Smart contract is an important building block of blockchain. Automated
market makers are working without an order book, and they determine the
price of assets automatically. It is reported that he automated market
makers have the impermanent loss, which causes financial damage to
liquidity providers. Impermanent loss makes the liquidity providers
hesitant to deposit assets in the liquidity pool. Therefore, their
participation incentive from liquidity provision should be anticipated
by automatic market makers inherently. However, the existence of
impermanent gain has never been reported. Impermanent gain is important
to attract liquidity providers without giving compensation incentives.
This study shows that for some automated market makers, impermanent gain
coexists with impermanent loss. Examples showing the coexistence and
conditions are provided.