Higher Difficulty and Less Profit

So I mined with Claymore on Linux for 24 hours at a higher difficulty (16000). My shares were roughly half - as expected - but my profit was also roughly half. Isn’t double.difficulty supposed to double share value on average? Note that I also had about 10 invalid shares vs 20 normally in a day. Which is also expected. No other changes or anomalies.

p.s. By double profit I mean half shares at twice value so profit should be equal on average over time.

I don’t believe 24 hours is enough time to average. I would think anything from 3-7 days would paint a much clearer picture. Especially considering most pools increase your share the longer you stick to that pool.

You may be right. Based on probability it could do horribly for a few days
then suddenly become very lucky.

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