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FINAL TOTAL RESOLUTION [RES271] · 6-CARD PROOF

Player 0 + 5 (5) vs. Banker 4 (Draws 9 (9)): 6-Card Resolution #271

In walkthrough RES271, Player opens with 10+K (0) and draws fifth-card 5 (5) for a modulo-10 total of 5, while Banker opens with 2+2 (4) and draws sixth-card 9 (9) for 3 (6-card P outcome).

RES271 Player Path
P:0->5
RES271 Banker Path
B:4->3
RES271 Deal Length
6 Cards
RES271 Showdown
P (5v3)
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 B B B P P P B B B B P
Big Eye Boy = = ≠ = ≠ ≠ ≠ ≠ = ≠ = = = = = ≠ ≠
Small Road ≠ ≠ ≠ ≠ = = ≠ ≠ ≠ = ≠ = = ≠ ≠
Cockroach Pig ≠ = = = ≠ = ≠ = ≠ ≠ ≠ = = ≠

Scoreboard sequence paired with 6-card resolution RES271 (P0+5->5 vs B4->3).

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

RES271 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.

RES271 Fifth-Card Modulo Proof
(0 + 5) mod 10 = 5 via 5

Player draws fifth-card 5 (value 5), transforming two-card 0 into three-card 5.

RES271 Banker Tableau Lookup
BANKER_TABLEAU[4][5] = true

Banker 4 draws sixth-card 9 (9) so (4+9) mod 10 = 3.

RES271 Card Count & Winner
6 Cards -> P (5 vs 3)

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

RES271 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 · RES271

Step-by-Step Card Arithmetic for RES271: P(10+K)+5 vs B(2+2)

Under audit [RES271], Player opens on two-card 0 (10+K) opposite Banker 4 (2+2), triggering a mandatory fifth-card pull of 5 (value 5) that settles via mod-10 arithmetic from 5 into 5.

[RES271-B] Because BANKER_TABLEAU[4][5]=true (4-point six-value gate (2..7)) in [RES271], Banker 4 takes sixth-card 9 (9) and 4+9=13 settles at 3.

Complete 6-Card Resolution Trace for RES271
RES271 StageRES271 CardsRES271 Modulo MathRES271 Status
[RES271:Init]P(10+K)=0 vs B(2+2)=4playerShouldDraw(0)=true4-Card Deal
[RES271:5th]Player +5 (5)(0+5) mod 10 = 55th Card Sideways
[RES271:6th]Banker +9 (9)(4+9) mod 10 = 36-Card Final
[RES271:Settle]P=5 vs B=3Winner: PBig Road +P
  • [RES271-1] Confirm [RES271] opening P=0 (10+K) and B=4 (2+2) lack Natural 8/9.
  • [RES271-2] Add [RES271] fifth-card 5 (5) to P=0 for (0+5) mod 10 = 5.
  • [RES271-3] Run [RES271] BANKER_TABLEAU[4][5]=true to settle 5 vs 3 (P).
SETTLEMENT & SCOREBOARD · RES271

Showdown Settlement & Scoreboard Logging for RES271 (5 vs 3)

[RES271-C9] Comparing [RES271] final totals (6c), Player 5 vs Banker 3 awards [RES271] to Player (P), which pays 1:1 even money on [RES271] Player boxes with zero commission deducted and appends P to BBPPBPBBPB.

[RES271-D3] Side-bet & road check for [RES271] (P0+5->5 vs B4->3, 6c): [RES271] leaves [RES271] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=3) and leaves [RES271] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES271] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES271, Banker 4 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[4][5] = true.
MythBecause RES271 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

Read Every Derived Road at Table Speed

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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