We uncover an equivalence between two opposite behavioral microfoundations for the standard multinomial logit choice model: 1) agents optimize their choice accordingly to the random utility model under Gumbel idiosyncratic shocks; 2) agents randomize over options subject to a minimum utility requirement. Both generate identical multinomial logit choice probabilities, yet have different welfare implications: welfare is strictly lower under randomization, since only optimizing agents select into options with favorable realizations of idiosyncratic shocks.