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TABLEAU CELL [B3T4] · ENGINE VERIFIED

Banker 3 vs. Player Third Card 4 (B3T4): Why Banker Always Draws

In cell B3T4, a Banker holding two-card total 3 (9+4) faces a Player fifth card valued at 4 (4). Under BANKER_TABLEAU[3][4], the Banker DRAWS, resolving in 6 cards with a 15B / 39P / 6T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B3T4 Action
DRAW
B3T4 Card Count
6 Cards
B3T4 60-Branch B/P/T
15/39/6
Tableau Coordinates
B=3, P3=4
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 B3T4 (Banker 3 vs Player 3rd card 4).

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 B3T4 Tableau Lookup
true (Mandatory 6th Card)

Verified via bankerShouldDraw(3, 4) === true on pair 9+4.

Cell B3T4 60-Branch Matrix Split
15 Banker / 39 Player / 6 Tie

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

Cell B3T4 Resulting Player Totals
0+4=4, 1+4=5, 2+4=6, 3+4=7, 4+4=8, 5+4=9

Three-card Player totals produced when fifth card 4 (4) lands on P0..P5.

Cell B3T4 Standing Comparison
0W / 0T / 6L

How standing Banker 3 fares against the 6 Player 3-card totals for P3=4.

Cell B3T4 Sample Audition Hand
B(9+4=3) vs P3=4(4) -> DRAW

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

COMBINATORIAL PROOF · CELL B3T4

Cell B3T4 Analysis: Banker 3 (9+4) Facing Fifth-Card 4 (Value 4)

Under [B3T4], Banker holds two-card total 3 (9+4) while Player draws fifth-card 4 (point value 4) onto an initial 0–5 total. Across those six legal Player starts, [B3T4] produces three-card Player totals of P0+4->4, P1+4->5, P2+4->6, P3+4->7, P4+4->8, P5+4->9.

Because [B3T4] sits inside the active draw window for Banker 3, the dealer deals a sixth card to 9+4: across all 60 (P0..P5 × sixth-card 0..9) combinations in [B3T4], Banker captures 15 wins, Player captures 39 wins, and 6 branches tie.

Cell B3T4 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 4 (4)
B3T4 Player StartB3T4 5th CardB3T4 Banker 3 ActionB3T4 10-Card SplitB3T4 Sample Result
[B3T4:P0] 6+4=0[B3T4:5th] +4(4) -> P=4[B3T4:6th] B=3 draws (+10->3)[B3T4:Split] 5B/4P/1T[B3T4:Cards] 6c (P)
[B3T4:P1] 10+A=1[B3T4:5th] +4(4) -> P=5[B3T4:6th] B=3 draws (+10->3)[B3T4:Split] 4B/5P/1T[B3T4:Cards] 6c (P)
[B3T4:P2] 8+4=2[B3T4:5th] +4(4) -> P=6[B3T4:6th] B=3 draws (+10->3)[B3T4:Split] 3B/6P/1T[B3T4:Cards] 6c (P)
[B3T4:P3] 10+3=3[B3T4:5th] +4(4) -> P=7[B3T4:6th] B=3 draws (+10->3)[B3T4:Split] 2B/7P/1T[B3T4:Cards] 6c (P)
[B3T4:P4] A+3=4[B3T4:5th] +4(4) -> P=8[B3T4:6th] B=3 draws (+10->3)[B3T4:Split] 1B/8P/1T[B3T4:Cards] 6c (P)
[B3T4:P5] 2+3=5[B3T4:5th] +4(4) -> P=9[B3T4:6th] B=3 draws (+10->3)[B3T4:Split] 0B/9P/1T[B3T4:Cards] 6c (P)
  • [B3T4-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 3 (9+4).
  • [B3T4-Step2] Confirm Player drew fifth-card 4 (value 4) onto a 0–5 start.
  • [B3T4-Step3] Execute BANKER_TABLEAU[3][4] = true (DRAW at 6 cards).
FLOOR PROCEDURE & SIDE BETS · B3T4

How Cell B3T4 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 6-card cell [B3T4], Banker 3 (9+4) can reach a 3-card 7 (Dragon 7) by drawing rank 4 or a 3-card 6 (Super 6) by drawing rank 3 after Player's 4.

Once [B3T4] resolves (15B/39P/6T across 60 branches), the winning side logs to the Big Road on shoe BBBBPBPBPP.

Table Reality Check

Myth vs. Truth

MythIn cell B3T4, the dealer checks the Player's 3-card sum (7) before acting on Banker 3.
TruthCell B3T4 inspects only the fifth card's face value (4 from 4), ordering Banker 3 to draws.
MythWinning cell B3T4 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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