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TABLEAU CELL [B6T5] · ENGINE VERIFIED

Banker 6 vs. Player Third Card 5 (B6T5): Why Banker Always Stands

In cell B6T5, a Banker holding two-card total 6 (2+4) faces a Player fifth card valued at 5 (5). Under BANKER_TABLEAU[6][5], the Banker STANDS, resolving in 5 cards with a 20B / 30P / 10T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B6T5 Action
STAND
B6T5 Card Count
5 Cards
B6T5 60-Branch B/P/T
20/30/10
Tableau Coordinates
B=6, P3=5
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Verified scoreboard paired with tableau cell B6T5 (Banker 6 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

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 4 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 4 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 B6T5 Tableau Lookup
false (Mandatory 5-Card Stand)

Verified via bankerShouldDraw(6, 5) === false on pair 2+4.

Cell B6T5 60-Branch Matrix Split
20 Banker / 30 Player / 10 Tie

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

Cell B6T5 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 B6T5 Standing Comparison
2W / 1T / 3L

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

Cell B6T5 Sample Audition Hand
B(2+4=6) vs P3=5(5) -> STAND

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

COMBINATORIAL PROOF · CELL B6T5

Cell B6T5 Analysis: Banker 6 (2+4) Facing Fifth-Card 5 (Value 5)

Under [B6T5], Banker holds two-card total 6 (2+4) while Player draws fifth-card 5 (point value 5) onto an initial 0–5 total. Across those six legal Player starts, [B6T5] 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 [B6T5] falls outside the draw window for Banker 6, the dealer stands pat on 2+4 (6) at 5 cards: across the 60 (P0..P5 × unpulled 6th card 0..9) branches in [B6T5], standing yields 20 Banker wins, 30 Player wins, and 10 ties without wraparound risk.

Cell B6T5 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 5 (5)
B6T5 Player StartB6T5 5th CardB6T5 Banker 6 ActionB6T5 10-Card SplitB6T5 Sample Result
[B6T5:P0] 10+K=0[B6T5:5th] +5(5) -> P=5[B6T5:Pat] B=6 stands at 6[B6T5:Split] 10B/0P/0T[B6T5:Cards] 5c (B)
[B6T5:P1] 7+4=1[B6T5:5th] +5(5) -> P=6[B6T5:Pat] B=6 stands at 6[B6T5:Split] 0B/0P/10T[B6T5:Cards] 5c (T)
[B6T5:P2] 10+2=2[B6T5:5th] +5(5) -> P=7[B6T5:Pat] B=6 stands at 6[B6T5:Split] 0B/10P/0T[B6T5:Cards] 5c (P)
[B6T5:P3] 9+4=3[B6T5:5th] +5(5) -> P=8[B6T5:Pat] B=6 stands at 6[B6T5:Split] 0B/10P/0T[B6T5:Cards] 5c (P)
[B6T5:P4] 2+2=4[B6T5:5th] +5(5) -> P=9[B6T5:Pat] B=6 stands at 6[B6T5:Split] 0B/10P/0T[B6T5:Cards] 5c (P)
[B6T5:P5] A+4=5[B6T5:5th] +5(5) -> P=0[B6T5:Pat] B=6 stands at 6[B6T5:Split] 10B/0P/0T[B6T5:Cards] 5c (B)
  • [B6T5-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 6 (2+4).
  • [B6T5-Step2] Confirm Player drew fifth-card 5 (value 5) onto a 0–5 start.
  • [B6T5-Step3] Execute BANKER_TABLEAU[6][5] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B6T5

How Cell B6T5 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B6T5], Banker 6 (2+4) never takes a sixth card, so 3-card Banker Dragon 7 is impossible while Player reaches 3-card 8 (Panda 8) whenever P=3 draws 5 (5).

Once [B6T5] resolves (20B/30P/10T across 60 branches), the winning side logs to the Big Road on shoe BBBBPPBPPP.

Table Reality Check

Myth vs. Truth

MythIn cell B6T5, the dealer checks the Player's 3-card sum (8) before acting on Banker 6.
TruthCell B6T5 inspects only the fifth card's face value (5 from 5), ordering Banker 6 to stands.
MythWinning cell B6T5 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.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

Read Every Derived Road at Table Speed

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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