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TABLEAU CELL [B5T0] · ENGINE VERIFIED

Banker 5 vs. Player Third Card 0 (B5T0): Why Banker Always Stands

In cell B5T0, a Banker holding two-card total 5 (A+4) faces a Player fifth card valued at 0 (10). Under BANKER_TABLEAU[5][0], the Banker STANDS, resolving in 5 cards with a 50B / 0P / 10T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B5T0 Action
STAND
B5T0 Card Count
5 Cards
B5T0 60-Branch B/P/T
50/0/10
Tableau Coordinates
B=5, P3=0
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Verified scoreboard paired with tableau cell B5T0 (Banker 5 vs Player 3rd card 0).

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

  1. Column 3 goes down to Row 2, so use Rule 2: look 1 column 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.

Small Road Mark #3

This bead is at Row 4. Column 1 stopped at Row 1, 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 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 1 stopped exactly one row above this bead.

Cockroach Pig Mark #3

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

  1. Column 7 starts, so use Rule 1: compare Column 6 with Column 3, 3 columns further back.
  2. Column 6 has 1 bead. Column 3 has 4 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 6, the one that just finished, with Column 3.

Verified Reference Data

Key Facts & Table Specifications

Cell B5T0 Tableau Lookup
false (Mandatory 5-Card Stand)

Verified via bankerShouldDraw(5, 0) === false on pair A+4.

Cell B5T0 60-Branch Matrix Split
50 Banker / 0 Player / 10 Tie

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

Cell B5T0 Resulting Player Totals
0+0=0, 1+0=1, 2+0=2, 3+0=3, 4+0=4, 5+0=5

Three-card Player totals produced when fifth card 10 (0) lands on P0..P5.

Cell B5T0 Standing Comparison
5W / 1T / 0L

How standing Banker 5 fares against the 6 Player 3-card totals for P3=0.

Cell B5T0 Sample Audition Hand
B(A+4=5) vs P3=10(0) -> STAND

Sample sixth card 4 (4) verified through resolveHand().

COMBINATORIAL PROOF · CELL B5T0

Cell B5T0 Analysis: Banker 5 (A+4) Facing Fifth-Card 10 (Value 0)

Under [B5T0], Banker holds two-card total 5 (A+4) while Player draws fifth-card 10 (point value 0) onto an initial 0–5 total. Across those six legal Player starts, [B5T0] produces three-card Player totals of P0+0->0, P1+0->1, P2+0->2, P3+0->3, P4+0->4, P5+0->5.

Because [B5T0] falls outside the draw window for Banker 5, the dealer stands pat on A+4 (5) at 5 cards: across the 60 (P0..P5 × unpulled 6th card 0..9) branches in [B5T0], standing yields 50 Banker wins, 0 Player wins, and 10 ties without wraparound risk.

Cell B5T0 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 10 (0)
B5T0 Player StartB5T0 5th CardB5T0 Banker 5 ActionB5T0 10-Card SplitB5T0 Sample Result
[B5T0:P0] 6+4=0[B5T0:5th] +10(0) -> P=0[B5T0:Pat] B=5 stands at 5[B5T0:Split] 10B/0P/0T[B5T0:Cards] 5c (B)
[B5T0:P1] 10+A=1[B5T0:5th] +10(0) -> P=1[B5T0:Pat] B=5 stands at 5[B5T0:Split] 10B/0P/0T[B5T0:Cards] 5c (B)
[B5T0:P2] 8+4=2[B5T0:5th] +10(0) -> P=2[B5T0:Pat] B=5 stands at 5[B5T0:Split] 10B/0P/0T[B5T0:Cards] 5c (B)
[B5T0:P3] 10+3=3[B5T0:5th] +10(0) -> P=3[B5T0:Pat] B=5 stands at 5[B5T0:Split] 10B/0P/0T[B5T0:Cards] 5c (B)
[B5T0:P4] A+3=4[B5T0:5th] +10(0) -> P=4[B5T0:Pat] B=5 stands at 5[B5T0:Split] 10B/0P/0T[B5T0:Cards] 5c (B)
[B5T0:P5] 2+3=5[B5T0:5th] +10(0) -> P=5[B5T0:Pat] B=5 stands at 5[B5T0:Split] 0B/0P/10T[B5T0:Cards] 5c (T)
  • [B5T0-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 5 (A+4).
  • [B5T0-Step2] Confirm Player drew fifth-card 10 (value 0) onto a 0–5 start.
  • [B5T0-Step3] Execute BANKER_TABLEAU[5][0] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B5T0

How Cell B5T0 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B5T0], Banker 5 (A+4) never takes a sixth card, so 3-card Banker Dragon 7 is impossible while Player reaches 3-card 8 (Panda 8) whenever P=8 draws 10 (0).

Once [B5T0] resolves (50B/0P/10T across 60 branches), the winning side logs to the Big Road on shoe BPPBBBBPBP.

Table Reality Check

Myth vs. Truth

MythIn cell B5T0, the dealer checks the Player's 3-card sum (3) before acting on Banker 5.
TruthCell B5T0 inspects only the fifth card's face value (0 from 10), ordering Banker 5 to stands.
MythWinning cell B5T0 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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