The Dragons are blocking cards. You can't stack them on anything other than the top left slots, so if you have more than two in the visible positions, it's time to restart. You can't move enough cards to matter.

Look for the dragons in "layers", i.e. you can remove one suit at a time. If one is block the other, it's probably time to restart.

Look for 1's as low as possible, and NOT block by dragons. If your 1's are buried deep in the stack, it's probably easier to restart and hope the RNG is kinder to you next time.

You can put ANYTHING in an empty center stack! So, if you can create a couple of empty slots, you can almost certainly win the round ;P

I'm almost certain that, after all the dragon cards have been removed, it's actually impossible to lose at that point (at least if you're actually trying to win).

Another thing to note, is that you sometimes have to go against what the game recommends, as in manually moving number cards to the top-right slots, even when the game doesn't do it automatically. This has probably saved a few thousand of my games, and sometimes it's entirely possible to remove one color from the game, effectively gaining an empty slot.

I'm so pissed that they made a minigame mandatory. It's so annoying and I nearly drove myself insane because for some reason I can't win this stupid solitaire game.

Also if you have stack like 8,7,6,5... you can grab card number 8 and move multiple cards at once

The primary advice I'd give is to focus on the dragons first. The best play is usually the one that goes through the dragon that requires moving the least number of opposing dragons into your free cells. If you have a bunch of dragons stacked up in the same column or if you have dependency locks where a red dragon is blocking a black dragon and a black dragon is blocking a green dragon and a green dragon is blocking a red dragon, those tend to be the hardest games. They aren't necessarily unwinnable if you can find a path to getting rid of the number cards, but that tends to be a much harder objective to go for than getting rid of dragons.

Aside from that, keep in mind that any trade where you give up a free cell up top for a free foundation square (IE a column), that's almost always a safe move. Try not to give up your free cells unless you are fulfilling a major objective.

It's a shame Zachtronics solitaire games never have undo buttons, because if they did it'd be a whole lot easier to learn these games. Still, almost all of these are winnable if you can think about 6 steps ahead or so.