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NON-NATURAL MATCHUP [M3V5] · 100-BRANCH MATRIX

Player Starts 3 vs. Banker Starts 5 (M3V5): 100-Branch Resolution Matrix

When Player opens at 3 (10+3) and Banker opens at 5 (A+4) in matchup M3V5, neither side holds a Natural. Evaluating all 100 (fifth-card 0..9 × sixth-card 0..9) branches through resolveHand() yields 52 Banker wins, 34 Player wins, and 14 ties (0 four-card, 60 five-card, and 40 six-card branches).

Matchup M3V5 Start
P=3 vs B=5
M3V5 100-Branch Split
52B/34P/14T
M3V5 4c/5c/6c Branches
0/60/40
M3V5 Step 2 Action
P Draws
Engine-Verified Scoreboard · 34 Hands

Read the Board at Table Speed

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

Scoreboard trajectory paired with the 100-branch matchup matrix M3V5 (Player 3 vs Banker 5).

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 4 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 4 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

Matchup M3V5 Initial Deal
Player 10+3=3 vs Banker A+4=5

Non-natural 4-card opening verified via playerShouldDraw(3)=true.

M3V5 100-Branch Outcome Split
52 Banker / 34 Player / 14 Tie

Exact enumeration across all 100 (fifthCard 0..9 × sixthCard 0..9) value pairs.

M3V5 Card-Count Distribution
0 (4-card) / 60 (5-card) / 40 (6-card)

Branch counts by total cards dealt in matchup M3V5.

M3V5 Player Action Rule
Draws 5th Card on 3

Determines whether Banker 5 uses BANKER_TABLEAU[5][p3] or the null-stand rule.

M3V5 Banker Action Rule
Draws on 4/10 5th Cards

Exact Banker response profile in matchup M3V5.

EXACT 100-BRANCH ENUMERATION · M3V5

How Matchup M3V5 (Player 3 vs. Banker 5) Resolves Across Fifth & Sixth Cards

In matchup [M3V5], Player starts with 10+3=3 against Banker A+4=5. Because P=3 is in 0–5, Player always draws the fifth card (0..9), shifting Player to 3..2 and prompting Banker 5 to consult BANKER_TABLEAU[5].

Summing all 100 (fifth 0..9 × sixth 0..9) branches for [M3V5] produces 52 Banker wins, 34 Player wins, and 14 ties across 0 four-card, 60 five-card, and 40 six-card outcomes.

Matchup M3V5 100-Branch Breakdown by Fifth Card Value (0–9)
M3V5 5th CardM3V5 Player PathM3V5 Banker PathM3V5 10-Branch B/P/TM3V5 Hand Size
[M3V5:5th=0] 10(0)[M3V5:P3] P:3+0->3[M3V5:BPat] B=5 stands[M3V5:Split] 10B/0P/0T[M3V5:Size] 5 cards
[M3V5:5th=1] A(1)[M3V5:P3] P:3+1->4[M3V5:BPat] B=5 stands[M3V5:Split] 10B/0P/0T[M3V5:Size] 5 cards
[M3V5:5th=2] 2(2)[M3V5:P3] P:3+2->5[M3V5:BPat] B=5 stands[M3V5:Split] 0B/0P/10T[M3V5:Size] 5 cards
[M3V5:5th=3] 3(3)[M3V5:P3] P:3+3->6[M3V5:BPat] B=5 stands[M3V5:Split] 0B/10P/0T[M3V5:Size] 5 cards
[M3V5:5th=4] 4(4)[M3V5:P3] P:3+4->7[M3V5:B3] B=5 draws 6th[M3V5:Split] 2B/7P/1T[M3V5:Size] 6 cards
[M3V5:5th=5] 5(5)[M3V5:P3] P:3+5->8[M3V5:B3] B=5 draws 6th[M3V5:Split] 1B/8P/1T[M3V5:Size] 6 cards
[M3V5:5th=6] 6(6)[M3V5:P3] P:3+6->9[M3V5:B3] B=5 draws 6th[M3V5:Split] 0B/9P/1T[M3V5:Size] 6 cards
[M3V5:5th=7] 7(7)[M3V5:P3] P:3+7->0[M3V5:B3] B=5 draws 6th[M3V5:Split] 9B/0P/1T[M3V5:Size] 6 cards
[M3V5:5th=8] 8(8)[M3V5:P3] P:3+8->1[M3V5:BPat] B=5 stands[M3V5:Split] 10B/0P/0T[M3V5:Size] 5 cards
[M3V5:5th=9] 9(9)[M3V5:P3] P:3+9->2[M3V5:BPat] B=5 stands[M3V5:Split] 10B/0P/0T[M3V5:Size] 5 cards
  • [M3V5-Rule1] Verify non-natural opening: P(10+3)=3 vs B(A+4)=5.
  • [M3V5-Rule2] Apply Player 0–5 draw rule first, then Banker 5 response.
  • [M3V5-Rule3] Audit 52B/34P/14T matrix total and record onto shoe BBBBPPBPP.
Table Reality Check

Myth vs. Truth

MythWhen Player starts with 3 against Banker 5 (M3V5), the higher two-card start always wins most branches.
TruthIn [M3V5], third-card draw rules shift the 100-branch total to 52B / 34P / 14T.
MythA 6-card finish in M3V5 forces a Blue break mark on Small Road.
TruthSmall Road compares Big Road column depths two columns back; card count in M3V5 never affects derived road color.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

Read Every Derived Road at Table Speed

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