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How to earn the most rewards in iZUMi’s LiquidBox?

The best strategy to earn rewards is to set the price range on Uni V3 exactly the same as the izumi liquidity mining price range, which will enable the liquidity providers to earn the most profits.
The rewards for LiquidBox will be distributed as iZi tokens combined project tokens, which are provided by each project team to incentivize their tokens’ liquidity.
In izumi's LiquidBox, the algorithm converts each NFT into an FT to calculate the percentage of rewards that should be earned for that NFT. The algorithm for converting NFTs into FTs is freely customizable, and the izumi official version is used by default, which is the following:
vLiquidity=LN2vLiquidity=L*N^2
The “L” is the Liquidity contained in the NFT and “N” represents the number of ticks contained in the part of the incentive price range that overlaps with the NFT liquidity placement price range.
N=max[min(tick_Upper,Rewardtick_Upper)max(tick_Lower,Rewardtick_Lower),0]N=max[min(tick\_Upper,Rewardtick\_Upper)-max(tick\_Lower,Rewardtick\_Lower),0]
The “vLiquidity” computed by the izumi official version will calculate the proportion of the incentive reward that each NFT receives in each block:
In one block,
Reward(NFT_i)=Rewardperblock/Sum(NFT_i)Reward(NFT\_i)=Reward per block/ Sum(NFT\_i)
As the graph shows, the user provide liquidity that covers n price ticks on Uniswap V3 and the liquidity mining program have the specific incentive price range with N price ticks. Then the vLiquidity will only calculate the part of n price ticks that are included by N price ticks. The formula is as following:
vLiquidity=L(ninside/N)2vLiquidity = L * ( ninside / N )^2
herefore, if the liquidity (user’s fund) is constant, the best strategy to earn more liquidity mining rewards is to set n same as N, which will let the above function to get the largest result.
This version of the algorithm has the following features:
1.Inclusiveness:
LP will get rewards when the price range in the NFT of Uniswap V3 overlaps with the price range of the liquidity mining inventive.
2.Effective bootability:
Based on the same amount of token0 and token1, the maximum gain is obtained when the upper and lower bounds of the liquidity price range overlap exactly with the upper and lower bounds of the liquidity mining incentive price interval. For example, the user, who provides liquidity into a very small price range, will get a large Liquidity number and a small
NN
, and eventually the liquidity mining incentive weight obtained by
LN2L*N^2
is less than the case of tiling the token to complete the incentive price range.
Note: This algorithm for converting NFTs into FTs is freely customizable, and the above is the default version for Ethereum Mainnet. izumi will publish advanced default versions of incentive algorithms when launches on Layer 2 and other EVM compatible blockchains with low transaction fees to better compensate liquidity providers’ impermanent loss.