Winning Banker bets pay 0.975 to 1 (2.5% commission), crossing below the 2.6932% zero-house-edge boundary. Never offered as an unconditioned walk-up game without offsetting rules because 2.5% vig is below the combinatorial break-even tax. Setting 0.458597 × (1 − c) − 0.446247 = 0 solves to c = 0.026932 (2.6932% exact break-even commission in an 8-deck shoe). At c = 2.5%, expected return is 0.458597 × 0.975 − 0.446247 = +0.000886 (+0.0886% in favor of the Banker ticket holder).
COMM25 rule audit scoreboard. Derived roads record past hand symmetry and never change COMM25 house edge.
This bead is at Row 2. Column 2 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 2 stopped exactly one row above this bead.
Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.
This bead is at Row 2. Column 2 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 2 stopped exactly one row above this bead.
Winning Banker bets pay 0.975 to 1 (2.5% commission), crossing below the 2.6932% zero-house-edge boundary
At c = 2.5%, expected return is 0.458597 × 0.975 − 0.446247 = +0.000886 (+0.0886% in favor of the Banker ticket holder)
Unchanged 1:1 even-money settlement on all winning Player hands (44.6247% win rate).
Evaluated across 9.5156% 8-deck Tie frequency (8:1 payout).
Theoretical actuarial boundary and promotional loss-cap coupon audits
[COMM25-MECHANISM] Winning Banker bets pay 0.975 to 1 (2.5% commission), crossing below the 2.6932% zero-house-edge boundary. Never offered as an unconditioned walk-up game without offsetting rules because 2.5% vig is below the combinatorial break-even tax. Across Theoretical actuarial boundary and promotional loss-cap coupon audits, pit supervisors enforce this exact settlement table on every 416-card shoe.
[COMM25-PROOF] Setting 0.458597 × (1 − c) − 0.446247 = 0 solves to c = 0.026932 (2.6932% exact break-even commission in an 8-deck shoe). At c = 2.5%, expected return is 0.458597 × 0.975 − 0.446247 = +0.000886 (+0.0886% in favor of the Banker ticket holder). Because each six-card deal is governed by the fixed third-card tableau, scoreboard trends on Big Eye Boy, Small Road, and Cockroach Pig cannot shift the -0.0886% (Player Adv.) Banker expectation.
| COMM25 Metric | COMM25 Banker | COMM25 Player | COMM25 Tie | COMM25 Baseline Ref |
|---|---|---|---|---|
| COMM25 Gross Payout | 0.975 to 1 | 1.000 to 1 | 8.000 to 1 | 8-Deck 416 Cards |
| COMM25 Win Probability | 45.8597% | 44.6247% | 9.5156% | Naturals 34.3049% |
| COMM25 House Edge | -0.0886% (Player Adv.) | 1.2351% | 14.3596% | Std 5%: 1.0579% |
| COMM25 Variance / Unit | 0.8822 | 0.9047 | 6.9742 | Code COMM25-V8 |
Enter any sequence to inspect the Big Road, Big Eye Boy, Small Road, Cockroach Pig, and next-hand previews.
About 64 minutes of lessons covering outcomes, the Bead Plate, Big Road columns, and dragon tails.
Train Third-Card Rule decisions, depth counting, lookback column references, and derived-road speed recognition.
Visual step-by-step breakdowns with closed captions, chapter markers, and full searchable transcripts.
Macau Cantonese, French, and mathematical table terms explained in plain English with road diagrams.
Direct answers to real student questions on dragon tails, tie handling, lookback rules, and table variants.
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