I think this game is really cool. I don't know if there is a way to rig the probability to get the correct number but if there is I think it would be sick. It's pretty short but it was enjoyable. I would really wonder if there is a tournament for rolling dices... I do hope you game idea comes into fruition so I would be able to play it!! Good Luck!
Thanks so much for recording your playthrough, videos like this are so valuable to understanding the flaws in the game.
The random numbers aren't really random at all - they appear in a looping sequence. It's possible to 'use up' random numbers so that they get out of the way of the numbers you want. In the Randomlabs building there's a box which uses up a random number to pull an item from the pile - but I've noticed a few people miss it when looking around. This is because the box is never specifically mentioned, and the sprite makes it appear like it's a background decoration.
In version 2 I'll look into making the mechanics tighter and more refined, and make it easier on the player for understanding the sequence of events.
Thanks so much for your feedback!