They thought the pigeons would develop a favourite button or a favourite pattern. But the pigeons prefer variety over favourites.

With rules like that I would expect people to split onto two groups: ones that learn one pattern and repeat it because it's a guaranteed result, and one that tries to find a counterexample to the rule they thought of at first. The fact that pigeons try different patterns kind of makes them more clever in my eyes.

But it's known that pigeons perform better than humans in Monty Hall problem, so they are really pretty smart when it comes to statistics, it seems

Well, it does tend to happen with rats/monkeys/people.

If 5 buttons all work the same way, you just hit whichever one is closest or whatever, over and over again. You spam it, hit it as fast as you can.

I can wake up my computer by hitting any key, I have something like 50 keys to choose from, I click the mouse every time.

nothing mattered

So pigeons are both chaotic AND nihilistic !

Yeah maybe they were wondering if they could get something better to happen and there was no cost in just pushing random buttons so why not

Trains wild pigeons where?