Joshua

You want laundry set to Uncommon or better and monk for high roller. Then it's very easy to get a powered laundry room, like multiple chances in the first two rows. With high roller you can immediately get infinite dice, gems, and coins, making it trivial to select any room even if you have to reroll 100 times. Every few days High Roller will wear off but if you really want you can just force freezer and bank a few hundred gem/dice. At this point you are the master of the house, even rare items are easy to get since you can force trading post, shops, and workshop.

If you know how (ie in a challenge mode) you can get to this point surprisingly early. The hardest part is making laundry room common but at least five ways come to mind for accomplishing that. Worst case you can just use the king until getting lucky with wrench/conservatory.

In my first game I discovered this right before the blue doors, which is later than most players ever get but there is still a good amount of game left. Before that I think there is enough content that I never really had a day where I was stuck on RNG and couldn't find any new puzzles to solve.

Geist bedroom is almost certainly the best, because lategame you only need two or three dice to remove all RNG from a run.

Early game a couple of dice can often save a run, regardless of other resources.