Coin Flip Probability Calculator

📖 Overview

Use this calculator to model fair or biased coin sequences and repeated session outcomes.

Use these default and higher-pressure example inputs to explore how sensitive this calculator is before using your real numbers.

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.

Use this tool when you need a fast decision during active planning or execution.
Use this before committing money, time, or tradeoffs that are hard to reverse.
Use this to compare options using the same assumptions across scenarios.

Results can be misleading if key inputs are missing, stale, or unrealistic.
Very small or very large values may amplify rounding effects and interpretation risk.
If assumptions change mid-decision, recalculate before acting.

💡 Small changes in target heads can heavily change odds for short sequences.

💡 Use multiple sessions to model repeated attempts over a night.

💡 Run a best-case, base-case, and worst-case scenario before deciding.

💡 Use recent real values, not ideal assumptions, for better accuracy.

❓ 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.