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OPTIMAL

CHOICE

Can intuition outsmart mathematics when choices are irreversible? Challenge Game Theory’s famous Optimal Stopping problem.

HOW TO PLAY

1

REVEAL

The system randomly generates an array according to a set rule and displays it element by element

2

DECIDE

You must immediately Accept or Reject each number

3

NO RETURN

Once rejected, it's gone forever. Once accepted, game ends

YOUR GOAL

Pick the highest value in the sequence without knowing what comes next!

Behind this seemingly simple number-picking game lies a fascinating field of decision science: Optimal Stopping Theory.

e

The Math Core: The 1/e Strategy & 37% Rule

The logical prototype of this game is known as the "Secretary Problem". Mathematicians have rigorously proven that when facing n randomly presented options with no ability to go back, the optimal strategy is: reject the first n/e (approx. 36.8%) options as pure observation; then, select the first option that surpasses all previously seen values. By following this mathematical rule, you have approximately a 36.8% chance of landing the absolute best value — whether the total is 10 or 1 million. This is the certainty that the constant e points to in a chaotic world.

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The Economics Angle: Search Cost & Opportunity Cost

From an economics perspective, this game simulates real-world Search Theory. In hiring, renting, or dating, information is not free — every "skip" carries a dual cost:

  • Opportunity Cost: You may have just passed the globally optimal choice.
  • Search Cost: As the sequence progresses, fewer options remain, and psychological pressure and risk intensify.

It tests not just your luck, but how you rationally balance "continued exploration (gathering information)" vs. "immediate exploitation (locking in gains)" under incomplete information and uncertainty.

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Why Do We Test This?

The human brain has developed unique "heuristic biases" through evolution. We tend to stop too early (due to risk aversion) or decide too late (due to greed). With this tool, you can intuitively compare your own decision-making behavior against the mathematical optimum, training your calm intuition in complex strategic situations.