Are there any good digital board games on sale right now that can be played against the AI ?

Gloomhaven or Talisman Origins are designed for solo play

The best board game here is Carcassonne.
But the base game alone does not make much sense. The River and the Inns & cathedrals DLCs are obligatory, if you want to have fun. Which doubles the price. Each session lasts about 20 - 30 min.

A Game of Thrones is another good board game. But with the 2 DLCs the price for it is even discounted quite high.

Well, not here on GOG. However, I know of plenty of digital board games. What sort are you seeking?

nothing special yet
just one that i can play for multiple times

Well, there's good ole Gnuchess, Droidfish, Super Tux Party*, Connect Four

, a boatload of Unix/Linux TTY games, and plenty more.

If you don't restrict yourself to digital board games here on GOG, or on PC in general - but are interested in digital BGs on mobile, too: there's a whole plethora of pretty good conversions available (though I can't tell you, whether any of them are on sale right now).

Here are some that I like to play on my mobile:

Alhambra Game
Camel Up
Carcassonne
Cottage Garden
D&D Lords of Waterdeep
Eight-Minute-Empire
Isle of Skye
Kingdom Builder
Jaipur: A Card Game of Duels
Deus Ex GO
Hitman GO
Lara Croft GO
Lanterns: The Harvest Festival
Le Havre: The Inland Port
Onitama
Pandemic: The Board Game
Patchwork The Game
Potion Explosion
Splendor
Star Realms
Ticket to Ride Classic Edition
Tokaido
Tsuro - The Game of the Path

You can find them all on the Google Playstore.
(Mind you: I play them mostly on my tablet, since - for some of them - the screen of my mobile phone is a little too small for my liking)

Perhaps not strictly what you mean, but Druid's Duel plays a lot like a board game, and it's great fun. Not on GOG, but it's available DRM free from the game's website (I'm not sure if I'm allowed to link it, but it's a google search away).

Wingspan is on sale. Also, you can check the board game tag. There are 143 entries.

Talisman: Digital Edition (actually based on the boardgame - not to be confused with Talisman Origins) and its DLC Bundle are both on sale (17% and 55% discount respectively).

However Talisman DE is regularly discounted by as much as 80% so I'd suggest holding out for that.

If your definition of "boardgame" includes wargames (and big, complicated ones at that) then Gary Grigsby's War in the East and Gary Grigsby's War in the West are both 60% off...

I would recommend Through the Ages. Very good AI, excellent tutorial, and none of the fiddliness of the physical version.

Oh, are we counting card games?

any tabletop games