Formulas

The formula below is to determine the specific rewards a user has made between time t=s and t=s+n, calculated per vault the user has locked tokens on in the game:

where:

and

s: Rebalancing period of the vault when the user basket has been created.

n: Number of rebalancing periods of the underlying vaults.

i: Underlying protocol number from whitelist.

Rs,s+n: Rewards build up for a specific user between t=s and t=s+n, in the same currency as Ut when Rs,s+n0.

RLTt,i: Reward per locked token, share of rewards from protocol i at time t per locked token on a specific vault, in the same currency as Ut when RLTt,i0.

cumRLTt: Cumulative Reward per locked token on time t.

Ai: Allocation on protocol i by game player (in nr of DRB tokens).

Pt,i: Price of protocol LP token i at time t.

PFt: Performance Fee at time t, set by the DAO, currently 10%.

Ut: Total Underlying amount in the vault at time t.

TLTt: Total Locked Tokens, total amount of Derby Tokens (DRB) locked in the game on a vault at time t.

To penalize bad behavior, game players receive a small penalty in the form of slashed Derby tokens if the performance of their underlying portfolio is negative. This penalty is computed using a simple formula:

Ps,s+n: Penalty in amount of Derby tokens (DRB) to be slashed

Ed,u: Exchangerate DRB/UnderlyingToken

NRF: Negative Reward Factor (between 0 and 1), not 100% of the negative rewards have to be slashed.