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TABLEAU CELL [B5T1] · ENGINE VERIFIED

Banker 5 vs. Player Third Card 1 (B5T1): Why Banker Always Stands

In cell B5T1, a Banker holding two-card total 5 (2+3) faces a Player fifth card valued at 1 (A). Under BANKER_TABLEAU[5][1], the Banker STANDS, resolving in 5 cards with a 40B / 10P / 10T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B5T1 Action
STAND
B5T1 Card Count
5 Cards
B5T1 60-Branch B/P/T
40/10/10
Tableau Coordinates
B=5, P3=1
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road P P 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 B5T1 (Banker 5 vs Player 3rd card 1).

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 3, one row above → blue (≠).

  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 3, one row above → blue (≠).

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

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

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 4 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #3

This bead is at Row 3. Column 2 has a bead at Row 3 too → red (=).

  1. Column 5 goes down to Row 3, so use Rule 2: look 3 columns back, at Column 2.
  2. Column 2 has a bead at Row 3 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.

Verified Reference Data

Key Facts & Table Specifications

Cell B5T1 Tableau Lookup
false (Mandatory 5-Card Stand)

Verified via bankerShouldDraw(5, 1) === false on pair 2+3.

Cell B5T1 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 B5T1 Resulting Player Totals
0+1=1, 1+1=2, 2+1=3, 3+1=4, 4+1=5, 5+1=6

Three-card Player totals produced when fifth card A (1) lands on P0..P5.

Cell B5T1 Standing Comparison
4W / 1T / 1L

How standing Banker 5 fares against the 6 Player 3-card totals for P3=1.

Cell B5T1 Sample Audition Hand
B(2+3=5) vs P3=A(1) -> STAND

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

COMBINATORIAL PROOF · CELL B5T1

Cell B5T1 Analysis: Banker 5 (2+3) Facing Fifth-Card A (Value 1)

Under [B5T1], Banker holds two-card total 5 (2+3) while Player draws fifth-card A (point value 1) onto an initial 0–5 total. Across those six legal Player starts, [B5T1] produces three-card Player totals of P0+1->1, P1+1->2, P2+1->3, P3+1->4, P4+1->5, P5+1->6.

Because [B5T1] 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 [B5T1], standing yields 40 Banker wins, 10 Player wins, and 10 ties without wraparound risk.

Cell B5T1 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card A (1)
B5T1 Player StartB5T1 5th CardB5T1 Banker 5 ActionB5T1 10-Card SplitB5T1 Sample Result
[B5T1:P0] 6+4=0[B5T1:5th] +A(1) -> P=1[B5T1:Pat] B=5 stands at 5[B5T1:Split] 10B/0P/0T[B5T1:Cards] 5c (B)
[B5T1:P1] 10+A=1[B5T1:5th] +A(1) -> P=2[B5T1:Pat] B=5 stands at 5[B5T1:Split] 10B/0P/0T[B5T1:Cards] 5c (B)
[B5T1:P2] 8+4=2[B5T1:5th] +A(1) -> P=3[B5T1:Pat] B=5 stands at 5[B5T1:Split] 10B/0P/0T[B5T1:Cards] 5c (B)
[B5T1:P3] 10+3=3[B5T1:5th] +A(1) -> P=4[B5T1:Pat] B=5 stands at 5[B5T1:Split] 10B/0P/0T[B5T1:Cards] 5c (B)
[B5T1:P4] A+3=4[B5T1:5th] +A(1) -> P=5[B5T1:Pat] B=5 stands at 5[B5T1:Split] 0B/0P/10T[B5T1:Cards] 5c (T)
[B5T1:P5] 2+3=5[B5T1:5th] +A(1) -> P=6[B5T1:Pat] B=5 stands at 5[B5T1:Split] 0B/10P/0T[B5T1:Cards] 5c (P)
  • [B5T1-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 5 (2+3).
  • [B5T1-Step2] Confirm Player drew fifth-card A (value 1) onto a 0–5 start.
  • [B5T1-Step3] Execute BANKER_TABLEAU[5][1] = false (STAND at 5 cards).
FLOOR PROCEDURE & SIDE BETS · B5T1

How Cell B5T1 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 5-card cell [B5T1], 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=7 draws A (1).

Once [B5T1] resolves (40B/10P/10T across 60 branches), the winning side logs to the Big Road on shoe PPPBBBBPPB.

Table Reality Check

Myth vs. Truth

MythIn cell B5T1, the dealer checks the Player's 3-card sum (4) before acting on Banker 5.
TruthCell B5T1 inspects only the fifth card's face value (1 from A), ordering Banker 5 to stands.
MythWinning cell B5T1 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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