Skip to main content
Baccarat Smart
  1. Home
  2. Third-Card Rule Chart
  3. Resolution #139
FINAL TOTAL RESOLUTION [RES139] · 6-CARD PROOF

Player 0 + 3 (3) vs. Banker 2 (Draws 9 (9)): 6-Card Resolution #139

In walkthrough RES139, Player opens with 10+K (0) and draws fifth-card 3 (3) for a modulo-10 total of 3, while Banker opens with 10+2 (2) and draws sixth-card 9 (9) for 1 (6-card P outcome).

RES139 Player Path
P:0->3
RES139 Banker Path
B:2->1
RES139 Deal Length
6 Cards
RES139 Showdown
P (3v1)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES139 (P0+3->3 vs B2->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

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 2 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 2 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

RES139 Four-Card Opening Deal
Player 10+K=0 vs Banker 10+2=2

Verified non-natural start via handTotal([10,K])=0 and handTotal([10,2])=2.

RES139 Fifth-Card Modulo Proof
(0 + 3) mod 10 = 3 via 3

Player draws fifth-card 3 (value 3), transforming two-card 0 into three-card 3.

RES139 Banker Tableau Lookup
BANKER_TABLEAU[2][3] = true

Banker 2 draws sixth-card 9 (9) so (2+9) mod 10 = 1.

RES139 Card Count & Winner
6 Cards -> P (3 vs 1)

Computed directly from resolveHand() with zero discretionary dealer options.

RES139 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not P vs B.

MODULO-10 ARITHMETIC · RES139

Step-by-Step Card Arithmetic for RES139: P(10+K)+3 vs B(10+2)

Hand record [RES139] tracks Player 0 (10+K) facing Banker 2 (10+2); with zero naturals on the felt, the fifth card 3 (worth 3) arrives and 3 calculates the mod-10 residue to 3.

[RES139-B] Next in [RES139], Banker consults 2-point mandatory draw band: facing fifth-card 3 (3), Banker 2 draws 9 (9) so 2+9=11 -> 1.

Complete 6-Card Resolution Trace for RES139
RES139 StageRES139 CardsRES139 Modulo MathRES139 Status
[RES139:Init]P(10+K)=0 vs B(10+2)=2playerShouldDraw(0)=true4-Card Deal
[RES139:5th]Player +3 (3)(0+3) mod 10 = 35th Card Sideways
[RES139:6th]Banker +9 (9)(2+9) mod 10 = 16-Card Final
[RES139:Settle]P=3 vs B=1Winner: PBig Road +P
  • [RES139-1] Confirm [RES139] opening P=0 (10+K) and B=2 (10+2) lack Natural 8/9.
  • [RES139-2] Add [RES139] fifth-card 3 (3) to P=0 for (0+3) mod 10 = 3.
  • [RES139-3] Run [RES139] BANKER_TABLEAU[2][3]=true to settle 3 vs 1 (P).
SETTLEMENT & SCOREBOARD · RES139

Showdown Settlement & Scoreboard Logging for RES139 (3 vs 1)

[RES139-C9] Comparing [RES139] final totals (6c), Player 3 vs Banker 1 awards [RES139] to Player (P), which pays 1:1 even money on [RES139] Player boxes with zero commission deducted and appends P to BBPPBPPPBB.

[RES139-D11] Side-bet & road check for [RES139] (P0+3->3 vs B2->1, 6c): [RES139] leaves [RES139] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=1) and leaves [RES139] Panda 8 inactive (needs winning 3c Player 8, got P=3); on [RES139] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES139, Banker 2 evaluates Player's three-card total (3) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 3 (value 3) via BANKER_TABLEAU[2][3] = true.
MythBecause RES139 resolves as P, the next derived-road mark must match P's colour.
TruthDerived roads record Red (=) when Big Road structure repeats and Blue (≠) when it breaks—never Banker or Player.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

Read Every Derived Road at Table Speed

Every reference guide, glossary definition, and road calculator on Baccarat Smart is open for everyone. When you want all 6 modules and 36 lessons (about 5.5 hours of lessons) organized in structured step-by-step order with 74 hands-on boards, 94 quiz checks along the way, and Cloud Shoe Log sync across web, iPhone, and Android, start Module 1 (10 lessons, about 64 minutes of lessons) free or unlock full membership for $25 a month.

  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android