DeepSeek R1 vs GPT-4o: Advanced Reasoning Compared

Introduction

DeepSeek R1 introduces chain-of-thought reasoning at $0.27/1M tokens — a feature that GPT-4o lacks natively. This comparison tests both models on complex reasoning tasks that require step-by-step problem-solving.

How R1's Chain-of-Thought Works

DeepSeek R1 internally generates a reasoning trace before producing the final answer. You see both the thought process and the conclusion.

Prompt: "Solve this math problem..."
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R1 Internal: "Let me think step by step. First..."
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R1 Output: "<think>Step 1: ... Step 2: ...</think> Final answer: 42"

Test 1: Mathematical Proofs

Prompt: "Prove that the square root of 2 is irrational."

GPT-4o: Standard proof by contradiction. Clean, concise, 150 words. DeepSeek R1: Detailed step-by-step proof with explicit algebraic derivation. 400 words including reasoning trace.

Winner: DeepSeek R1 (more thorough, shows work).

Test 2: Logic Puzzle

Prompt: "There are 5 houses in a row. The Norwegian lives in the first house. The person who drinks milk lives in the middle..."

GPT-4o: Correct solution in 200 words. Logical but terse. DeepSeek R1: Full constraint propagation with explicit elimination steps. 600 words.

Winner: DeepSeek R1 (verifiable reasoning).

Test 3: Code Review with Reasoning

Prompt: "Find the security vulnerability in this code: [100 lines of Python]"

GPT-4o: Identified SQL injection and XSS. Good explanation. DeepSeek R1: Identified same issues plus subtle race condition. Better systematic approach.

Winner: DeepSeek R1 (more thorough analysis).

When to Use Each

| Task | Best Model | Why | |---|---|---| | Simple Q&A | GPT-4o | Faster, sufficient | | Math proofs | DeepSeek R1 | Step-by-step reasoning | | Logic puzzles | DeepSeek R1 | Systematic approach | | Quick coding | GPT-4o | Faster responses | | Security review | DeepSeek R1 | More thorough | | Essay writing | GPT-4o | Better prose flow | | Debugging | DeepSeek R1 | Shows reasoning path |

Cost Comparison

| Model | Complex Math (avg tokens) | Cost | |---|---|---| | DeepSeek R1 | 800 in / 1200 out | $0.0015 | | GPT-4o | 400 in / 600 out | $0.0070 | | R1 saves | — | 78% |

All testing done through AI API Hub's unified endpoint.

FAQ

Q: Can I use R1 for everyday chat? A: DeepSeek V3 is better for general chat. R1 is specialized for reasoning-heavy tasks.

Q: Does GPT-4o support chain-of-thought? A: Not natively. You must prompt it explicitly. R1 does it automatically.

Q: Which model handles ambiguous questions better? A: Both are good. R1 shows its reasoning, making it easier to understand decisions.