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TABLEAU CELL [B2T0] · ENGINE VERIFIED

Banker 2 vs. Player Third Card 0 (B2T0): Why Banker Always Draws

In cell B2T0, a Banker holding two-card total 2 (10+2) faces a Player fifth card valued at 0 (10). Under BANKER_TABLEAU[2][0], the Banker DRAWS, resolving in 6 cards with a 39B / 15P / 6T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B2T0 Action
DRAW
B2T0 Card Count
6 Cards
B2T0 60-Branch B/P/T
39/15/6
Tableau Coordinates
B=2, P3=0
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Verified scoreboard paired with tableau cell B2T0 (Banker 2 vs Player 3rd card 0).

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 4 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 3, 1 column further back.
  2. Column 4 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 3.

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 B2T0 Tableau Lookup
true (Mandatory 6th Card)

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

Cell B2T0 60-Branch Matrix Split
39 Banker / 15 Player / 6 Tie

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

Cell B2T0 Resulting Player Totals
0+0=0, 1+0=1, 2+0=2, 3+0=3, 4+0=4, 5+0=5

Three-card Player totals produced when fifth card 10 (0) lands on P0..P5.

Cell B2T0 Standing Comparison
2W / 1T / 3L

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

Cell B2T0 Sample Audition Hand
B(10+2=2) vs P3=10(0) -> DRAW

Sample sixth card 7 (7) verified through resolveHand().

COMBINATORIAL PROOF · CELL B2T0

Cell B2T0 Analysis: Banker 2 (10+2) Facing Fifth-Card 10 (Value 0)

Under [B2T0], Banker holds two-card total 2 (10+2) while Player draws fifth-card 10 (point value 0) onto an initial 0–5 total. Across those six legal Player starts, [B2T0] produces three-card Player totals of P0+0->0, P1+0->1, P2+0->2, P3+0->3, P4+0->4, P5+0->5.

Because [B2T0] sits inside the active draw window for Banker 2, the dealer deals a sixth card to 10+2: across all 60 (P0..P5 × sixth-card 0..9) combinations in [B2T0], Banker captures 39 wins, Player captures 15 wins, and 6 branches tie.

Cell B2T0 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 10 (0)
B2T0 Player StartB2T0 5th CardB2T0 Banker 2 ActionB2T0 10-Card SplitB2T0 Sample Result
[B2T0:P0] 10+K=0[B2T0:5th] +10(0) -> P=0[B2T0:6th] B=2 draws (+7->9)[B2T0:Split] 9B/0P/1T[B2T0:Cards] 6c (B)
[B2T0:P1] 7+4=1[B2T0:5th] +10(0) -> P=1[B2T0:6th] B=2 draws (+7->9)[B2T0:Split] 8B/1P/1T[B2T0:Cards] 6c (B)
[B2T0:P2] 10+2=2[B2T0:5th] +10(0) -> P=2[B2T0:6th] B=2 draws (+7->9)[B2T0:Split] 7B/2P/1T[B2T0:Cards] 6c (B)
[B2T0:P3] 9+4=3[B2T0:5th] +10(0) -> P=3[B2T0:6th] B=2 draws (+7->9)[B2T0:Split] 6B/3P/1T[B2T0:Cards] 6c (B)
[B2T0:P4] 2+2=4[B2T0:5th] +10(0) -> P=4[B2T0:6th] B=2 draws (+7->9)[B2T0:Split] 5B/4P/1T[B2T0:Cards] 6c (B)
[B2T0:P5] A+4=5[B2T0:5th] +10(0) -> P=5[B2T0:6th] B=2 draws (+7->9)[B2T0:Split] 4B/5P/1T[B2T0:Cards] 6c (B)
  • [B2T0-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 2 (10+2).
  • [B2T0-Step2] Confirm Player drew fifth-card 10 (value 0) onto a 0–5 start.
  • [B2T0-Step3] Execute BANKER_TABLEAU[2][0] = true (DRAW at 6 cards).
FLOOR PROCEDURE & SIDE BETS · B2T0

How Cell B2T0 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 6-card cell [B2T0], Banker 2 (10+2) 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 10.

Once [B2T0] resolves (39B/15P/6T across 60 branches), the winning side logs to the Big Road on shoe BBBBPBPBPP.

Table Reality Check

Myth vs. Truth

MythIn cell B2T0, the dealer checks the Player's 3-card sum (3) before acting on Banker 2.
TruthCell B2T0 inspects only the fifth card's face value (0 from 10), ordering Banker 2 to draws.
MythWinning cell B2T0 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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