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Take a sheet of paper or text file and write down every good, normal and bad draw you have over a run.
6 burns in a 24 card deck is 25% of your current deck. So you'd expect 25% of your hand to be burns. 1-2 cards. 3 is unlucky but possible.
An odds calculator says 7.2% which is unlucky, but around 1/14, so yea your chances are 1/14 to draw 3 burns each time you reshuffle your deck.
(As a side note, drawing exactly 0 is 20%, 1 is 43% and more than 1 is 36%)
Like it's more noticeable when something bad happens in comparison to when it works well or neutrally.
Let me tell you a hilarious story about Spotify's shuffle. People complained the playlist shuffler was broken as it played songs in the same order as on album. They spent a lot of money checking it, and found there was no problem. Sometimes dice just do that. It was all cognitive bias. But they "fixed" it, by making it less random so that it could never play songs in the same order as on the album, and complaints went away.