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FINAL TOTAL RESOLUTION [RES241] · 5-CARD PROOF

Player 0 + 10 (0) vs. Banker 4 (Stands at 4): 5-Card Resolution #241

In walkthrough RES241, Player opens with 10+K (0) and draws fifth-card 10 (0) for a modulo-10 total of 0, while Banker opens with 2+2 (4) and stands pat at 4 (5-card B outcome).

RES241 Player Path
P:0->0
RES241 Banker Path
B:4->4
RES241 Deal Length
5 Cards
RES241 Showdown
B (0v4)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 5-card resolution RES241 (P0+0->0 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

RES241 Four-Card Opening Deal
Player 10+K=0 vs Banker 2+2=4

Verified non-natural start via handTotal([10,K])=0 and handTotal([2,2])=4.

RES241 Fifth-Card Modulo Proof
(0 + 0) mod 10 = 0 via 10

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

RES241 Banker Tableau Lookup
BANKER_TABLEAU[4][0] = false

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

RES241 Card Count & Winner
5 Cards -> B (0 vs 4)

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

RES241 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 · RES241

Step-by-Step Card Arithmetic for RES241: P(10+K)+10 vs B(2+2)

During tableau case [RES241], Player holds 10+K for 0 while Banker holds 2+2 for 4; drawing fifth-card 10 (0) shifts Player from 0 to 0, which reduces mod-10 to 0.

[RES241-B] Guided by 4-point six-value gate (2..7) against 10 (0) in [RES241], Banker 4 stands on 4 so the coup finishes in 5c without 4 (4).

Complete 5-Card Resolution Trace for RES241
RES241 StageRES241 CardsRES241 Modulo MathRES241 Status
[RES241:Init]P(10+K)=0 vs B(2+2)=4playerShouldDraw(0)=true4-Card Deal
[RES241:5th]Player +10 (0)(0+0) mod 10 = 05th Card Sideways
[RES241:6th]Banker Stands (skip 4=4)Locked at 45-Card Final
[RES241:Settle]P=0 vs B=4Winner: BBig Road +B
  • [RES241-1] Confirm [RES241] opening P=0 (10+K) and B=4 (2+2) lack Natural 8/9.
  • [RES241-2] Add [RES241] fifth-card 10 (0) to P=0 for (0+0) mod 10 = 0.
  • [RES241-3] Run [RES241] BANKER_TABLEAU[4][0]=false to settle 0 vs 4 (B).
SETTLEMENT & SCOREBOARD · RES241

Showdown Settlement & Scoreboard Logging for RES241 (0 vs 4)

[RES241-C2] Comparing [RES241] final totals (5c), Player 0 vs Banker 4 awards [RES241] to Banker (B), which pays 0.95:1 on 5%-commission [RES241] layouts (or 0.5:1 on 6 at No-Commission [RES241] tables) and appends B to BBPPBPBBPP.

[RES241-D6] Side-bet & road check for [RES241] (P0+0->0 vs B4->4, 5c): [RES241] leaves [RES241] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=4) and leaves [RES241] Panda 8 inactive (needs winning 3c Player 8, got P=0); on [RES241] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES241, Banker 4 evaluates Player's three-card total (0) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 10 (value 0) via BANKER_TABLEAU[4][0] = false.
MythBecause RES241 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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