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FINAL TOTAL RESOLUTION [RES290] · 5-CARD PROOF

Player 1 + 8 (8) vs. Banker 4 (Stands at 4): 5-Card Resolution #290

In walkthrough RES290, Player opens with 7+4 (1) and draws fifth-card 8 (8) for a modulo-10 total of 9, while Banker opens with A+3 (4) and stands pat at 4 (5-card P outcome).

RES290 Player Path
P:1->9
RES290 Banker Path
B:4->4
RES290 Deal Length
5 Cards
RES290 Showdown
P (9v4)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 5-card resolution RES290 (P1+8->9 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 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 2. Column 3 stopped at Row 1, one row above → blue (≠).

  1. Column 5 goes down to Row 2, so use Rule 2: look 2 columns back, at Column 3.
  2. Column 3 stopped at Row 1, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 3 stopped exactly one row above this bead.

Cockroach Pig Mark #3

Column 5 has 2 beads. Column 2 has 2 beads. Same depth → red (=).

  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 2 beads. Same depth → red (=).

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

RES290 Four-Card Opening Deal
Player 7+4=1 vs Banker A+3=4

Verified non-natural start via handTotal([7,4])=1 and handTotal([A,3])=4.

RES290 Fifth-Card Modulo Proof
(1 + 8) mod 10 = 9 via 8

Player draws fifth-card 8 (value 8), transforming two-card 1 into three-card 9.

RES290 Banker Tableau Lookup
BANKER_TABLEAU[4][8] = false

Banker 4 stands pat at 4 without pulling sixth-card 10 (0).

RES290 Card Count & Winner
5 Cards -> P (9 vs 4)

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

RES290 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 · RES290

Step-by-Step Card Arithmetic for RES290: P(7+4)+8 vs B(A+3)

In coup [RES290], initial cards deal 7+4=1 to Player and A+3=4 to Banker; lacking a four-card natural, Player takes fifth-card 8 (8) where raw sum 9 projects onto the 0..9 ring to 9.

[RES290-B] Evaluating bankerShouldDraw(4, 8)=false (4-point six-value gate (2..7)) in [RES290], Banker 4 preserves 4 while 10 (0) remains undealt.

Complete 5-Card Resolution Trace for RES290
RES290 StageRES290 CardsRES290 Modulo MathRES290 Status
[RES290:Init]P(7+4)=1 vs B(A+3)=4playerShouldDraw(1)=true4-Card Deal
[RES290:5th]Player +8 (8)(1+8) mod 10 = 95th Card Sideways
[RES290:6th]Banker Stands (skip 10=0)Locked at 45-Card Final
[RES290:Settle]P=9 vs B=4Winner: PBig Road +P
  • [RES290-1] Confirm [RES290] opening P=1 (7+4) and B=4 (A+3) lack Natural 8/9.
  • [RES290-2] Add [RES290] fifth-card 8 (8) to P=1 for (1+8) mod 10 = 9.
  • [RES290-3] Run [RES290] BANKER_TABLEAU[4][8]=false to settle 9 vs 4 (P).
SETTLEMENT & SCOREBOARD · RES290

Showdown Settlement & Scoreboard Logging for RES290 (9 vs 4)

[RES290-C5] Comparing [RES290] final totals (5c), Player 9 vs Banker 4 awards [RES290] to Player (P), which pays 1:1 even money on [RES290] Player boxes with zero commission deducted and appends P to PPBBPBPPBB.

[RES290-D5] Side-bet & road check for [RES290] (P1+8->9 vs B4->4, 5c): [RES290] leaves [RES290] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=4) and leaves [RES290] Panda 8 inactive (needs winning 3c Player 8, got P=9); on [RES290] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES290, Banker 4 evaluates Player's three-card total (9) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 8 (value 8) via BANKER_TABLEAU[4][8] = false.
MythBecause RES290 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.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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