I'm pretty much exclusively the DM with my group. None of them has ever run the game before. My people are pretty trusting, because I've done nothing to betray them. I don't grin evilly when they get killed, and I always congratulate them if they make it out of a sticky predicament. I have never rolled dice in the open because I want the players to strategize based on the action, not the dice. Imagine what happens when a golem trudges in and whacks their best armored character with a roll of 3. It's no longer just a hit, it's a reason to bolt. Likewise, if some daunting-looking foe swings and misses with an 18, those characters aren't going anywhere. If I roll a 20 or a 1 at a critical or questionable moment, I'll show the die to them to avoid the eye-rolling.
Rolling behind the screen doesn't foster distrust in my game, it increases the tension (like when I roll and just stare wide-eyed for a few seconds), and allows me to "shave damage" on occasion. Treating the players like fodder, like each dungeon is...
I absolutely agree with Asberdies. I have never rolled the dice in the open, and I don't intend to start. There are too many situations where rolling secretly allows you to preserve the mystery and tension of the game. Heck, I'll generally throw in a few completely meaningless dice throws just to keep them off balance.
Of course, my players all know that I am not out to kill their characters (though I will), and that I tend to reward smart play. My games are not all about playing the odds.
I had a new player complain about this once, but before I could even open my mouth, my other players were jumping in and defending me. I can't ask for a better endorsement than that.
I've also had my share of min/max type players. I have found that they either change their approach to the game, or they eventually leave the group when they find that their super stats or skill combos don't mean as much to me as creative role playing. When they stay, that tells me I have done a good job.
Here's a tip: If you have to kill a character off, make it as dramatic as you can. Play it up. Make it part of the mythos. If you can, arrange it so that the "sacrifice" of the character saves the party from "sure destruction", or something to that effect. Don't be afraid to fudge a bit to make it happen - just don't be too obvious, or do it every time, or it will get boring. If you do it right, your players will love it, and be eager to jump back in with a new character.