How Does the Concept of ‘Expected Value’ Apply to Solo versus Pool Mining?

The expected value (EV) of mining is theoretically the same for both solo and pool mining over a very long period, assuming the pool fee is zero. EV is the block reward multiplied by the probability of finding a block.

In reality, a pool's EV is slightly lower due to fees, but the pool offers a distribution of that EV over time, while solo mining offers a single, large, but highly uncertain payout.