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FINAL TOTAL RESOLUTION [RES172] · 6-CARD PROOF

Player 3 + 8 (8) vs. Banker 2 (Draws 6 (6)): 6-Card Resolution #172

In walkthrough RES172, Player opens with 9+4 (3) and draws fifth-card 8 (8) for a modulo-10 total of 1, while Banker opens with 8+4 (2) and draws sixth-card 6 (6) for 8 (6-card B outcome).

RES172 Player Path
P:3->1
RES172 Banker Path
B:2->8
RES172 Deal Length
6 Cards
RES172 Showdown
B (1v8)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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Big Road P P B B P B B B P P P P B P P B B P P B
Big Eye Boy = = ≠ ≠ = ≠ = = ≠ ≠ ≠ ≠ ≠ = = = =
Small Road ≠ = ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = =
Cockroach Pig = ≠ ≠ = ≠ = ≠ = = ≠ = ≠ ≠ ≠

Scoreboard sequence paired with 6-card resolution RES172 (P3+8->1 vs B2->8).

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

RES172 Four-Card Opening Deal
Player 9+4=3 vs Banker 8+4=2

Verified non-natural start via handTotal([9,4])=3 and handTotal([8,4])=2.

RES172 Fifth-Card Modulo Proof
(3 + 8) mod 10 = 1 via 8

Player draws fifth-card 8 (value 8), transforming two-card 3 into three-card 1.

RES172 Banker Tableau Lookup
BANKER_TABLEAU[2][8] = true

Banker 2 draws sixth-card 6 (6) so (2+6) mod 10 = 8.

RES172 Card Count & Winner
6 Cards -> B (1 vs 8)

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

RES172 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

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

MODULO-10 ARITHMETIC · RES172

Step-by-Step Card Arithmetic for RES172: P(9+4)+8 vs B(8+4)

Within resolution [RES172], Player's opening 9+4 totals 3 against Banker's 8+4 (2); Punto Banco rules require drawing 8 (8), and 3+8=11 extracts the terminal digit to 1.

[RES172-B] Evaluating bankerShouldDraw(2, 8)=true (2-point mandatory draw band) in [RES172], sixth-card 6 (6) advances Banker 2 via 2+6=8 to 8.

Complete 6-Card Resolution Trace for RES172
RES172 StageRES172 CardsRES172 Modulo MathRES172 Status
[RES172:Init]P(9+4)=3 vs B(8+4)=2playerShouldDraw(3)=true4-Card Deal
[RES172:5th]Player +8 (8)(3+8) mod 10 = 15th Card Sideways
[RES172:6th]Banker +6 (6)(2+6) mod 10 = 86-Card Final
[RES172:Settle]P=1 vs B=8Winner: BBig Road +B
  • [RES172-1] Confirm [RES172] opening P=3 (9+4) and B=2 (8+4) lack Natural 8/9.
  • [RES172-2] Add [RES172] fifth-card 8 (8) to P=3 for (3+8) mod 10 = 1.
  • [RES172-3] Run [RES172] BANKER_TABLEAU[2][8]=true to settle 1 vs 8 (B).
SETTLEMENT & SCOREBOARD · RES172

Showdown Settlement & Scoreboard Logging for RES172 (1 vs 8)

[RES172-C9] Comparing [RES172] final totals (6c), Player 1 vs Banker 8 awards [RES172] to Banker (B), which pays 0.95:1 on 5%-commission [RES172] layouts (or 0.5:1 on 6 at No-Commission [RES172] tables) and appends B to PPBBPBBBPP.

[RES172-D9] Side-bet & road check for [RES172] (P3+8->1 vs B2->8, 6c): [RES172] leaves [RES172] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=8) and leaves [RES172] Panda 8 inactive (needs winning 3c Player 8, got P=1); on [RES172] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES172, Banker 2 evaluates Player's three-card total (1) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 8 (value 8) via BANKER_TABLEAU[2][8] = true.
MythBecause RES172 resolves as B, the next derived-road mark must match B'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