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TABLEAU CELL [B5T9] · ENGINE VERIFIED

Banker 5 vs. Player Third Card 9 (B5T9): Why Banker Always Stands

In cell B5T9, a Banker holding two-card total 5 (2+3) faces a Player fifth card valued at 9 (9). Under BANKER_TABLEAU[5][9], the Banker STANDS, resolving in 5 cards with a 50B / 10P / 0T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B5T9 Action
STAND
B5T9 Card Count
5 Cards
B5T9 60-Branch B/P/T
50/10/0
Tableau Coordinates
B=5, P3=9
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Verified scoreboard paired with tableau cell B5T9 (Banker 5 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

This bead is at Row 4. Column 1 stopped at Row 2, more than one row above → red (=).

  1. Column 2 goes down to Row 4, so use Rule 2: look 1 column 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.

Small Road Mark #3

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 columns back, at Column 2.
  2. Column 2 has a bead at Row 2 too → 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.

Cockroach Pig Mark #3

Column 5 has 1 bead. Column 2 has 4 beads. Different depth → blue (≠).

  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 4 beads. Different depth → blue (≠).

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 B5T9 Tableau Lookup
false (Mandatory 5-Card Stand)

Verified via bankerShouldDraw(5, 9) === false on pair 2+3.

Cell B5T9 60-Branch Matrix Split
50 Banker / 10 Player / 0 Tie

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

Cell B5T9 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 B5T9 Standing Comparison
5W / 0T / 1L

How standing Banker 5 fares against the 6 Player 3-card totals for P3=9.

Cell B5T9 Sample Audition Hand
B(2+3=5) vs P3=9(9) -> STAND

Sample sixth card 3 (3) verified through resolveHand().

COMBINATORIAL PROOF · CELL B5T9

Cell B5T9 Analysis: Banker 5 (2+3) Facing Fifth-Card 9 (Value 9)

Under [B5T9], Banker holds two-card total 5 (2+3) while Player draws fifth-card 9 (point value 9) onto an initial 0–5 total. Across those six legal Player starts, [B5T9] 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 [B5T9] falls outside the draw window for Banker 5, the dealer stands pat on 2+3 (5) at 5 cards: across the 60 (P0..P5 × unpulled 6th card 0..9) branches in [B5T9], standing yields 50 Banker wins, 10 Player wins, and 0 ties without wraparound risk.

Cell B5T9 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 9 (9)
B5T9 Player StartB5T9 5th CardB5T9 Banker 5 ActionB5T9 10-Card SplitB5T9 Sample Result
[B5T9:P0] 6+4=0[B5T9:5th] +9(9) -> P=9[B5T9:Pat] B=5 stands at 5[B5T9:Split] 0B/10P/0T[B5T9:Cards] 5c (P)
[B5T9:P1] 10+A=1[B5T9:5th] +9(9) -> P=0[B5T9:Pat] B=5 stands at 5[B5T9:Split] 10B/0P/0T[B5T9:Cards] 5c (B)
[B5T9:P2] 8+4=2[B5T9:5th] +9(9) -> P=1[B5T9:Pat] B=5 stands at 5[B5T9:Split] 10B/0P/0T[B5T9:Cards] 5c (B)
[B5T9:P3] 10+3=3[B5T9:5th] +9(9) -> P=2[B5T9:Pat] B=5 stands at 5[B5T9:Split] 10B/0P/0T[B5T9:Cards] 5c (B)
[B5T9:P4] A+3=4[B5T9:5th] +9(9) -> P=3[B5T9:Pat] B=5 stands at 5[B5T9:Split] 10B/0P/0T[B5T9:Cards] 5c (B)
[B5T9:P5] 2+3=5[B5T9:5th] +9(9) -> P=4[B5T9:Pat] B=5 stands at 5[B5T9:Split] 10B/0P/0T[B5T9:Cards] 5c (B)
  • [B5T9-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 5 (2+3).
  • [B5T9-Step2] Confirm Player drew fifth-card 9 (value 9) onto a 0–5 start.
  • [B5T9-Step3] Execute BANKER_TABLEAU[5][9] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B5T9

How Cell B5T9 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B5T9], Banker 5 (2+3) never takes a sixth card, so 3-card Banker Dragon 7 is impossible while Player reaches 3-card 8 (Panda 8) whenever P=9 draws 9 (9).

Once [B5T9] resolves (50B/10P/0T across 60 branches), the winning side logs to the Big Road on shoe PPBBBBPPBB.

Table Reality Check

Myth vs. Truth

MythIn cell B5T9, the dealer checks the Player's 3-card sum (2) before acting on Banker 5.
TruthCell B5T9 inspects only the fifth card's face value (9 from 9), ordering Banker 5 to stands.
MythWinning cell B5T9 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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