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TABLEAU CELL [B5T6] · ENGINE VERIFIED

Banker 5 vs. Player Third Card 6 (B5T6): Why Banker Always Draws

In cell B5T6, a Banker holding two-card total 5 (A+4) faces a Player fifth card valued at 6 (6). Under BANKER_TABLEAU[5][6], the Banker DRAWS, resolving in 6 cards with a 23B / 31P / 6T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B5T6 Action
DRAW
B5T6 Card Count
6 Cards
B5T6 60-Branch B/P/T
23/31/6
Tableau Coordinates
B=5, P3=6
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Verified scoreboard paired with tableau cell B5T6 (Banker 5 vs Player 3rd card 6).

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 3 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

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

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 2.

Small Road Mark #3

This bead is at Row 3. Column 2 stopped at Row 2, one row above → blue (≠).

  1. Column 4 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 2.
  2. Column 2 stopped at Row 2, one row above → blue (≠).

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

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. Column 4 has 3 beads. Column 1 has 6 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

Cell B5T6 Tableau Lookup
true (Mandatory 6th Card)

Verified via bankerShouldDraw(5, 6) === true on pair A+4.

Cell B5T6 60-Branch Matrix Split
23 Banker / 31 Player / 6 Tie

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

Cell B5T6 Resulting Player Totals
0+6=6, 1+6=7, 2+6=8, 3+6=9, 4+6=0, 5+6=1

Three-card Player totals produced when fifth card 6 (6) lands on P0..P5.

Cell B5T6 Standing Comparison
2W / 0T / 4L

How standing Banker 5 fares against the 6 Player 3-card totals for P3=6.

Cell B5T6 Sample Audition Hand
B(A+4=5) vs P3=6(6) -> DRAW

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

COMBINATORIAL PROOF · CELL B5T6

Cell B5T6 Analysis: Banker 5 (A+4) Facing Fifth-Card 6 (Value 6)

Under [B5T6], Banker holds two-card total 5 (A+4) while Player draws fifth-card 6 (point value 6) onto an initial 0–5 total. Across those six legal Player starts, [B5T6] produces three-card Player totals of P0+6->6, P1+6->7, P2+6->8, P3+6->9, P4+6->0, P5+6->1.

Because [B5T6] sits inside the active draw window for Banker 5, the dealer deals a sixth card to A+4: across all 60 (P0..P5 × sixth-card 0..9) combinations in [B5T6], Banker captures 23 wins, Player captures 31 wins, and 6 branches tie.

Cell B5T6 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 6 (6)
B5T6 Player StartB5T6 5th CardB5T6 Banker 5 ActionB5T6 10-Card SplitB5T6 Sample Result
[B5T6:P0] 6+4=0[B5T6:5th] +6(6) -> P=6[B5T6:6th] B=5 draws (+10->5)[B5T6:Split] 3B/6P/1T[B5T6:Cards] 6c (P)
[B5T6:P1] 10+A=1[B5T6:5th] +6(6) -> P=7[B5T6:6th] B=5 draws (+10->5)[B5T6:Split] 2B/7P/1T[B5T6:Cards] 6c (P)
[B5T6:P2] 8+4=2[B5T6:5th] +6(6) -> P=8[B5T6:6th] B=5 draws (+10->5)[B5T6:Split] 1B/8P/1T[B5T6:Cards] 6c (P)
[B5T6:P3] 10+3=3[B5T6:5th] +6(6) -> P=9[B5T6:6th] B=5 draws (+10->5)[B5T6:Split] 0B/9P/1T[B5T6:Cards] 6c (P)
[B5T6:P4] A+3=4[B5T6:5th] +6(6) -> P=0[B5T6:6th] B=5 draws (+10->5)[B5T6:Split] 9B/0P/1T[B5T6:Cards] 6c (B)
[B5T6:P5] 2+3=5[B5T6:5th] +6(6) -> P=1[B5T6:6th] B=5 draws (+10->5)[B5T6:Split] 8B/1P/1T[B5T6:Cards] 6c (B)
  • [B5T6-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 5 (A+4).
  • [B5T6-Step2] Confirm Player drew fifth-card 6 (value 6) onto a 0–5 start.
  • [B5T6-Step3] Execute BANKER_TABLEAU[5][6] = true (DRAW at 6 cards).
FLOOR PROCEDURE & SIDE BETS · B5T6

How Cell B5T6 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 6-card cell [B5T6], Banker 5 (A+4) can reach a 3-card 7 (Dragon 7) by drawing rank 2 or a 3-card 6 (Super 6) by drawing rank 1 after Player's 6.

Once [B5T6] resolves (23B/31P/6T across 60 branches), the winning side logs to the Big Road on shoe BBBBBBPPBP.

Table Reality Check

Myth vs. Truth

MythIn cell B5T6, the dealer checks the Player's 3-card sum (9) before acting on Banker 5.
TruthCell B5T6 inspects only the fifth card's face value (6 from 6), ordering Banker 5 to draws.
MythWinning cell B5T6 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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Read Every Derived Road at Table Speed

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