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FINAL TOTAL RESOLUTION [RES245] · 5-CARD PROOF

Player 4 + 10 (0) vs. Banker 4 (Stands at 4): 5-Card Resolution #245

In walkthrough RES245, Player opens with 2+2 (4) and draws fifth-card 10 (0) for a modulo-10 total of 4, while Banker opens with 2+2 (4) and stands pat at 4 (5-card T outcome).

RES245 Player Path
P:4->4
RES245 Banker Path
B:4->4
RES245 Deal Length
5 Cards
RES245 Showdown
T (4v4)
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 RES245 (P4+0->4 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

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

RES245 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.

RES245 Fifth-Card Modulo Proof
(4 + 0) mod 10 = 4 via 10

Player draws fifth-card 10 (value 0), transforming two-card 4 into three-card 4.

RES245 Banker Tableau Lookup
BANKER_TABLEAU[4][0] = false

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

RES245 Card Count & Winner
5 Cards -> T (4 vs 4)

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

RES245 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not T vs B.

MODULO-10 ARITHMETIC · RES245

Step-by-Step Card Arithmetic for RES245: P(2+2)+10 vs B(2+2)

Matrix coordinate [RES245] isolates Player two-card 4 (2+2) and Banker 4 (2+2); dealing fifth-card 10 (0) yields raw 4 that retains the rightmost digit to 4.

[RES245-B] Because BANKER_TABLEAU[4][0]=false (4-point six-value gate (2..7)) in [RES245], Banker 4 locks 4 at 5c (leaving 10=0 -> 4 unpulled).

Complete 5-Card Resolution Trace for RES245
RES245 StageRES245 CardsRES245 Modulo MathRES245 Status
[RES245:Init]P(2+2)=4 vs B(2+2)=4playerShouldDraw(4)=true4-Card Deal
[RES245:5th]Player +10 (0)(4+0) mod 10 = 45th Card Sideways
[RES245:6th]Banker Stands (skip 10=0)Locked at 45-Card Final
[RES245:Settle]P=4 vs B=4Winner: TBig Road +T
  • [RES245-1] Confirm [RES245] opening P=4 (2+2) and B=4 (2+2) lack Natural 8/9.
  • [RES245-2] Add [RES245] fifth-card 10 (0) to P=4 for (4+0) mod 10 = 4.
  • [RES245-3] Run [RES245] BANKER_TABLEAU[4][0]=false to settle 4 vs 4 (T).
SETTLEMENT & SCOREBOARD · RES245

Showdown Settlement & Scoreboard Logging for RES245 (4 vs 4)

[RES245-C0] Comparing [RES245] final totals (5c), Player 4 vs Banker 4 awards [RES245] to Tie (T), which pushes main [RES245] Player/Banker wagers while settling [RES245] Tie bets at 8:1 or 9:1 and appends T to BBPPBBPBPB.

[RES245-D3] Side-bet & road check for [RES245] (P4+0->4 vs B4->4, 5c): [RES245] leaves [RES245] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=4) and leaves [RES245] Panda 8 inactive (needs winning 3c Player 8, got P=4); on [RES245] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES245, Banker 4 evaluates Player's three-card total (4) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 10 (value 0) via BANKER_TABLEAU[4][0] = false.
MythBecause RES245 resolves as T, the next derived-road mark must match T'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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