The 37% Rule
The Secretary Problem & Optimal Stopping Strategy
📚 Introduction
🤔 What is the Secretary Problem?
Imagine hiring from 100 candidates with these rules:
- Candidates interviewed in random order
- Must decide immediately after each interview
- Once rejected, cannot go back
- Once hired, process ends
这个问题的核心困境是：你永远不知道后面还有没有更好的人选。 太早选择可能错过更优秀的候选人，太晚选择可能已经错过了最佳人选。
✨ The 37% Rule (Optimal Stopping)
Mathematicians found an elegant solution:
- Observation Phase：Interview first 37%, only observe, remember the best
- Selection Phase：From 38% onwards, pick first one better than observed best
Optimal ratio = 1/e ≈ 0.368 ≈ 37%
This gives ~36.8% chance of picking the best - the highest achievable!
🌍 Real Applications
The 37% rule also applies to:
- Renting：How many apartments to view?
- Dating：How many people to date?
- Shopping：How many options to compare?
- Investing：How long to observe?
Reality is complex, but the 37% rule provides a valuable framework.
⚙️ Parameters
Preview
Observation Phase: First 7
Selection Phase: # 8 onwards
Selection Phase: # 8 onwards
🎮 Interactive Simulation
🎲
Click to start simulation
Experience the 37% rule
📊 Batch Statistics
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Click to run batch simulation
Verify the 37% rule