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TABLEAU CELL [B4T0] · ENGINE VERIFIED

Banker 4 vs. Player Third Card 0 (B4T0): Why Banker Always Stands

In cell B4T0, a Banker holding two-card total 4 (2+2) faces a Player fifth card valued at 0 (10). Under BANKER_TABLEAU[4][0], the Banker STANDS, resolving in 5 cards with a 40B / 10P / 10T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B4T0 Action
STAND
B4T0 Card Count
5 Cards
B4T0 60-Branch B/P/T
40/10/10
Tableau Coordinates
B=4, P3=0
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 B P B B P P B B P P P B B B B P P B P B B
Big Eye Boy = ≠ ≠ ≠ = ≠ = = ≠ ≠ ≠ ≠ ≠ = = = = = ≠ ≠ = = ≠ ≠ = ≠ ≠ = ≠
Small Road ≠ = ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = = = ≠ ≠ = ≠ = ≠ = ≠ ≠ ≠ ≠
Cockroach Pig = = ≠ = ≠ = ≠ = = ≠ = ≠ ≠ ≠ = ≠ ≠ = ≠ = ≠ = = ≠ ≠ =

Verified scoreboard paired with tableau cell B4T0 (Banker 4 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

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 B4T0 Tableau Lookup
false (Mandatory 5-Card Stand)

Verified via bankerShouldDraw(4, 0) === false on pair 2+2.

Cell B4T0 60-Branch Matrix Split
40 Banker / 10 Player / 10 Tie

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

Cell B4T0 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 B4T0 Standing Comparison
4W / 1T / 1L

How standing Banker 4 fares against the 6 Player 3-card totals for P3=0.

Cell B4T0 Sample Audition Hand
B(2+2=4) vs P3=10(0) -> STAND

Sample sixth card 5 (5) verified through resolveHand().

COMBINATORIAL PROOF · CELL B4T0

Cell B4T0 Analysis: Banker 4 (2+2) Facing Fifth-Card 10 (Value 0)

Under [B4T0], Banker holds two-card total 4 (2+2) while Player draws fifth-card 10 (point value 0) onto an initial 0–5 total. Across those six legal Player starts, [B4T0] 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 [B4T0] falls outside the draw window for Banker 4, the dealer stands pat on 2+2 (4) at 5 cards: across the 60 (P0..P5 × unpulled 6th card 0..9) branches in [B4T0], standing yields 40 Banker wins, 10 Player wins, and 10 ties without wraparound risk.

Cell B4T0 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 10 (0)
B4T0 Player StartB4T0 5th CardB4T0 Banker 4 ActionB4T0 10-Card SplitB4T0 Sample Result
[B4T0:P0] 10+K=0[B4T0:5th] +10(0) -> P=0[B4T0:Pat] B=4 stands at 4[B4T0:Split] 10B/0P/0T[B4T0:Cards] 5c (B)
[B4T0:P1] 7+4=1[B4T0:5th] +10(0) -> P=1[B4T0:Pat] B=4 stands at 4[B4T0:Split] 10B/0P/0T[B4T0:Cards] 5c (B)
[B4T0:P2] 10+2=2[B4T0:5th] +10(0) -> P=2[B4T0:Pat] B=4 stands at 4[B4T0:Split] 10B/0P/0T[B4T0:Cards] 5c (B)
[B4T0:P3] 9+4=3[B4T0:5th] +10(0) -> P=3[B4T0:Pat] B=4 stands at 4[B4T0:Split] 10B/0P/0T[B4T0:Cards] 5c (B)
[B4T0:P4] 2+2=4[B4T0:5th] +10(0) -> P=4[B4T0:Pat] B=4 stands at 4[B4T0:Split] 0B/0P/10T[B4T0:Cards] 5c (T)
[B4T0:P5] A+4=5[B4T0:5th] +10(0) -> P=5[B4T0:Pat] B=4 stands at 4[B4T0:Split] 0B/10P/0T[B4T0:Cards] 5c (P)
  • [B4T0-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 4 (2+2).
  • [B4T0-Step2] Confirm Player drew fifth-card 10 (value 0) onto a 0–5 start.
  • [B4T0-Step3] Execute BANKER_TABLEAU[4][0] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B4T0

How Cell B4T0 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B4T0], Banker 4 (2+2) 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 [B4T0] resolves (40B/10P/10T across 60 branches), the winning side logs to the Big Road on shoe BBBBPPBPPP.

Table Reality Check

Myth vs. Truth

MythIn cell B4T0, the dealer checks the Player's 3-card sum (3) before acting on Banker 4.
TruthCell B4T0 inspects only the fifth card's face value (0 from 10), ordering Banker 4 to stands.
MythWinning cell B4T0 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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