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FINAL TOTAL RESOLUTION [RES293] · 5-CARD PROOF

Player 4 + 8 (8) vs. Banker 4 (Stands at 4): 5-Card Resolution #293

In walkthrough RES293, Player opens with 2+2 (4) and draws fifth-card 8 (8) for a modulo-10 total of 2, while Banker opens with 2+2 (4) and stands pat at 4 (5-card B outcome).

RES293 Player Path
P:4->2
RES293 Banker Path
B:4->4
RES293 Deal Length
5 Cards
RES293 Showdown
B (2v4)
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 RES293 (P4+8->2 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

RES293 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.

RES293 Fifth-Card Modulo Proof
(4 + 8) mod 10 = 2 via 8

Player draws fifth-card 8 (value 8), transforming two-card 4 into three-card 2.

RES293 Banker Tableau Lookup
BANKER_TABLEAU[4][8] = false

Banker 4 stands pat at 4 without pulling sixth-card 2 (2).

RES293 Card Count & Winner
5 Cards -> B (2 vs 4)

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

RES293 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 · RES293

Step-by-Step Card Arithmetic for RES293: P(2+2)+8 vs B(2+2)

Hand record [RES293] tracks Player 4 (2+2) facing Banker 4 (2+2); with zero naturals on the felt, the fifth card 8 (worth 8) arrives and 12 calculates the mod-10 residue to 2.

[RES293-B] Guided by 4-point six-value gate (2..7) against 8 (8) in [RES293], Banker 4 stands on 4 so the coup finishes in 5c without 2 (2).

Complete 5-Card Resolution Trace for RES293
RES293 StageRES293 CardsRES293 Modulo MathRES293 Status
[RES293:Init]P(2+2)=4 vs B(2+2)=4playerShouldDraw(4)=true4-Card Deal
[RES293:5th]Player +8 (8)(4+8) mod 10 = 25th Card Sideways
[RES293:6th]Banker Stands (skip 2=2)Locked at 45-Card Final
[RES293:Settle]P=2 vs B=4Winner: BBig Road +B
  • [RES293-1] Confirm [RES293] opening P=4 (2+2) and B=4 (2+2) lack Natural 8/9.
  • [RES293-2] Add [RES293] fifth-card 8 (8) to P=4 for (4+8) mod 10 = 2.
  • [RES293-3] Run [RES293] BANKER_TABLEAU[4][8]=false to settle 2 vs 4 (B).
SETTLEMENT & SCOREBOARD · RES293

Showdown Settlement & Scoreboard Logging for RES293 (2 vs 4)

[RES293-C9] Comparing [RES293] final totals (5c), Player 2 vs Banker 4 awards [RES293] to Banker (B), which pays 0.95:1 on 5%-commission [RES293] layouts (or 0.5:1 on 6 at No-Commission [RES293] tables) and appends B to BBPPBBPBPB.

[RES293-D6] Side-bet & road check for [RES293] (P4+8->2 vs B4->4, 5c): [RES293] leaves [RES293] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=4) and leaves [RES293] Panda 8 inactive (needs winning 3c Player 8, got P=2); on [RES293] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES293, Banker 4 evaluates Player's three-card total (2) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 8 (value 8) via BANKER_TABLEAU[4][8] = false.
MythBecause RES293 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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