Staking Rarible

1. The main formula for RARI token holders: Y = 0,35 / 365 * N + 0,3 -> Y - end value
   -> N - number of full staking days (numbering starts at zero)
2. Rewards of each staker exclusive of rewards of the others:
   V = A * (0,3 + 0,35 * (N - 1) / 365) -> V - total rewards of each staker inclusive of their locked token amount -> A - locked amount
3. Distribution formulas for each staker for day i :

• V(1).i - first staker’s reward
• V(2).i - second staker’s reward.
  ……………….
• V(N).i - N staker’s reward.

4. Calculation of each staker’s reward amount in the context of all other stakers’ contributions for day i: V(I am).i / V(all stakers).i = P.i V(all stakers).i = V(1).i + V(2).i + V(3).i + ... + V(N).i where -> P.i - is the amount of an individual reward against the contributions of all stakers.
5. Dividing the weekly rewards of all stakers by 7 to get the daily reward amount: 25000 / 7 days = 3571,43
6. S - my reward for day i among other stakers’ rewards: S.i = P.i * 3571,43
7. At the end of the week we get: S(1...7) = S(1) + S(2) + ... + S(i) + ... + S(7)

Example:

1. I own 100 RARI and I wish to stake them.
2. There is a total of 3 such stakers (including myself). Let Alice stake 300 Rari and Bob - 600 Rari. - “I am” started staking at the beginning of the week. - Alice started staking on day 3 (incl).
   - Bob started staking on day 5 (incl).
3. All of us will hold tokens until the end of the week: - “I am” held his token for 7 days
   - Alice held hers for 5 days
   - Bob held his tokens for 3 days
4. Let’s calculate the final reward amount for day 1 for “I am”: V(I am).1 = 100 * (0,3 * 2 + 0,35 * (1 - 1)/365) = 30,00
5. The final reward amount for “I am” for day 2: V(I am).2 = V(I am).1 + 100 * 0,35 * (2 - 1)/365) = 30,10
6. And so on in the same fashion the reward amount increases every day as per the formula below:
   V(I am) = A * (0,3 + 0,35 * (N - 1)/365)
7. We then calculate the reward amount (P) of all stakers per certain day. Let’s take day 5: - by this day I am has held his tokens for 5 full days. - Alice - for 3 full days. - Bob - for 1 full day.

P(I am).5 = V(I am).5 / ( V(I am).5 + V(Alice).5 + V(Bob).5) = = 100 * (0,3 + 0,35 * (5 -1)/365) / (100 * (0,3 + 0,35 * (5 -1)/365) + 300 * (0,3 + 0,35 * (3 -1)/365 + 600 *(0,3 + 0,35 * (1 - 1) / 365) = 0,100956

9. Hence, the reward for day 5 from the daily norm of 3571,43 RARI would equal: S(I am).5 = P(I am).5 * 3571,43 = 360, 56 RARI
10. This happens every day and once 25000 tokens are given to all stakers, you get: S(I am)(1..7) = 3571,43 + 3571,43 + 897,13 + 897,12+ 360, 56 + 360, 55 + 360,54 = 10018,76 RARI

Full version (with graphics and spreadsheet): https://docs.google.com/document/d/1W6PpRnALfMZi3m2dAhvfCt7uEJTODs3vo5YWGDJ7p-Y/edit?usp=sharing