Add game environment: numeric dueling

[cwing-nvidia]

Add Numeric Dueling Environment

Overview

Adds a new probabilistic, simultaneous-move, multi-round number-selection game designed to train LLM capabilities in numerical reasoning, risk assessment, and strategic thinking under uncertainty.

What's Implemented

Game engine with 9 rule variants:

• 3 bust rules (Standard, Soft, Probabilistic)
• 3 win rules (Highest, Closest to R, Cumulative)
• Flexible configuration (rounds, number ranges, opponent types)

Infrastructure:

• Session-based state management for multi-round games
• Dynamic prompt generation based on game state
• Pluggable opponent interface (Random, Fixed, Adaptive)
• Per-round verification with immediate reward signals
• Full game history tracking

Testing:

• 42 automated tests (18 unit + 13 integration + 11 error handling) - all passing
• Human interactive client for manual testing
• Tested all 9 rule variants with GPT-4

Documentation:

• Comprehensive README with game spec
• Detailed usage instructions
• Test documentation

Request for Guidance: Multi-Round Support

This environment is designed for multi-round gameplay (e.g., 5 rounds per game), where the agent should:

1. Call /seed_session (initialize game)
2. Loop for N rounds:
   • Call /get_prompt (get current round's dynamic prompt)
   • Send prompt to LLM
   • Call /verify (submit LLM response, get reward)
3. Game state persists across rounds via session management

Observed Behavior:

• ng_collect_rollouts + simple_agent calls /verify once per JSONL row
• Human interactive client successfully loops through all rounds by repeatedly calling /verify
• Server correctly maintains state across multiple /verify calls

Questions:

• Does NeMo Gym currently support multi-turn environments where agents need to call /verify multiple times per episode (not just multiple tool calls within one turn)?
• Are there existing environments with similar multi-round patterns I can reference?
• What's the intended pattern for environments where:
  • Prompts are dynamically generated based on evolving game state (via /get_prompt)
  • State persists across multiple agent-environment interaction cycles
  • Multiple verification steps are needed per episode

The environment itself is fully functional - it's the agent workflow integration that needs guidance.

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