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FINAL TOTAL RESOLUTION [RES251] · 5-CARD PROOF

Player 4 + A (1) vs. Banker 4 (Stands at 4): 5-Card Resolution #251

In walkthrough RES251, Player opens with 2+2 (4) and draws fifth-card A (1) for a modulo-10 total of 5, while Banker opens with 2+2 (4) and stands pat at 4 (5-card P outcome).

RES251 Player Path
P:4->5
RES251 Banker Path
B:4->4
RES251 Deal Length
5 Cards
RES251 Showdown
P (5v4)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 5-card resolution RES251 (P4+1->5 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 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

RES251 Four-Card Opening Deal
Player 2+2=4 vs Banker 2+2=4

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

RES251 Fifth-Card Modulo Proof
(4 + 1) mod 10 = 5 via A

Player draws fifth-card A (value 1), transforming two-card 4 into three-card 5.

RES251 Banker Tableau Lookup
BANKER_TABLEAU[4][1] = false

Banker 4 stands pat at 4 without pulling sixth-card 9 (9).

RES251 Card Count & Winner
5 Cards -> P (5 vs 4)

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

RES251 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 · RES251

Step-by-Step Card Arithmetic for RES251: P(2+2)+A vs B(2+2)

Hand record [RES251] tracks Player 4 (2+2) facing Banker 4 (2+2); with zero naturals on the felt, the fifth card A (worth 1) arrives and 5 calculates the mod-10 residue to 5.

[RES251-B] Evaluating bankerShouldDraw(4, 1)=false (4-point six-value gate (2..7)) in [RES251], Banker 4 preserves 4 while 9 (9) remains undealt.

Complete 5-Card Resolution Trace for RES251
RES251 StageRES251 CardsRES251 Modulo MathRES251 Status
[RES251:Init]P(2+2)=4 vs B(2+2)=4playerShouldDraw(4)=true4-Card Deal
[RES251:5th]Player +A (1)(4+1) mod 10 = 55th Card Sideways
[RES251:6th]Banker Stands (skip 9=9)Locked at 45-Card Final
[RES251:Settle]P=5 vs B=4Winner: PBig Road +P
  • [RES251-1] Confirm [RES251] opening P=4 (2+2) and B=4 (2+2) lack Natural 8/9.
  • [RES251-2] Add [RES251] fifth-card A (1) to P=4 for (4+1) mod 10 = 5.
  • [RES251-3] Run [RES251] BANKER_TABLEAU[4][1]=false to settle 5 vs 4 (P).
SETTLEMENT & SCOREBOARD · RES251

Showdown Settlement & Scoreboard Logging for RES251 (5 vs 4)

[RES251-C8] Comparing [RES251] final totals (5c), Player 5 vs Banker 4 awards [RES251] to Player (P), which pays 1:1 even money on [RES251] Player boxes with zero commission deducted and appends P to BBPPBPPPBB.

[RES251-D5] Side-bet & road check for [RES251] (P4+1->5 vs B4->4, 5c): [RES251] leaves [RES251] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=4) and leaves [RES251] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES251] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES251, Banker 4 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card A (value 1) via BANKER_TABLEAU[4][1] = false.
MythBecause RES251 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.
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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