A new format does not necessarily have to be unknown. There are two types of banlists that we will be talking about throughout the article, the first we will call a minor adjustment banlist, and the second type we'll call a game-changing banlist. Both serve different purposes and have different effects on how players build their side decks to counter the meta, especially at the very beginning of the format.
Side Decking After a Minor Adjustment
A minor adjustment banlist usually keeps the previous format somewhat unchanged by hitting specific cards that directly or indirectly make the top strategies somewhat unfair relative to its competitors. This happens either by decreasing a deck's consistency or by taking away one or more cards that give a strategy an unfair advantage. This allows weaker decks a better chance to compete with these strategies. Alternatively, instead of hitting cards, others can be released from the banlist to help counter the existing metagame.
As a result — especially at the beginning of the format — most players tend to stick with their current deck. They'll try to figure out how to update and innovate before evaluating whether or not it is still competitively viable. Siding in this specific scenario is relatively straightforward as the principle here is simple: whatever was good against the meta previously is most likely still effective directly after the banlist drops.
Unless the banlist gives a major boost to a deck that was not on the competitive radar, the side deck choices will largely remain same. For example, let's assume there is a banlist and the Eldlich core cards are not touched. Then side deck cards such as
Of course throughout the life of any banlist, new sets will be introduced; players will figure out how to use new cards to improve their current decks; new strategies will emerge that will naturally cause older ones to phase out of the competitive scene. The side deck will have to adjust accordingly.

Side Decking After a Game-Changing Banlist
This is where it gets more interesting. A game-changing banlist immediately wipes out the previous format as we know it. A good example is the banlist effective from January 20 until April 1, 2020. This banlist hit Sky Strikers, Thunder Dragons, Orcust, Pendulums, and Salamangreats. While some of these decks managed to keep a seat at the top tables on occasion even today, none of them can do it consistently anymore because they are surpassed by newer strategies. No one allocates space in the side deck for Thunder Dragons anymore, and the rest are viewed as rogue decks that general side deck cards can deal with.
How to side against the unknown at the beginning of a format though? At the beginning of such formats, it is prime time for players to test anything and everything that they deem to be remotely viable. With so many options available, it is impossible to prepare for every potential matchup. Therefore the safest route would be to side deck staple cards that can put work against a wide range of strategies at the same time.
Of course, side deck options would be affected by whether the deck you are using is better suited for going first or going second. If it is a going-first deck, side deck cards that prevent the opponent from breaking your board or cards that interrupt your opponent's plays are the best options. They include:

On the other hand, going-second decks need cards that either help prevent boards or break them. Some popular and effective monster removal options are
Additionally, there are some general utility cards that can be used either when going first or second such as

Closing Thoughts
Whether side deck cards from the previous format are kept as they are or a new meta forces a reconstruction, once the format is somewhat defined, players will come up with spicy tech choices for their side deck. If these choices prove to be successful, they will be copied by other players. However, once the meta fully develops, side deck options will be somewhat standardized and tech choices will not be as prominent unless they prove their effectiveness against the meta.
Of course, certain decks might require certain side deck cards that are specific to such decks, such as archetype-specific cards or cards that work very well in combination with certain decks. But that is where the spice comes in!
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