Proof of stake reward: 1 wallet with "x" ADAs vs. "n" wallets with "x/n" ADAs

English Education
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I would like to know if there is a difference running 1 Daedalus wallet with “x” ADAs (for example, x = 1,000,000 ADAs) and running “n” Daedalus wallets (lets say in this case n = 2, using two PCs), each wallet containing “x/n” ADAs (i.e. x/n = 500,000 ADAs). Which way gives your more rewards? Or there is no difference?

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I think you would earn more rewards with one wallet, let’s assume the interest is around 10% for staking. You would receive 100 000 :ada:, if you have 2 wallets with 500 000 :ada: you would not increase your chances a lot of being selected a slot leader for that epoch, let’s say 100 people are staking. The chance of you being selected is 1/100 thus 1% chance. If you have 2 wallets you would have 2/100 thus 2% chance. If a 100 000 people would be staking you would raise your odds with 0.001%. And the interest would only yield half of the one wallet hypothesis. I think the number for n needs to be insanely high in comparison to the number of total people staking to have an edge.

It all depends on the number of people staking.
Also there will be staking pools and I’m not sure how that would effect this hypothesis.

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Excellent explanation, thanks! Reading it I was thinking: will people be able to make “staking pool” (analogous to mining pools) so they can earn more constantly but in small quantities? I mean, how will people join and make the pools?

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You will be able to join a stake pool in the daedalus wallet. You can check the screenshots
at https://cardanoroadmap.com next to the Ouroboros delegating item under shelley, I’m afraid I can’t answer your question on how to create a staking pool, I’m guessing you would have to do so trough the api when running a full node but I’m not sure about this.

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I think this rule is not yet defined.
I guess, the bigger the stake, the bigger the node influence on the proof of stake. So, a single wallet would hold a bigger stack than two with half each. Besides, the cost of keeping two wallets running may increase by the divisions grow.

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The way I see it, the PoS rewards are proportional to how much ADA you have in your wallet, so in theory it should be exactly the same.

Example: 1 wallet with 100.000 would for example have 1% chance of winning. 2 wallets with each 50.000 would have both 0.5% chance of winning, added up 1%. So it wouldn’t matter.