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TABLEAU CELL [B4T5] · ENGINE VERIFIED

Banker 4 vs. Player Third Card 5 (B4T5): Why Banker Always Draws

In cell B4T5, a Banker holding two-card total 4 (A+3) faces a Player fifth card valued at 5 (5). Under BANKER_TABLEAU[4][5], the Banker DRAWS, resolving in 6 cards with a 19B / 35P / 6T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B4T5 Action
DRAW
B4T5 Card Count
6 Cards
B4T5 60-Branch B/P/T
19/35/6
Tableau Coordinates
B=4, P3=5
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Verified scoreboard paired with tableau cell B4T5 (Banker 4 vs Player 3rd card 5).

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

This bead is at Row 3. Column 2 stopped at Row 1, more than one row above → red (=).

  1. Column 3 goes down to Row 3, so use Rule 2: look 1 column back, at Column 2.
  2. Column 2 stopped at Row 1, more than one row above → 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.

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 5 has 1 bead. Column 2 has 1 bead. Same depth → red (=).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Cell B4T5 Tableau Lookup
true (Mandatory 6th Card)

Verified via bankerShouldDraw(4, 5) === true on pair A+3.

Cell B4T5 60-Branch Matrix Split
19 Banker / 35 Player / 6 Tie

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

Cell B4T5 Resulting Player Totals
0+5=5, 1+5=6, 2+5=7, 3+5=8, 4+5=9, 5+5=0

Three-card Player totals produced when fifth card 5 (5) lands on P0..P5.

Cell B4T5 Standing Comparison
1W / 0T / 5L

How standing Banker 4 fares against the 6 Player 3-card totals for P3=5.

Cell B4T5 Sample Audition Hand
B(A+3=4) vs P3=5(5) -> DRAW

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

COMBINATORIAL PROOF · CELL B4T5

Cell B4T5 Analysis: Banker 4 (A+3) Facing Fifth-Card 5 (Value 5)

Under [B4T5], Banker holds two-card total 4 (A+3) while Player draws fifth-card 5 (point value 5) onto an initial 0–5 total. Across those six legal Player starts, [B4T5] produces three-card Player totals of P0+5->5, P1+5->6, P2+5->7, P3+5->8, P4+5->9, P5+5->0.

Because [B4T5] sits inside the active draw window for Banker 4, the dealer deals a sixth card to A+3: across all 60 (P0..P5 × sixth-card 0..9) combinations in [B4T5], Banker captures 19 wins, Player captures 35 wins, and 6 branches tie.

Cell B4T5 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 5 (5)
B4T5 Player StartB4T5 5th CardB4T5 Banker 4 ActionB4T5 10-Card SplitB4T5 Sample Result
[B4T5:P0] 10+K=0[B4T5:5th] +5(5) -> P=5[B4T5:6th] B=4 draws (+10->4)[B4T5:Split] 4B/5P/1T[B4T5:Cards] 6c (P)
[B4T5:P1] 7+4=1[B4T5:5th] +5(5) -> P=6[B4T5:6th] B=4 draws (+10->4)[B4T5:Split] 3B/6P/1T[B4T5:Cards] 6c (P)
[B4T5:P2] 10+2=2[B4T5:5th] +5(5) -> P=7[B4T5:6th] B=4 draws (+10->4)[B4T5:Split] 2B/7P/1T[B4T5:Cards] 6c (P)
[B4T5:P3] 9+4=3[B4T5:5th] +5(5) -> P=8[B4T5:6th] B=4 draws (+10->4)[B4T5:Split] 1B/8P/1T[B4T5:Cards] 6c (P)
[B4T5:P4] 2+2=4[B4T5:5th] +5(5) -> P=9[B4T5:6th] B=4 draws (+10->4)[B4T5:Split] 0B/9P/1T[B4T5:Cards] 6c (P)
[B4T5:P5] A+4=5[B4T5:5th] +5(5) -> P=0[B4T5:6th] B=4 draws (+10->4)[B4T5:Split] 9B/0P/1T[B4T5:Cards] 6c (B)
  • [B4T5-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 4 (A+3).
  • [B4T5-Step2] Confirm Player drew fifth-card 5 (value 5) onto a 0–5 start.
  • [B4T5-Step3] Execute BANKER_TABLEAU[4][5] = true (DRAW at 6 cards).
FLOOR PROCEDURE & SIDE BETS · B4T5

How Cell B4T5 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 6-card cell [B4T5], Banker 4 (A+3) can reach a 3-card 7 (Dragon 7) by drawing rank 3 or a 3-card 6 (Super 6) by drawing rank 2 after Player's 5.

Once [B4T5] resolves (19B/35P/6T across 60 branches), the winning side logs to the Big Road on shoe BBPBBBBPPB.

Table Reality Check

Myth vs. Truth

MythIn cell B4T5, the dealer checks the Player's 3-card sum (8) before acting on Banker 4.
TruthCell B4T5 inspects only the fifth card's face value (5 from 5), ordering Banker 4 to draws.
MythWinning cell B4T5 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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