The Formula
Probability of finding at least one share at target difficulty:
P(≥1 share) = 1 - e^(-λ)
Where λ = (hashrate / target_hashrate) × (duration / 600)
Best Share Distribution
The chart shows the probability distribution of your best share using Gumbel distribution (extreme value theory). The distribution is right-skewed — most sessions land near the peak, but occasionally luck pushes it much higher.
Median Expected Best Share
The yellow dashed line marks the median — the difficulty you have a 50/50 chance of beating in the given time window. Half of all mining sessions of this length will produce a best share above this value, half below. It's a more intuitive benchmark than the mean, since the long right tail pulls the mean higher.
Calculated as: median = (total_hashes / 2³²) × 1.4427
Why It Matters
Your best share is your closest attempt at finding a block. If it exceeds network difficulty, you found a block. The median line gives you a realistic expectation for any given session.