] 5c (T)
  • [B7T2-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 7 (2+5).
  • [B7T2-Step2] Confirm Player drew fifth-card 2 (value 2) onto a 0–5 start.
  • [B7T2-Step3] Execute BANKER_TABLEAU[7][2] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B7T2

How Cell B7T2 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B7T2], 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=6 draws 2 (2).

Once [B7T2] resolves (50B/0P/10T across 60 branches), the winning side logs to the Big Road on shoe BBBBBBPPBP.

Table Reality Check

Myth vs. Truth

MythIn cell B7T2, the dealer checks the Player's 3-card sum (5) before acting on Banker 7.
TruthCell B7T2 inspects only the fifth card's face value (2 from 2), ordering Banker 7 to stands.
MythWinning cell B7T2 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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