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TABLEAU CELL [B0T2] · ENGINE VERIFIED

Banker 0 vs. Player Third Card 2 (B0T2): Why Banker Always Draws

In cell B0T2, a Banker holding two-card total 0 (10+K) faces a Player fifth card valued at 2 (2). Under BANKER_TABLEAU[0][2], the Banker DRAWS, resolving in 6 cards with a 27B / 27P / 6T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B0T2 Action
DRAW
B0T2 Card Count
6 Cards
B0T2 60-Branch B/P/T
27/27/6
Tableau Coordinates
B=0, P3=2
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Verified scoreboard paired with tableau cell B0T2 (Banker 0 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 2 has 3 beads. Column 1 has 3 beads. Same depth → red (=).

  1. Column 3 starts, so use Rule 1: compare Column 2 with Column 1, 1 column further back.
  2. Column 2 has 3 beads. Column 1 has 3 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

Small Road Mark #3

This bead is at Row 4. Column 1 stopped at Row 3, one row above → blue (≠).

  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 3, one row above → blue (≠).

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

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 5 goes down to Row 2, so use Rule 2: look 3 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.

Verified Reference Data

Key Facts & Table Specifications

Cell B0T2 Tableau Lookup
true (Mandatory 6th Card)

Verified via bankerShouldDraw(0, 2) === true on pair 10+K.

Cell B0T2 60-Branch Matrix Split
27 Banker / 27 Player / 6 Tie

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

Cell B0T2 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 B0T2 Standing Comparison
0W / 0T / 6L

How standing Banker 0 fares against the 6 Player 3-card totals for P3=2.

Cell B0T2 Sample Audition Hand
B(10+K=0) vs P3=2(2) -> DRAW

Sample sixth card A (1) verified through resolveHand().

COMBINATORIAL PROOF · CELL B0T2

Cell B0T2 Analysis: Banker 0 (10+K) Facing Fifth-Card 2 (Value 2)

Under [B0T2], Banker holds two-card total 0 (10+K) while Player draws fifth-card 2 (point value 2) onto an initial 0–5 total. Across those six legal Player starts, [B0T2] 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 [B0T2] sits inside the active draw window for Banker 0, the dealer deals a sixth card to 10+K: across all 60 (P0..P5 × sixth-card 0..9) combinations in [B0T2], Banker captures 27 wins, Player captures 27 wins, and 6 branches tie.

Cell B0T2 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 2 (2)
B0T2 Player StartB0T2 5th CardB0T2 Banker 0 ActionB0T2 10-Card SplitB0T2 Sample Result
[B0T2:P0] 10+K=0[B0T2:5th] +2(2) -> P=2[B0T2:6th] B=0 draws (+A->1)[B0T2:Split] 7B/2P/1T[B0T2:Cards] 6c (P)
[B0T2:P1] 7+4=1[B0T2:5th] +2(2) -> P=3[B0T2:6th] B=0 draws (+A->1)[B0T2:Split] 6B/3P/1T[B0T2:Cards] 6c (P)
[B0T2:P2] 10+2=2[B0T2:5th] +2(2) -> P=4[B0T2:6th] B=0 draws (+A->1)[B0T2:Split] 5B/4P/1T[B0T2:Cards] 6c (P)
[B0T2:P3] 9+4=3[B0T2:5th] +2(2) -> P=5[B0T2:6th] B=0 draws (+A->1)[B0T2:Split] 4B/5P/1T[B0T2:Cards] 6c (P)
[B0T2:P4] 2+2=4[B0T2:5th] +2(2) -> P=6[B0T2:6th] B=0 draws (+A->1)[B0T2:Split] 3B/6P/1T[B0T2:Cards] 6c (P)
[B0T2:P5] A+4=5[B0T2:5th] +2(2) -> P=7[B0T2:6th] B=0 draws (+A->1)[B0T2:Split] 2B/7P/1T[B0T2:Cards] 6c (P)
  • [B0T2-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 0 (10+K).
  • [B0T2-Step2] Confirm Player drew fifth-card 2 (value 2) onto a 0–5 start.
  • [B0T2-Step3] Execute BANKER_TABLEAU[0][2] = true (DRAW at 6 cards).
FLOOR PROCEDURE & SIDE BETS · B0T2

How Cell B0T2 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 6-card cell [B0T2], Banker 0 (10+K) can reach a 3-card 7 (Dragon 7) by drawing rank 7 or a 3-card 6 (Super 6) by drawing rank 6 after Player's 2.

Once [B0T2] resolves (27B/27P/6T across 60 branches), the winning side logs to the Big Road on shoe BBBPPPBBBB.

Table Reality Check

Myth vs. Truth

MythIn cell B0T2, the dealer checks the Player's 3-card sum (5) before acting on Banker 0.
TruthCell B0T2 inspects only the fifth card's face value (2 from 2), ordering Banker 0 to draws.
MythWinning cell B0T2 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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