📖 Overview
Use this calculator to model fair or biased coin sequences and repeated session outcomes.
⚙️ How It Works
Uses a binomial model to estimate the probability of getting at least a target number of heads in a sequence of flips.
The Formula
P(X >= k) = sum_{i=k..n} C(n,i) * p^i * (1-p)^(n-i)
| n | Number of flips per session |
| p | Probability of heads for each flip |
| k | Minimum heads target |
💡Fair coin default is p = 0.5. For biased coins, use your estimated heads probability.
Quick Reference
| Scenario | Probability |
|---|---|
| At least 1 head in 3 fair flips | 87.5% |
| At least 3 heads in 5 fair flips | 50.0% |
| At least 6 heads in 10 fair flips | 37.7% |
| At least 8 heads in 10 fair flips | 5.47% |
Practical Tips
💡 Small changes in target heads can heavily change odds for short sequences.
💡 Use multiple sessions to model repeated attempts over a night.
Frequently Asked Questions
❓ Can I model biased coins?
Yes, set heads probability to any value between 0 and 100.
❓ Does order of heads/tails matter here?
No, only the total count of heads matters.