NumTrade
A Skill-Based Interactive Game Platform with Behavioral Design
& Transparent Payout Mechanics

Engineering Team — NumTrade Labs | 11 May 2025

Abstract. NumTrade combines behavioral economics, deterministic mathematics and RBI-compliant escrow. Single-node benchmarks sustain 2 137 bets/s at 230 ms p₉₅ latency. Hourly Merkle roots and SQL-verified supply invariants guarantee that not a single paisa appears without cryptographic proof.

Executive Summary

Strategic purpose: tap-to-play, real-money contests where outcomes are provably fair.
Frontend: React 19 (Vite) powering Web + RN apps via a single code-base.
Backend: Node 20 | PostgreSQL 16 (Timescale) | Socket.IO < 1 s bet ticks.
Payout design: pool splits among accounts that chose the least-staked digit, weighted by stake and time.
Merkle trust layer: every round hashed; root stored in round_results.merkle_root and exposed publicly.
Legal framing: “game of mere skill” (§ 12, Public Gambling Act 1867); INR custody via RBI-licensed nodal escrow.

Mathematics of Winner Selection & Payouts

1 · Winner Picking

Players stake an amount \(A_i\) on digit \(n\in\{0,\dots,9\}\). The digit with the minimum aggregate stake wins:

\[ n^{\star} = \underset{n}{\arg\min}\; S(n), \quad S(n) = \sum_{i \in B_n} A_i \]

2 · Contribution Score

Each winning bet’s contribution weighs stake (\(\gamma=1.3\)) and time (logistic decay):

\[ C_i = A_i^{\gamma} \left( \frac{1}{1 + e^{\alpha (t_i / T - 0.5)}} \right) \\ P_i = \frac{C_i}{\sum_{j \in W} C_j} \cdot \text{Pool} \]

3 · Pool Split

For round pool \(P\) and winning set \(W\):

\[ P_i \;=\; \frac{C_i}{\sum_{j\in W} C_j}\; P \]

Conservation holds: \(\sum_i P_i = P\).

Transparency & Compliance Pillars

Merkle-Tree Ledger

Each bet → SHA-256 → Merkle tree; root committed to round_results. Anyone can verify inclusion with an \(O(\log n)\) proof.

MERKLE_ROOT = MerkleTree([
  sha256(tx_1), sha256(tx_2), …
]).root

Avoid-the-Crowd Strategy

Echoing a “Keynesian beauty contest,” the least-staked digit wins.

\[ n^{\star}= \arg\min_{n}\sum_{i\in B_n}A_i \]

Audited Payouts

SQL triggers block any mint/burn drift (supply_audit_v2); deviations halt cron and page SRE.

RBI-Compliant Escrow

INR funds sit in a segregated nodal account with a licensed aggregator; withdrawals require KYC and move via audited UPI/IMPS rails.

Independent Audit Access

Request read-only database access and sample Merkle proofs via legal@numtrade.in.

Download PDF — Mathematical Model & Payout Logic

NumTrade A Skill-Based Interactive Game Platform with Behavioral Design & Transparent Payout Mechanics