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I'm trying to solidify my understanding of Proof-Of-Stake consensus, and one thing I've been left wondering is how to figure the probability of being chosen to be a validator. Are the chances of being selected based on the amount of currency in circulation, or the amount of currency being staked on the network?

As a follow up (if it applies); in a PoS system that has a probability of being chosen only based on the total network amount being staked, wouldn't that mean a theoretical "51%" attack wouldn't have to own 51% of the market cap per-se, but actually only 51% of the "total stake"? In this scenario it seems like an attack like this would be much easier to carry out if the network isn't being widely staked with a moderate percentage of the total circulation.

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