Pokémon TCG: Sword and Shield—Brilliant Stars

What qualifies as "sufficiently randomizing" your deck?

Of course, a computer's randomness is not true randomness. It is a simulation of randomness.
And depending on the algorithm used to generate that simulation, some are better than others.
Unless one knows the algorithm used, it's impossible to comment on how good PTCGO's randomness truely is.
 
However it is possible to make the cards in your deck "random" without declumping and a major bout of shuffling taking place - or having either a computer program or a judge do the shuffling for you. If your cards were considered random at the start of the game, and through card effects you did a search, and then you destroy your knowledge of the top few cards by properly shuffling and/or cutting your deck, then the cards are still random - as was mentioned by losjackal. Theoretically any random groupings of any combinations of cards are still possible - even clumps which may occur naturally. The question is: What qualifies as "sufficiently randomizing" your deck? The answer is simple. Everyone has their own version of sufficiently random due to their knowledge of the deck, their preferences and fears and their manner of shuffling/cutting. If, in your opinion, you feel confident that your opponent has made a proper effort to sufficiently randomize their deck, then by all means cut/don't cut, and shuffle/don't shuffle according to what your conscience advises. However if you don't think they have made a proper effort in your opinion, then take my advice and shuffle/cut their deck for your own protection. Just don't take forever to do it, since once you shuffle or cut, even as few as 1 time, can make the deck random once again.
 
Even algorithms have limits- computers have speed advantage, to me that is about it for the algorithms having to work with what is left to shuffle- just the same as what cards a human has left to shuffle.
 
The primary difference between computer and real-world shuffling is how the pre-shuffled content influences the post-shuffled content. In each case, the amount of randomization that can be achieved per action is limited by how far any card can move within the stack. In a perfect system, there would be an equal chance that any card could move to any position, but if you analyze most manual methods of shuffling, you can see where these limits show up. For example, in a single riffle shuffle, it's easy to see that cards 1 & 2 will likely stay near each other, with at most one or two cards sandwiched in between. Even with multiple riffle shuffles, there will still likely be some correlation between the original and shuffled order. Computers can come closer to this ideal, but they have other issues, mainly in the area of generating a seed value, the starting point from which random number generation begins. Typically a seed is generated based on the time (in fractions of a second) since the device or application was started, but sometimes seed values are kept for a very long time (ever notice how your digital music player sometimes "shuffles" to the exact same playlist from a few days earlier?).
 
We're losing perspective. We're not trying to randomize/shuffle a 6-deck shoe to deal 80 hands of blackjack! In the end, the challenge is to just randomize the next few cards drawn. I purport the randomness of the cut has the final influence.
 
To the OP, if you see your opponent has made a decent attempt to shuffle, but its insufficient in number, shuffle their deck. You only need a few more riffles midgame if they stopped at say 2.

If someone has ordered their deck (declump, selecting/returning cards, etc.). I would make sure there was a sufficient shuffle to randomize the deck, by shuffling myself.

If you see something shady happening, e.g. shuffling in some way to float known cards to top or bottom, or just plain weak happening, e.g. cut+cut, call a judge, explain the deficiency and ask the judge to explain a proper shuffle. Then its up to the judge to assess the proper penalty, if any.
 
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