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FINAL TOTAL RESOLUTION [RES309] · 5-CARD PROOF

Player 2 + A (1) vs. Banker 5 (Stands at 5): 5-Card Resolution #309

In walkthrough RES309, Player opens with 10+2 (2) and draws fifth-card A (1) for a modulo-10 total of 3, while Banker opens with A+4 (5) and stands pat at 5 (5-card B outcome).

RES309 Player Path
P:2->3
RES309 Banker Path
B:5->5
RES309 Deal Length
5 Cards
RES309 Showdown
B (3v5)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 5-card resolution RES309 (P2+1->3 vs B5->5).

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

  1. Column 3 goes down to Row 2, so use Rule 2: look 1 column 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.

Small Road Mark #3

Column 4 has 1 bead. Column 2 has 2 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 2 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

Column 6 has 1 bead. Column 3 has 2 beads. Different depth → blue (≠).

  1. Column 7 starts, so use Rule 1: compare Column 6 with Column 3, 3 columns further back.
  2. Column 6 has 1 bead. Column 3 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 6, the one that just finished, with Column 3.

Verified Reference Data

Key Facts & Table Specifications

RES309 Four-Card Opening Deal
Player 10+2=2 vs Banker A+4=5

Verified non-natural start via handTotal([10,2])=2 and handTotal([A,4])=5.

RES309 Fifth-Card Modulo Proof
(2 + 1) mod 10 = 3 via A

Player draws fifth-card A (value 1), transforming two-card 2 into three-card 3.

RES309 Banker Tableau Lookup
BANKER_TABLEAU[5][1] = false

Banker 5 stands pat at 5 without pulling sixth-card 2 (2).

RES309 Card Count & Winner
5 Cards -> B (3 vs 5)

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

RES309 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 · RES309

Step-by-Step Card Arithmetic for RES309: P(10+2)+A vs B(A+4)

[RES309] Walkthrough #309 begins with Player holding 10+2 (2) against Banker A+4 (5); since neither side holds 8 or 9, Player draws fifth-card A (1) so 2+1=3 applies base-10 modular addition to 3.

[RES309-B] Because BANKER_TABLEAU[5][1]=false (5-point four-value window (4..7)) in [RES309], Banker 5 locks 5 at 5c (leaving 2=2 -> 7 unpulled).

Complete 5-Card Resolution Trace for RES309
RES309 StageRES309 CardsRES309 Modulo MathRES309 Status
[RES309:Init]P(10+2)=2 vs B(A+4)=5playerShouldDraw(2)=true4-Card Deal
[RES309:5th]Player +A (1)(2+1) mod 10 = 35th Card Sideways
[RES309:6th]Banker Stands (skip 2=2)Locked at 55-Card Final
[RES309:Settle]P=3 vs B=5Winner: BBig Road +B
  • [RES309-1] Confirm [RES309] opening P=2 (10+2) and B=5 (A+4) lack Natural 8/9.
  • [RES309-2] Add [RES309] fifth-card A (1) to P=2 for (2+1) mod 10 = 3.
  • [RES309-3] Run [RES309] BANKER_TABLEAU[5][1]=false to settle 3 vs 5 (B).
SETTLEMENT & SCOREBOARD · RES309

Showdown Settlement & Scoreboard Logging for RES309 (3 vs 5)

[RES309-C1] Comparing [RES309] final totals (5c), Player 3 vs Banker 5 awards [RES309] to Banker (B), which pays 0.95:1 on 5%-commission [RES309] layouts (or 0.5:1 on 6 at No-Commission [RES309] tables) and appends B to BBPPBBPBPB.

[RES309-D7] Side-bet & road check for [RES309] (P2+1->3 vs B5->5, 5c): [RES309] leaves [RES309] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=5) and leaves [RES309] Panda 8 inactive (needs winning 3c Player 8, got P=3); on [RES309] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES309, Banker 5 evaluates Player's three-card total (3) before deciding whether to draw.
TruthBanker 5 inspects only Player's fifth card A (value 1) via BANKER_TABLEAU[5][1] = false.
MythBecause RES309 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

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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