Games that sort the cards are the worst / most interesting for this. Gin rummy, etc, where the end result of a game is sorted groups of same-numbers and runs. You can really tell when then shuffling has just transposed a few cards.

I am in a tarot group where we have a lot of decks that people share. Many tarot users believe that a deck develops a personality specific to the user and because of that I got my own deck which I take to the group.

There's the general belief that all magical tools develop significance for the user over time, something that my wife who is a "secular green witch" who doesn't believe in psi at all would tell you all about.

Scientifically though, if somebody isn't a good shuffler their deck is not going to be well shuffled and they'll get readings that deviate from what you'd get from a well shuffled deck. It's harder to shuffle a tarot deck well because it has more cards and these are frequently larger. (Personally my riffle shuffle is awful and probably not much better than an overhand)

A new deck usually has the major arcana together and in order and other cards might be sorted by suit and then number. We do a 5 card spread and if your have a new and poorly shuffled deck of course you are going to have more spreads where you get both the Emperor and the Empress or the 4 of Swords and the 7 of Swords.

Magic the gathering has this problem. You have 2 types of cards, and drawing an imbalanced mixture is pretty detrimental. During play you tend to sort them into 2 piles though. Consequently it's a not uncommon sight to see people manually interweaving their cards after a match, then shuffling. Logically, this is either pointless or cheating depending on the quality of that shuffle, but people do it anyways haha.