Background (feel free to skip):
My mom and I often play RFTG together (I am a very fortunate child to have a game-playing parent :), and we've noticed that there usually isn't as much luck in the game as we initially thought; there are few situations where you cannot find some favorable way to play out your cards and tableau. While the luck factor is definite present, as it will be in any game that involves powerful combinations of randomly drawn cards, but smart play can mitigate the effect. In fact, one of my favorite situations in the game is when I have a bunch of cards with no obvious strong combos and have to work with what I have to find some sort of strategy.
However, I've noticed that there is substantially more luck in the early parts of the game. If you get an initial draw that contains mostly high-drop cards, cards that aren't good in the early game, or no good combinations (tons of goods, but no way to actually do anything with them except trade ONE of them for 2-4 cards). Some luck later on can easily fix this if you get a nice card, but sometimes I feel like the game is decided after turn 4 when one of us has a killer initial combo and the other has had a bad start.
I understand that the luck factor is relatively small and will be minimal in a series of 5 or more games, but I would still like to reduce it since we purely play for fun and rarely get to play 2 games in a row. I don't consider myself anywhere near an expert player, and I'm sure we're not always playing our cards optimally. However, I am sure that there are some opening hands that are sufficiently worse than others to drastically effect the outcome of the game, and I'd like to adjust this in our friendly games.
Here's some ways I've thought to prevent players from getting screwed over by bad initial draws in RFTG:
Start with 7 or 8 cards instead of 6. Still discard down to 4.
Implement a mulligan system for initial hands. You can discard your 6 initial cards, reshuffle the deck, and draw 5 (still discard down to 4). I suppose this could probably be extended to allow players to discard those 5 to draw 4 and keep all of them, even though I don't think many people would go for the second mulligan.
Would these methods potentially be effective in reducing some of the initial luck in the game? How might I improve them? What other methods might be effective towards reaching this goal of a slightly more 'skill-based' RFTG by mitigating the effect of terrible initial draws?