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TABLEAU CELL [B0T9] · ENGINE VERIFIED

Banker 0 vs. Player Third Card 9 (B0T9): Why Banker Always Draws

In cell B0T9, a Banker holding two-card total 0 (6+4) faces a Player fifth card valued at 9 (9). Under BANKER_TABLEAU[0][9], the Banker DRAWS, resolving in 6 cards with a 35B / 19P / 6T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B0T9 Action
DRAW
B0T9 Card Count
6 Cards
B0T9 60-Branch B/P/T
35/19/6
Tableau Coordinates
B=0, P3=9
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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Big Road B B P P P B B B B P B P B B P P P B B P B B B B P P B P P P B B B P
Big Eye Boy = ≠ ≠ = = ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ = ≠ ≠ ≠ = = ≠ = ≠ ≠ ≠ = ≠ = = =
Small Road = ≠ = ≠ ≠ ≠ = ≠ ≠ ≠ = ≠ = = ≠ = ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ ≠ = ≠
Cockroach Pig ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ ≠ ≠ = = ≠ ≠ = = = = = ≠ = ≠ ≠

Verified scoreboard paired with tableau cell B0T9 (Banker 0 vs Player 3rd card 9).

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 2 beads. Different depth → blue (≠).

  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 2 beads. Different depth → blue (≠).

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 2, more than one row above → red (=).

  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 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.

Cockroach Pig Mark #3

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

  1. Column 7 starts, so use Rule 1: compare Column 6 with Column 3, 3 columns further back.
  2. Column 6 has 1 bead. Column 3 has 4 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 6, the one that just finished, with Column 3.

Verified Reference Data

Key Facts & Table Specifications

Cell B0T9 Tableau Lookup
true (Mandatory 6th Card)

Verified via bankerShouldDraw(0, 9) === true on pair 6+4.

Cell B0T9 60-Branch Matrix Split
35 Banker / 19 Player / 6 Tie

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

Cell B0T9 Resulting Player Totals
0+9=9, 1+9=0, 2+9=1, 3+9=2, 4+9=3, 5+9=4

Three-card Player totals produced when fifth card 9 (9) lands on P0..P5.

Cell B0T9 Standing Comparison
0W / 1T / 5L

How standing Banker 0 fares against the 6 Player 3-card totals for P3=9.

Cell B0T9 Sample Audition Hand
B(6+4=0) vs P3=9(9) -> DRAW

Sample sixth card 8 (8) verified through resolveHand().

COMBINATORIAL PROOF · CELL B0T9

Cell B0T9 Analysis: Banker 0 (6+4) Facing Fifth-Card 9 (Value 9)

Under [B0T9], Banker holds two-card total 0 (6+4) while Player draws fifth-card 9 (point value 9) onto an initial 0–5 total. Across those six legal Player starts, [B0T9] produces three-card Player totals of P0+9->9, P1+9->0, P2+9->1, P3+9->2, P4+9->3, P5+9->4.

Because [B0T9] sits inside the active draw window for Banker 0, the dealer deals a sixth card to 6+4: across all 60 (P0..P5 × sixth-card 0..9) combinations in [B0T9], Banker captures 35 wins, Player captures 19 wins, and 6 branches tie.

Cell B0T9 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 9 (9)
B0T9 Player StartB0T9 5th CardB0T9 Banker 0 ActionB0T9 10-Card SplitB0T9 Sample Result
[B0T9:P0] 10+K=0[B0T9:5th] +9(9) -> P=9[B0T9:6th] B=0 draws (+8->8)[B0T9:Split] 0B/9P/1T[B0T9:Cards] 6c (P)
[B0T9:P1] 7+4=1[B0T9:5th] +9(9) -> P=0[B0T9:6th] B=0 draws (+8->8)[B0T9:Split] 9B/0P/1T[B0T9:Cards] 6c (B)
[B0T9:P2] 10+2=2[B0T9:5th] +9(9) -> P=1[B0T9:6th] B=0 draws (+8->8)[B0T9:Split] 8B/1P/1T[B0T9:Cards] 6c (B)
[B0T9:P3] 9+4=3[B0T9:5th] +9(9) -> P=2[B0T9:6th] B=0 draws (+8->8)[B0T9:Split] 7B/2P/1T[B0T9:Cards] 6c (B)
[B0T9:P4] 2+2=4[B0T9:5th] +9(9) -> P=3[B0T9:6th] B=0 draws (+8->8)[B0T9:Split] 6B/3P/1T[B0T9:Cards] 6c (B)
[B0T9:P5] A+4=5[B0T9:5th] +9(9) -> P=4[B0T9:6th] B=0 draws (+8->8)[B0T9:Split] 5B/4P/1T[B0T9:Cards] 6c (B)
  • [B0T9-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 0 (6+4).
  • [B0T9-Step2] Confirm Player drew fifth-card 9 (value 9) onto a 0–5 start.
  • [B0T9-Step3] Execute BANKER_TABLEAU[0][9] = true (DRAW at 6 cards).
FLOOR PROCEDURE & SIDE BETS · B0T9

How Cell B0T9 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 6-card cell [B0T9], Banker 0 (6+4) 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 9.

Once [B0T9] resolves (35B/19P/6T across 60 branches), the winning side logs to the Big Road on shoe BBPPPBBBBP.

Table Reality Check

Myth vs. Truth

MythIn cell B0T9, the dealer checks the Player's 3-card sum (2) before acting on Banker 0.
TruthCell B0T9 inspects only the fifth card's face value (9 from 9), ordering Banker 0 to draws.
MythWinning cell B0T9 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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