Random Is Random
Has this ever happened to you? You are playing some game which requires every player to draw a card from a shuffled deck. You accidentally draw before your right-hand opponent, and they exclaim, "Hey! That's my card!" I only tolerate this sort of irrational behavior if the player is less than, say, 10 years old.
Let's ignore mathematical definitions of true randomness for this discussion and say that any reasonably-well-shuffled deck of cards/tiles, and any rolled dice are random enough for game purposes.
In college, I had a friend who claimed that if no one knew the order of cards in a shuffled deck, then all the cards changed when you touched them. In his facetious way, he quite nicely summed up the "quantum" nature of the unknown. It doesn't matter if you draw the top card, the bottom card, or any card in the middle.
In games like Die Macher, some cards are drawn and placed face-down to be revealed at some point in the future. Does this give players the false sense of some eventuality set in stone? It's no different from waiting to draw the cards until the point that they would be revealed. Unless this changes the distributions in the deck for intervening actions (I've only played once), but you get the point.
In Arkham Horror, there's a plethora of decks. Among these are the 9 decks of Location Cards, 7 per deck. When you need one, you draw the top card from the appropriate deck. When a card is "discarded", it is returned to the deck which is then shuffled. 9 decks take a lot of space! It's much easier to simply put all the Location Cards together in a single deck, and shuffle them all. When you need a card from a specific "deck", just fan the cards out and draw an appropriate card. When you return a card to the pile, slip it in the middle and give the whole stack a quick shuffle.
Some games require the rolling of varying numbers of dice. Some people are very sensitive to the "rules of conduct" when there are abnormalities (cocked dice, wrong number rolled, rolled off the table, etc), or when the intention of the roll was incorrect ("I wasn't rolling for attack! I get to re-roll!"). The bottom line is that it doesn't matter, as long as everyone agrees how to resolve all situations. My preferences:
- If you roll too many dice, always re-roll all of them regardless of the outcome.
- If you roll too few dice, only roll the extras needed.
- Re-roll only cocked/off-table dice.
- In all cases, previously-rolled dice may not be "bumped".