We investigate the recent fee mechanism EIP1559 of the Ethereum network. Whereas previous studies have focused on myopic miners, we here focus on rational miners in the sense of having level-k foresight. We derive expressions for optimal miner behavior (in terms of setting block sizes) in the case of level-2 foresight for varying degrees of hashing power. Results indicate that a sufficiently large mining pool will have enough hashing power to gain by strategic foresight. We further use a simulation study to examine the impact of foresight for levels k > 2. In particular, the simulation study indicates that for realistic levels of hashing power greater than 10% miners/pools can not gain from the foresight of levels k > 2.