I don’t like chains. Chains are a terrible balancing mechanic in my opinion, and I don’t want to use them. I have tested Adaptive with Æmber gains instead of Chains, and while it works, it feels a little bit clunky. Especially since you need to jump through hoops to prevent a very large bid into a turn 1 TMTP, or simply enabling a Shadows deck by having Æmber. It is not an elegant solution.

Tesla
Each player brings one deck to the event. The TO ransomizes the first round between Standard and Reversal. Following rounds will Alternate.
Each round of the tournament is a best-of-one game.
Tesla was coined so by Mortivas, who runs a weekly Tesla tournament with a monthly leaderboard. Experienced players have said it is a challenging variant, and going 4-0 in a Tesla tournament is considered an achievement. The strength of the variant is that a much wider range of decks is applicable than the ones usually successful in Archon Solo games. It does not use chains, and yet has an internal balancing factor as you play with opponents’ decks half the time.
The downside is that it can feel a little random at times. If you bring a mediocre deck and your round 1 opponent brings a top deck or a bottom deck, you might lose round 1 through deck disparity. That said, Ugluk routinely wins the monthly leaderboard, so it is hard to claim that skill doesn’t play a big factor.
For tournament structure, it is recommended to run an even number of rounds, to get an equal amount of Standard and Reversal games.
Newton
Players bring one deck to the event. Each Match you play one game of Standard and one game of Reversal.
Games are scored as 1-1 or 3-0, giving the player that manages to win with both decks an edge.

Formerly known as Adaptive best of 2, Newton is a solution that is elegant and works some of the time. The name was suggested by joelker41 as “Equal and Opposite”. Newton works a lot like Tesla but if your opponent brings a very powerful or weak deck to your mediocre one, then you would likely go 1-1, which is not as bad as recording a loss. Good Adaptive players will tell you that most Adaptive matches end after 2 games, which means that in most matches the third game with chain bidding is unnecessary.
The main downside of this variant is that it can cause ties more easily, and can’t effectively be used for single or double elimination tournament structures. It probably also usually can’t determine a winner in the same number of rounds as Archon Solo or Adaptive in a regular Swiss tournament. As such, the recommended tournament structure is Round Robin. I have run some events with Round Robin and did not need a tiebreaker.
Versatile Pairs
Players team up in pairs. Each pair brings one deck. One player always plays Standard and the other always plays Reversal.
This works exactly the same way as Tesla, only here if a player (me!) has a preference to playing Standard or Reversal, they don’t have to play the other way. The downside is that this variant is harder to run in a live event, as you can’t use the single deck twice at the same time. But it works really well for online tournaments and leagues. It is not impossible to run it in live play, but the overhead is probably too much.
Benchmark deck
It is possible to reign in the power variance by using a benchmark deck, but honestly, I found it is not necessary. Most games appear to end in 2-0 (3 points), which is the desired result, and shows that even with some power disparity, skill will often prevail. That said, if you’re running any of these variants and find a big power disparity is an issue, a benchmark deck will likely solve it.
These variants are currently my favorite alternatives to Adaptive. Tesla works well for Swiss tournaments. Newton works well for Round Robin leagues. I encourage you to give them a go.