We study how to allocate inference-time compute for competitive programming under fixed budgets. Evaluating 216 Codeforces problems across Divisions 1-3, we compare agent-based reasoning with repeated independent sampling (k-shot) as a function of both cost and number of model calls. Across models and difficulty levels, k-shot consistently achieves a better accuracy-cost and accuracy-query tradeoff. This gap persists despite prompt caching in agent frameworks, indicating lower per-call effectiveness. Our results show that, for self-contained algorithmic tasks, independent exploration can outperform deeper agentic reasoning under realistic resource constraints. We also provide a budget-allocation analysis when the inference budget is fixed, and prove that a cost-optimal solver minimizes the principled metric log failure likelihood per dollar.