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FINAL TOTAL RESOLUTION [RES244] · 5-CARD PROOF

Player 3 + 10 (0) vs. Banker 4 (Stands at 4): 5-Card Resolution #244

In walkthrough RES244, Player opens with 9+4 (3) and draws fifth-card 10 (0) for a modulo-10 total of 3, while Banker opens with A+3 (4) and stands pat at 4 (5-card B outcome).

RES244 Player Path
P:3->3
RES244 Banker Path
B:4->4
RES244 Deal Length
5 Cards
RES244 Showdown
B (3v4)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 5-card resolution RES244 (P3+0->3 vs B4->4).

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

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

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

Small Road Mark #3

Column 4 has 1 bead. Column 2 has 3 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 3 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 5 has 2 beads. Column 2 has 3 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 2 beads. Column 2 has 3 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

RES244 Four-Card Opening Deal
Player 9+4=3 vs Banker A+3=4

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

RES244 Fifth-Card Modulo Proof
(3 + 0) mod 10 = 3 via 10

Player draws fifth-card 10 (value 0), transforming two-card 3 into three-card 3.

RES244 Banker Tableau Lookup
BANKER_TABLEAU[4][0] = false

Banker 4 stands pat at 4 without pulling sixth-card 6 (6).

RES244 Card Count & Winner
5 Cards -> B (3 vs 4)

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

RES244 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 · RES244

Step-by-Step Card Arithmetic for RES244: P(9+4)+10 vs B(A+3)

Canonical test [RES244] examines Player 3 (9+4) against Banker 4 (A+3); the fifth card 10 (0) brings Player's raw count to 3, which computes the single-digit remainder to 3.

[RES244-B] Because BANKER_TABLEAU[4][0]=false (4-point six-value gate (2..7)) in [RES244], Banker 4 locks 4 at 5c (leaving 6=6 -> 0 unpulled).

Complete 5-Card Resolution Trace for RES244
RES244 StageRES244 CardsRES244 Modulo MathRES244 Status
[RES244:Init]P(9+4)=3 vs B(A+3)=4playerShouldDraw(3)=true4-Card Deal
[RES244:5th]Player +10 (0)(3+0) mod 10 = 35th Card Sideways
[RES244:6th]Banker Stands (skip 6=6)Locked at 45-Card Final
[RES244:Settle]P=3 vs B=4Winner: BBig Road +B
  • [RES244-1] Confirm [RES244] opening P=3 (9+4) and B=4 (A+3) lack Natural 8/9.
  • [RES244-2] Add [RES244] fifth-card 10 (0) to P=3 for (3+0) mod 10 = 3.
  • [RES244-3] Run [RES244] BANKER_TABLEAU[4][0]=false to settle 3 vs 4 (B).
SETTLEMENT & SCOREBOARD · RES244

Showdown Settlement & Scoreboard Logging for RES244 (3 vs 4)

[RES244-C6] Comparing [RES244] final totals (5c), Player 3 vs Banker 4 awards [RES244] to Banker (B), which pays 0.95:1 on 5%-commission [RES244] layouts (or 0.5:1 on 6 at No-Commission [RES244] tables) and appends B to PPBBBPPBPP.

[RES244-D7] Side-bet & road check for [RES244] (P3+0->3 vs B4->4, 5c): [RES244] leaves [RES244] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=4) and leaves [RES244] Panda 8 inactive (needs winning 3c Player 8, got P=3); on [RES244] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES244, Banker 4 evaluates Player's three-card total (3) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 10 (value 0) via BANKER_TABLEAU[4][0] = false.
MythBecause RES244 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.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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