What are some options for task resolution in the flip-a-card system?
One factor we don't have to take into account is "complication": every time a card flips over, you've opened yourself up to introducing complications. So our dice model can be simple.
If you flip a compatible card from topside to flipside, you succeed. If no card suits your needs, you fail. This is probably the most straightforward system.
Roll dice (see below). At your option, you can instead flip a card to automatically succeed. During playtest, this option felt a lot like Fate, where you can spend Fate points after rolling to boost the total into success territory.
The GM applies a "difficulty number" (1-3?) to a challenge. Flip that many cards (or otherwise generate some number of successes) and you succeed. Some people like variable difficulties, some people don't.
Flipping a card doesn't succeed, but it buys you a die to roll, e.g. a d6. The BITD version of this says you start with 1d, and each flipped card gives you +1d (or +2d, or....). Roll and take the highest result. 1-4 fails, 5-6 succeeds, maybe?
You always get 1 die. It starts at d8. The GM can scale difficulty up (e.g. to d10 or d12). You can flip cards to scale down one die size (e.g. 12 - 10 - 8 - 6 - 4). Roll the die, and a 3 or less (or whatever) succeeds. Adjust the target number to taste.