How the analyzer solves a hand
Every five-card deal has 32 possible holds. The analyzer plays out all of them against every card that could still come off the deck, scores each draw on the pay table you are actually playing, and reports the hold with the highest expected value. Nothing here is sampled or approximated — the answer is the exact one, and it is the same enumeration that grades your hands in the trainer.
The pay table changes the answer
Optimal video poker strategy is a property of the schedule, not of the cards. The same five cards can have one best hold in Jacks or Better and a different one in Double Double Bonus or Deuces Wild, so the analyzer prices the hand against whichever game is selected above — and against your own edited pay table, if you have one. Switch games and solve the hand again to see where the two disagree.