A weighted (or biased) coin flip is a probability tool where the two outcomes don't have equal 50/50 odds. Instead, you can customize the bias percentage — for example, setting a 70% chance for Option A and 30% for Option B. This is useful for making decisions when you're leaning toward one option but still want an element of chance. Unlike a physical coin, this digital tool gives you full control over the probability distribution.

The tool uses a pseudo-random number generator (Math.random()) which produces a value between 0 and 1 with uniform distribution. If your bias is set to 70% for Option A, then any random value ≤ 0.70 results in Option A, and values > 0.70 result in Option B. Over many flips, the Law of Large Numbers ensures the actual distribution converges toward your set bias. Each individual flip remains independent — past results don't influence future outcomes (no gambler's fallacy here!).

Biased coin flips have many real-world applications:
• Decision-making with preference: You're 80% sure about going with Plan A but want a small chance of picking Plan B for variety.
• Randomized testing (A/B testing): Route 70% of traffic to version A and 30% to version B.
• Game design: Create unbalanced random events (e.g., a boss drops rare loot 15% of the time).
• Teaching probability: Demonstrate how sample distributions converge to theoretical probabilities over many trials.
• Breaking decision paralysis: When you're stuck between two choices, a weighted flip can nudge you while still leaving room for spontaneity.

This depends on the Law of Large Numbers. With a small number of flips (e.g., 10-20), the actual percentage can deviate significantly from your set bias due to random variance. As you approach 100+ flips, the results typically converge closer to the theoretical probability. Beyond 1,000 flips, the actual distribution usually falls within a few percentage points of your bias setting. Use the "Flip 10×" button to quickly accumulate data and observe this convergence in real time!

While this tool is fun and can help break decision paralysis, we recommend using it as a thinking aid rather than a definitive decision-maker for critical life choices. A useful technique: assign your preferred option a higher bias (e.g., 75%), flip the coin, and observe your emotional reaction to the result. If you feel disappointed with the outcome, that's valuable data — it reveals what you actually wanted all along. The coin doesn't make the decision; it helps clarify your feelings.