The gaming analogy holds up better than most, with one correction that matters for the bankroll part: mining has no memory at all. Every hash is an independent draw, so "I am already ahead, raise the stake" or "stop at a profit target" cannot change the expected outcome. The only thing that changes your expected income is hashrate, i.e. how many tickets per second you buy, and the only thing bankroll management changes is the variance you personally feel.
Two concrete numbers, because they made it click for me when I wrote a tiny miner to watch this happen:
At difficulty 1, one share needs about 4.3 billion hashes on average. A pool assigns you a difficulty so that you produce a share every few seconds; those shares are your "tickets", not wins. A block is a share that also happens to beat the network target.
A 4-core laptop does roughly 0.8 MH/s in Python. At the current network difficulty that is about 15 billion years per block on average. Same coin flip as an ASIC, you just flip it a trillion times slower.
So the pool is not a casino that pays out on luck. It is a bookkeeper that converts your luck into a steady average by counting tickets, and solo mining is the same game without the bookkeeper: exact same expected value, wildly different variance.
The gaming analogy holds up better than most, with one correction that matters for the bankroll part: mining has no memory at all. Every hash is an independent draw, so "I am already ahead, raise the stake" or "stop at a profit target" cannot change the expected outcome. The only thing that changes your expected income is hashrate, i.e. how many tickets per second you buy, and the only thing bankroll management changes is the variance you personally feel.
Two concrete numbers, because they made it click for me when I wrote a tiny miner to watch this happen:
So the pool is not a casino that pays out on luck. It is a bookkeeper that converts your luck into a steady average by counting tickets, and solo mining is the same game without the bookkeeper: exact same expected value, wildly different variance.