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Yeah those words don't sound good together. That is how miners work though. Even in Bitcoin, a mining node could take minutes, hours, or days to become the "winner" of the next block and receive payout.

The "$10 / day" calculations are estimated payouts averaged out over time. If you look at a terminal for your own miner, the payments come at sporadic times.

Agreed. I think lottery isn’t the best term. It’s just a mechanism that randomly distributes based on how much “power” you’ve got. Having a more predictable distribution method would be nice

As long as it keeps dripping into my wallet I'm OK with it.