On red coin, you're usually playing to lose R1 with artifacts and traps. R2 your opponent typically passes, so play the mantis trap and activate it. However, you need to have pulled most of the movement card package in case your opponent decides to bleed or push for a 2-0 win. R3 you go for the win with the movement pack (sentries, matrons, cat witchers, Malena, Gezras) with some crushing traps thrown in if you're playing a 10 card round.
On blue coin, you have to go for a win in R1 using a mix of traps and movement cards. You want to just barely stay ahead of your opponent. If they don't pass at 5 cards remaining, then you go all in with your gold cards, bleed R2 and hope to win a short R3. You're much more likely to lose the blue coin games than the red.
In the PS version, you've got Brokilon Sentinels that you drop into the ranged row for Gezras to boost. In the Deadeye version, you've got the Deadeye tokens. The Deadeyes are guaranteed, whereas the Brokilon Sentinels run the risk of bricking or not having an opposing unit you can deathblow. If you've got Gaetan, then you drop the Deadeyes / Sentinels in the melee row and ensure you've got a ranged DB Sentry so you damage and boost while moving them into the ranged row with Gaetan (ideally also with a matron and cat witcher in the melee row). You can also use the Deadeyes/Sentinels to set up the Mahakam Horn in a single turn.
If you're looking strong in R3 then you go for the win, but if you've drawn badly then you mulligan for artifacts. In a winning game, you should have played about 8 artifacts. If you're surrendering in R3, you'll be playing 10+.
