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TABLEAU CELL [B1T1] · ENGINE VERIFIED

Banker 1 vs. Player Third Card 1 (B1T1): Why Banker Always Draws

In cell B1T1, a Banker holding two-card total 1 (10+A) faces a Player fifth card valued at 1 (A). Under BANKER_TABLEAU[1][1], the Banker DRAWS, resolving in 6 cards with a 33B / 21P / 6T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B1T1 Action
DRAW
B1T1 Card Count
6 Cards
B1T1 60-Branch B/P/T
33/21/6
Tableau Coordinates
B=1, P3=1
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 B1T1 (Banker 1 vs Player 3rd card 1).

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 B1T1 Tableau Lookup
true (Mandatory 6th Card)

Verified via bankerShouldDraw(1, 1) === true on pair 10+A.

Cell B1T1 60-Branch Matrix Split
33 Banker / 21 Player / 6 Tie

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

Cell B1T1 Resulting Player Totals
0+1=1, 1+1=2, 2+1=3, 3+1=4, 4+1=5, 5+1=6

Three-card Player totals produced when fifth card A (1) lands on P0..P5.

Cell B1T1 Standing Comparison
0W / 1T / 5L

How standing Banker 1 fares against the 6 Player 3-card totals for P3=1.

Cell B1T1 Sample Audition Hand
B(10+A=1) vs P3=A(1) -> DRAW

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

COMBINATORIAL PROOF · CELL B1T1

Cell B1T1 Analysis: Banker 1 (10+A) Facing Fifth-Card A (Value 1)

Under [B1T1], Banker holds two-card total 1 (10+A) while Player draws fifth-card A (point value 1) onto an initial 0–5 total. Across those six legal Player starts, [B1T1] produces three-card Player totals of P0+1->1, P1+1->2, P2+1->3, P3+1->4, P4+1->5, P5+1->6.

Because [B1T1] sits inside the active draw window for Banker 1, the dealer deals a sixth card to 10+A: across all 60 (P0..P5 × sixth-card 0..9) combinations in [B1T1], Banker captures 33 wins, Player captures 21 wins, and 6 branches tie.

Cell B1T1 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card A (1)
B1T1 Player StartB1T1 5th CardB1T1 Banker 1 ActionB1T1 10-Card SplitB1T1 Sample Result
[B1T1:P0] 6+4=0[B1T1:5th] +A(1) -> P=1[B1T1:6th] B=1 draws (+9->0)[B1T1:Split] 8B/1P/1T[B1T1:Cards] 6c (P)
[B1T1:P1] 10+A=1[B1T1:5th] +A(1) -> P=2[B1T1:6th] B=1 draws (+9->0)[B1T1:Split] 7B/2P/1T[B1T1:Cards] 6c (P)
[B1T1:P2] 8+4=2[B1T1:5th] +A(1) -> P=3[B1T1:6th] B=1 draws (+9->0)[B1T1:Split] 6B/3P/1T[B1T1:Cards] 6c (P)
[B1T1:P3] 10+3=3[B1T1:5th] +A(1) -> P=4[B1T1:6th] B=1 draws (+9->0)[B1T1:Split] 5B/4P/1T[B1T1:Cards] 6c (P)
[B1T1:P4] A+3=4[B1T1:5th] +A(1) -> P=5[B1T1:6th] B=1 draws (+9->0)[B1T1:Split] 4B/5P/1T[B1T1:Cards] 6c (P)
[B1T1:P5] 2+3=5[B1T1:5th] +A(1) -> P=6[B1T1:6th] B=1 draws (+9->0)[B1T1:Split] 3B/6P/1T[B1T1:Cards] 6c (P)
  • [B1T1-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 1 (10+A).
  • [B1T1-Step2] Confirm Player drew fifth-card A (value 1) onto a 0–5 start.
  • [B1T1-Step3] Execute BANKER_TABLEAU[1][1] = true (DRAW at 6 cards).
FLOOR PROCEDURE & SIDE BETS · B1T1

How Cell B1T1 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 6-card cell [B1T1], Banker 1 (10+A) can reach a 3-card 7 (Dragon 7) by drawing rank 6 or a 3-card 6 (Super 6) by drawing rank 5 after Player's A.

Once [B1T1] resolves (33B/21P/6T across 60 branches), the winning side logs to the Big Road on shoe PPBBBBPPBB.

Table Reality Check

Myth vs. Truth

MythIn cell B1T1, the dealer checks the Player's 3-card sum (4) before acting on Banker 1.
TruthCell B1T1 inspects only the fifth card's face value (1 from A), ordering Banker 1 to draws.
MythWinning cell B1T1 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.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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