[truculent]

The example only seems ridiculous because you've deliberately excluded relevant knowledge about the world from the model. Add a prior to the model and you'll have a much more reasonable function to maximise.

[anon946]

Yes, but then it is no longer MLE, but rather MAP: [https://www.cs.cmu.edu/~aarti/Class/10701_Spring23/Lecs/Lect....