OpenAI o3 reasoning models use "thinking tokens" to reason through complex problems before responding. When o3 wins: 1) Multi-step mathematical reasoning - solves competition math problems (AIME) that GPT-4o cannot. 2) Complex code debugging - traces through logic step by step to find subtle bugs. 3) Scientific analysis requiring hypothesis formation and testing. 4) Legal and financial reasoning with multiple conditions and exceptions. 5) Strategy games and planning with long action sequences. When to stick with GPT-4o: 1) Simple factual Q&A - o3 is slower and costs more. 2) Creative writing - reasoning models are less creative. 3) Summarization and extraction - no reasoning benefit. 4) High-volume, cost-sensitive tasks. Cost comparison: o3-mini ($1.1/1M input) vs GPT-4o ($5/1M) - o3-mini is cheaper! o3 full ($15/1M input) - premium for hardest problems. Prompting o3: 1) Do not explain your reasoning process - let o3 reason on its own. 2) Be direct about the final answer format needed. 3) Can use shorter prompts since o3 explores the problem space internally. 4) Set reasoning_effort to "low" for simpler problems to save tokens. Use case routing: implement task complexity classifier to route to o3-mini or o3 only when complexity justifies the higher latency (15-60 seconds) and potential cost.