Most competitive card games, where each player has a deck of cards that needs to be randomized, have one very major problem: Experienced cheaters can masterfully manipulate and "stack" the deck while shuffling, without their opponent or anybody else noticing. (This kind of cheating is sometimes caught on camera. With camera footage we have the advantage of seeing the shuffling as many times and as closely as we want, and in slow motion. In a real-life situation it's much harder, especially if we don't know what to look for, and sometimes even then.)
Experienced cheaters can stack the deck by moving certain cards to the top or the bottom of the deck.
To minimize the possibility of cheating, MtG tournament rules require for the opponent to also shuffle the deck afterward. The problem with this is that even though you can't stack your own deck, you can do it for your opponent's deck. For example you can mana-flood or mana-screw your opponent by stacking their deck appropriately.
Poker doesn't really have this problem because if you shuffle the deck, you have to present it to an opponent, and said opponent must only cut the deck once. (In fact, cutting it more than once, or even outright shuffling it, is forbidden at most places. It must be cut, and cut only once.) This way neither player can manipulate the deck. The shuffler can't know where the opponent will cut the deck, so there's no way to make certain cards end up on the top. (The only exception to this is that if both players are working together, and the other player cuts the deck where the shuffler "marked" it. This is a common cheating tactic in poker, but it only works if two players are working together, and only if they are sitting side by side on the table, as the cut is always made by the next player.)
Many have suggested using this same principle in MtG. In other words, shuffle your deck, and then your opponent cuts it once, and that's it. However, unlike in poker, this isn't a very effective anti-cheat measure in Magic. Yes, it prevents you from getting the cards you want on the top (or bottom, in the case of your opponent's deck in some situations), but there's another cheat that a single cut doesn't prevent: Mana weaving.
Mana weaving is distributing the lands evenly in the deck, so that you get a steady supply of lands and do not get mana flooded or mana screwed. An expert cheater can more or less easily mana weave their deck (eg. by shuffling in such a way that most lands go eg. to the bottom of the deck, and then mash-shuffling that bottom part into the rest of the deck once.) This is blatant cheating, of course, because the deck is not randomized.
And the thing is, a single cut to such a deck isn't going to undo any such mana weaving. And that's why the poker way doesn't really work in Magic. The opponent really needs to shuffle the deck in order to undo any possible mana weaving, and make the deck truly randomized. But, of course, when you can fully shuffle a deck, it allows cheating.
This is a dilemma that has no practical solution.
At the highest levels of poker cheating by shuffling trickery is impossible because players do not shuffle nor are allowed to touch the deck in any way. It's shuffled by a neutral dealer, employed by the tournament organizer or the casino.
In MtG tournaments the same could work if judges always shuffled the players' decks. The problem is that a typical tournament has over a hundred players and only a few judges. This solution is just impossible to implement in practice. (This could work on the top-8 matches, but for some reason it's not done that way. Perhaps it's not really needed either. The top-8 matches are always videoed and very closely watched, and it can be fairly assumed that nobody dares to cheat there. Although it does happen from time to time...)
