My understanding is that at the start of a game, the system shuffles and draws three hands for you, and then selects one of them to be your actual starting hand

My understanding is that at the start of a game, the system shuffles and draws three hands for you, and then selects one of them to be your actual starting hand. I don't know what heuristics it uses for which of the three to select, but typically in real life you would be hoping for three lands as a baseline, ideally that can tap for the colours of the spells in your hand as well. I believe this only applies in best of 1 matches, but not best of three matches. Unfortunately I don't have a credible source for this.