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TABLEAU CELL [B3T7] · ENGINE VERIFIED

Banker 3 vs. Player Third Card 7 (B3T7): Why Banker Always Draws

In cell B3T7, a Banker holding two-card total 3 (10+3) faces a Player fifth card valued at 7 (7). Under BANKER_TABLEAU[3][7], the Banker DRAWS, resolving in 6 cards with a 27B / 27P / 6T split across the 60 (P0..P5 × 6th-card 0..9) branches.

Cell B3T7 Action
DRAW
B3T7 Card Count
6 Cards
B3T7 60-Branch B/P/T
27/27/6
Tableau Coordinates
B=3, P3=7
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 B3T7 (Banker 3 vs Player 3rd card 7).

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 B3T7 Tableau Lookup
true (Mandatory 6th Card)

Verified via bankerShouldDraw(3, 7) === true on pair 10+3.

Cell B3T7 60-Branch Matrix Split
27 Banker / 27 Player / 6 Tie

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

Cell B3T7 Resulting Player Totals
0+7=7, 1+7=8, 2+7=9, 3+7=0, 4+7=1, 5+7=2

Three-card Player totals produced when fifth card 7 (7) lands on P0..P5.

Cell B3T7 Standing Comparison
3W / 0T / 3L

How standing Banker 3 fares against the 6 Player 3-card totals for P3=7.

Cell B3T7 Sample Audition Hand
B(10+3=3) vs P3=7(7) -> DRAW

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

COMBINATORIAL PROOF · CELL B3T7

Cell B3T7 Analysis: Banker 3 (10+3) Facing Fifth-Card 7 (Value 7)

Under [B3T7], Banker holds two-card total 3 (10+3) while Player draws fifth-card 7 (point value 7) onto an initial 0–5 total. Across those six legal Player starts, [B3T7] produces three-card Player totals of P0+7->7, P1+7->8, P2+7->9, P3+7->0, P4+7->1, P5+7->2.

Because [B3T7] sits inside the active draw window for Banker 3, the dealer deals a sixth card to 10+3: across all 60 (P0..P5 × sixth-card 0..9) combinations in [B3T7], Banker captures 27 wins, Player captures 27 wins, and 6 branches tie.

Cell B3T7 Resolution Across All 6 Legal Player Starts (0–5) with Fifth Card 7 (7)
B3T7 Player StartB3T7 5th CardB3T7 Banker 3 ActionB3T7 10-Card SplitB3T7 Sample Result
[B3T7:P0] 6+4=0[B3T7:5th] +7(7) -> P=7[B3T7:6th] B=3 draws (+3->6)[B3T7:Split] 2B/7P/1T[B3T7:Cards] 6c (P)
[B3T7:P1] 10+A=1[B3T7:5th] +7(7) -> P=8[B3T7:6th] B=3 draws (+3->6)[B3T7:Split] 1B/8P/1T[B3T7:Cards] 6c (P)
[B3T7:P2] 8+4=2[B3T7:5th] +7(7) -> P=9[B3T7:6th] B=3 draws (+3->6)[B3T7:Split] 0B/9P/1T[B3T7:Cards] 6c (P)
[B3T7:P3] 10+3=3[B3T7:5th] +7(7) -> P=0[B3T7:6th] B=3 draws (+3->6)[B3T7:Split] 9B/0P/1T[B3T7:Cards] 6c (B)
[B3T7:P4] A+3=4[B3T7:5th] +7(7) -> P=1[B3T7:6th] B=3 draws (+3->6)[B3T7:Split] 8B/1P/1T[B3T7:Cards] 6c (B)
[B3T7:P5] 2+3=5[B3T7:5th] +7(7) -> P=2[B3T7:6th] B=3 draws (+3->6)[B3T7:Split] 7B/2P/1T[B3T7:Cards] 6c (B)
  • [B3T7-Step1] Verify neither side opened with 8 or 9 before evaluating Banker 3 (10+3).
  • [B3T7-Step2] Confirm Player drew fifth-card 7 (value 7) onto a 0–5 start.
  • [B3T7-Step3] Execute BANKER_TABLEAU[3][7] = true (DRAW at 6 cards).
FLOOR PROCEDURE & SIDE BETS · B3T7

How Cell B3T7 Governs Dragon 7, Panda 8, and Scoreboard Tracking

In 6-card cell [B3T7], Banker 3 (10+3) can reach a 3-card 7 (Dragon 7) by drawing rank 4 or a 3-card 6 (Super 6) by drawing rank 3 after Player's 7.

Once [B3T7] resolves (27B/27P/6T across 60 branches), the winning side logs to the Big Road on shoe PPBBBBPPBB.

Table Reality Check

Myth vs. Truth

MythIn cell B3T7, the dealer checks the Player's 3-card sum (0) before acting on Banker 3.
TruthCell B3T7 inspects only the fifth card's face value (7 from 7), ordering Banker 3 to draws.
MythWinning cell B3T7 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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