murgatroid99‘s reply sufficiently solutions the query, that is extra of a philosophical tackle deck randomisation.
A wonderfully random ordering is such that each attainable order is equally seemingly. That is precisely equal to every place containing a uniformly random card, or every card being in a uniformly random place.
One other vital issue to shuffling a deck, is the quantity of data you have got concerning the order of the deck. Eg. In case you in some way completely shuffle a deck then have a look at it, out of your perspective the variety of attainable permutations went from N! to 1.
Does this imply that simply leaving your deck as is, can be random? Type of… It’s kind of like trying the face of a cube from the final recreation you performed as a substitute of rolling it, however a deck of playing cards has extra potentialities, subsequently extra room for unintentional ordering. From final time you performed, your lands and creatures are most likely in clumps. To not point out, it’s possible you’ll even bear in mind what you had final recreation, and the place they’re in your deck. Shuffling is a technique to mitigate this.
One technique to completely shuffle a deck, (though time consuming) can be to have one other particular person take your deck face-down, choose a card at random (utilizing a cube or different RNG), and put it in a brand new pile. They repeat this till each card is within the new pile. This satisfies each side of being completely random; every card might be wherever, and you understand nothing.
Clearly, that is impractical to do, so that you need one thing as shut as attainable. A number of (7-9) riffle shuffles are normally adequate to return shut sufficient to uniform randomness, and to obfuscate your reminiscence of card positions. Since that is the bodily world, there are some caveats. It relies on a specific amount of dexterity. In case your riffles persistently go away the highest or backside playing cards in the identical place, just a few overhand shuffles between riffles ought to suffice. Or, in case your playing cards are liable to sticking collectively whereas riffling, one pile shuffle (with out trying!) can separate them once more. Notice that overhand or pile shuffles alone are usually thought-about inadequate types of shuffling.
Pile shuffling alone, deterministically rearranges the deck, thus not rising randomisation. Equivalently, it is flipping a cube onto its reverse face as a substitute of rolling it.
Mana weaving is extra detrimental. It is actively arranging the deck in accordance with a rule. It could possibly by no means enhance the randomisation. Furthermore, it introduces info to you concerning the order. If not particular card locations, you now know that after drawing 2 nonlands, the highest card is probably going a land. It is the equal of turning your cube to a face you need as a substitute of rolling.
A wonderfully shuffled deck may be very unlikely to have a neat sample of land/nonland playing cards. Identical to how a regular deck of taking part in playing cards is unlikely to be shuffled so as of black, purple, black, purple, and many others. It is best to count on some clumping even in a wonderfully shuffled deck.
