Understanding Your Chances of Finding a Target Share
You've heard about that legendary 1 G share... but how special is it really? Adjust your hashrate and target difficulty below to discover the probability. The results might surprise you.
Your Mining Parameters
Probability by Time Period
| Time Period | Probability of Success | 1 in X Chance | Interpretation |
|---|---|---|---|
| 1 Hour | 0.21% | 1 in 476 | Very unlikely in such a short time |
| 1 Day | 4.88% | 1 in 20 | Small chance, but possible |
| 1 Week | 29.5% | 1 in 3 | About 1 in 3 chance |
| 1 Month (30 days) | 78.3% | 1 in 1.3 | Good odds, but not guaranteed |
| 1 Year (365 days) | ~100% | ~1 in 1 | Almost certain |
What This Chart Shows
This chart displays the cumulative probability of finding a share with your target difficulty over time. The curve shows that as time passes, your chances of success increase, but never reach 100% certainty.
Solo mining follows an exponential distribution, which means finding a share is a random event. You might find one quickly, or it might take much longer than expected. The "expected time" shown above is the mathematical average - but here's the key insight: you might expect a 100% chance after the "expected time," but that's not how random processes work. Some miners get lucky and find shares quickly, while others take much longer. The 63.2% represents the balance point - it's the mathematical certainty that comes from 1 - 1/e (where e β 2.718 is Euler's number). This constant appears in all exponential distributions, from radioactive decay to waiting times.
The median time (13.8 days) is the true 50/50 point. If you ran this scenario 100 times, you'd find a share faster than this time in 50 attempts, and slower in the other 50. It's always shorter than the expected time because a few very long waits pull the average up.
The Math Behind the Chart
The probability calculations are based on the exponential distribution, which models the time between random, independent events. In Bitcoin mining, each hash attempt is independent with a fixed probability of success.
Expected Time: The average time to find a share is calculated as:
Expected Time = (Difficulty Γ 2Β³Β²) / Hashrate
Where difficulty is your target share difficulty and hashrate is in hashes per second.
Cumulative Probability: The chance of finding a share within time t follows:
P(success within time t) = 1 - e-Ξ»t
Where Ξ» (lambda) = 1 / Expected Time, and e β 2.718 is Euler's number.
The 63.2% Constant: When t equals the expected time, the formula becomes:
P(success within expected time) = 1 - e-1 β 1 - 0.368 = 0.632 = 63.2%
This is why the probability at the expected time is always 63.2%, regardless of your hashrate or difficulty.
Median Time: The 50% probability point (median) occurs at:
Median = Expected Time Γ ln(2) β Expected Time Γ 0.693
Where ln(2) is the natural logarithm of 2 (β 0.693). This means the median time is always shorter than the expected timeβabout 69.3% of it.