Making sense of the square root curation reward curve

The allocation of curation rewards in the steem blockchain follows a square root curve. This means that your vote will get more weight if there are not already a lot of votes on the post.

To better understand this algorithm, let’s start from the beginning. Each vote is assigned two values: rshares and weight. The first one is straightforward:

    rshares = vesting_shares * voting_power * vote_percentage

But what determines your share of the total reward is the weight parameter. If the amount of rshares already contributed to the post is RS0 and your vote’s contribution is RS, then weight is calculated as follows:

    weight = sqrt(RS0 + RS) - sqrt(RS0)

Of course, if the upvote was done before 30 minutes, it is also multiplied by another value, say Δt. The value Δt accounts for the reverse auction in the first 30 minutes after the post is created.

    Δt =
        t / 30        (if t < 30)
        1             (otherwise)

After 7 days, the curation rewards are distributed proportional to the weight value of each vote.

I made the following drawing to make the square root curve easier to understand.