Blinkswift

Despite the best efforts of the playtesters and a very vocal crown on the main Ascension forums, there is an infinite combo in Ascension (and I couldn’t be happier about it). It requires the RotF expansion and is relatively difficult to pull off, but can occur.

To start, you need some way to thin/banish your deck down to the bare minimum. My preferred method of doing this is Black hole, as it doesn’t clog up your deck by way of drawing it multiple times. You will also need ONLY the following cards in your deck:
1x Hedron Link Device
1x Reclamax
1x Tablet of Time’s Dawn
2x Mystic
1x Lifebound Initiate

Basically, you need all the constructs in play. Crack the Tablet to take an extra turn, then pay 5 (gaining 1 honor in the process), discard Reclamax, and bring the Tablet back to your hand.

At the end of your turn, draw up to 5 (Tablet, Reclamax, 2 Mystics, and an Initiate). Later/Rinse/Repeat taking X number of consecutive turns and gaining 1 honor X number of times, presumably running the honor pool out and/or gaining enough honor to win the game.

In the iOS version of Ascension, the computer is programmed to automatically buy the card that gives the best cost to honor ratio. This is why you will often see your computer opponents purchasing an inordinate number of heavy infantries and mechana constructs. Having this knowledge under your belt can sometimes help in deciding what card to purchase (i.e. you can rest assured that it will be in the center row next turn if a better cost: honor card is present)