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TABLEAU CELL [B2T3] · ENGINE VERIFIED

Banker 2 vs. Player Third Card 3 (B2T3): Why Banker Always Draws

In cell B2T3, a Banker holding two-card total 2 (8+4) faces a Player fifth card valued at 3 (3). Under BANKER_TABLEAU[2][3], the Banker DRAWS, resolving in 6 cards with a 21B / 33P / 6T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B2T3 Action
DRAW
B2T3 Card Count
6 Cards
B2T3 60-Branch B/P/T
21/33/6
Tableau Coordinates
B=2, 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 B2T3 (Banker 2 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 B2T3 Tableau Lookup
true (Mandatory 6th Card)

Verified via bankerShouldDraw(2, 3) === true on pair 8+4.

Cell B2T3 60-Branch Matrix Split
21 Banker / 33 Player / 6 Tie

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

Cell B2T3 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 B2T3 Standing Comparison
0W / 0T / 6L

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

Cell B2T3 Sample Audition Hand
B(8+4=2) vs P3=3(3) -> DRAW

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

COMBINATORIAL PROOF · CELL B2T3

Cell B2T3 Analysis: Banker 2 (8+4) Facing Fifth-Card 3 (Value 3)

Under [B2T3], Banker holds two-card total 2 (8+4) while Player draws fifth-card 3 (point value 3) onto an initial 0–5 total. Across those six legal Player starts, [B2T3] 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 [B2T3] sits inside the active draw window for Banker 2, the dealer deals a sixth card to 8+4: across all 60 (P0..P5 × sixth-card 0..9) combinations in [B2T3], Banker captures 21 wins, Player captures 33 wins, and 6 branches tie.

Cell B2T3 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 3 (3)
B2T3 Player StartB2T3 5th CardB2T3 Banker 2 ActionB2T3 10-Card SplitB2T3 Sample Result
[B2T3:P0] 10+K=0[B2T3:5th] +3(3) -> P=3[B2T3:6th] B=2 draws (+10->2)[B2T3:Split] 6B/3P/1T[B2T3:Cards] 6c (P)
[B2T3:P1] 7+4=1[B2T3:5th] +3(3) -> P=4[B2T3:6th] B=2 draws (+10->2)[B2T3:Split] 5B/4P/1T[B2T3:Cards] 6c (P)
[B2T3:P2] 10+2=2[B2T3:5th] +3(3) -> P=5[B2T3:6th] B=2 draws (+10->2)[B2T3:Split] 4B/5P/1T[B2T3:Cards] 6c (P)
[B2T3:P3] 9+4=3[B2T3:5th] +3(3) -> P=6[B2T3:6th] B=2 draws (+10->2)[B2T3:Split] 3B/6P/1T[B2T3:Cards] 6c (P)
[B2T3:P4] 2+2=4[B2T3:5th] +3(3) -> P=7[B2T3:6th] B=2 draws (+10->2)[B2T3:Split] 2B/7P/1T[B2T3:Cards] 6c (P)
[B2T3:P5] A+4=5[B2T3:5th] +3(3) -> P=8[B2T3:6th] B=2 draws (+10->2)[B2T3:Split] 1B/8P/1T[B2T3:Cards] 6c (P)
  • [B2T3-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 2 (8+4).
  • [B2T3-Step2] Confirm Player drew fifth-card 3 (value 3) onto a 0–5 start.
  • [B2T3-Step3] Execute BANKER_TABLEAU[2][3] = true (DRAW at 6 cards).
FLOOR PROCEDURE & SIDE BETS · B2T3

How Cell B2T3 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 6-card cell [B2T3], Banker 2 (8+4) can reach a 3-card 7 (Dragon 7) by drawing rank 5 or a 3-card 6 (Super 6) by drawing rank 4 after Player's 3.

Once [B2T3] resolves (21B/33P/6T across 60 branches), the winning side logs to the Big Road on shoe PPBBBBPPBB.

Table Reality Check

Myth vs. Truth

MythIn cell B2T3, the dealer checks the Player's 3-card sum (6) before acting on Banker 2.
TruthCell B2T3 inspects only the fifth card's face value (3 from 3), ordering Banker 2 to draws.
MythWinning cell B2T3 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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