In terms of my preferences, I tend to like a balance between story and dice-rolling, and write 1-2 page backstories for my characters. I also like a cinematic style where failure means a temporary setback – however dire the situation looks, in the back of our minds we expect the heroes to succeed most of the time and achieve their objectives, and characters die only in dramatically satisfying ways if at all.
When I'm running a game, I can make that happen and people are usually OK with it. However, I also like playing. I live in a rural area so my steadiest opportunity to do so over the years is a group of friends from college, now long-distance. The GM likes a grittier, more dangerous style, where rules are rules and dice are dice and he won't save you if you do something stupid, and also the challenges are set slightly higher so there's a risk of real failure.
Now, let me be clear: I'm aware of the Same Page Tool, we've talked about it, and nowadays I generally don't play when they're doing Dark Heresy or similarly grim games. This time we're doing a 'standard' DND5e campaign, at what I perceive as a pretty average level of challenge, where the GM is setting us up against tough foes but trying to avoid TPK. I've accepted the game under these conditions and I am having fun, but I've realized that I would be having more fun if I took my character's setbacks a little less personally and adopted an attitude of "seeing how the story goes, one way or another" rather than trying to "win" all the time. (I'm not that competitive normally so this is kind of out of character.)
For example, recently we had a tough fight at the conclusion of a storyline, and the toughest foe got an humorously unreasonable number of crits. Three of us were down, the last had 5 HP, and we had a few death saving throw failures between us before we got some last-minute NPC help. So things worked out and it was a fun session, but I realized afterwards that if we hadn't had the crits to joke about and the fight had gone that poorly due to normal-high enemy rolls, I wouldn't necessarily have enjoyed it overall. If I were a neutral observer, though, I would have said it was a dramatic nail-biter but not a problem, just an interesting turn of events.
So, my question: Having made the decision to do so, how can I adjust my thinking to accommodate this more-challenging style? Especially hoping for personal experience of "How I Learned to Stop Worrying and Love the RNG", but more general advice is also OK. Note that I'm not only concerned with character death, but with smaller ups and downs where my character would reasonably get frustrated, but I as a player shouldn't.
(Note: I grew up playing GURPS where character creation is a big deal, and that's what I usually run. I've played Dark Heresy and really didn't like the system (40% chance of success is considered high, and permanently losing a Fate point to avoid death means a major tool for survivability goes down over time instead of up). I've also run Risus and played 3.5 and Star Wars Saga Edition, plus a little bit of: Hackmaster, Pathfinder, KAMB!, Call of Cthulhu, Serenity, and Microscope. I didn't really have this problem with KAMB! since it's a one-shot and the object of the game is more about seeing your characters fail hilariously than trying to accomplish anything, and I imagine Paranoia might be similar, but I'm not sure how that helps in DND where you expect to play for at least a couple months.)
Best Answer
On Death
You talk a fair amount about character creation being important to you, you create detailed back stories and you take time to shape each character. It seems natural to me, then, that you should also try to make sure that character deaths are important, impactful, and meaningful.
This might require talking to GMs, and adjusting the Social Contract at your tables, but it's a small change and I suspect most tables would be receptive to it. It also might require that you shift you perception a little bit, but again I don't think its a reasonable small shift to make.
Death should be avoided, but sacrifices are respected
What I mean by this is that whenever a character takes a dive, it should be a moment that is remembered and respected. In the scenario against the guy who always seems to crit, view him not as lucky, but rather as incredibly mighty. This foe has managed to cut to prices characters who have slain trolls, defeated liches, or saved villages from rampaging orcs. When he was finally defeated, at great cost, the weary remains of the party dragged themselves back to town where perhaps a shrine was raised to honor the loss.
This kind of respect and memory can be augmented by a gm giving dying characters a little extra liberty in their deaths. Once the table knows that a character is dying. I like to let the character act out a slightly elongated fight scene that ends in their demise. This might mean that a barbarian takes a sword through the chest, but pulls it out and throws a punch (mechanically no effect) that sends the baddy reeling before he collapses to his knees.
Another way, that doesn't require a change by anyone else at the table, is to view death as not an ending, but a new adventure. The loss of a character gives you a chance to view the rest of the campaign through a new lens, and to fill in gaps that may have only become evident once you're some ways into a campaign. In my personal view, I find that making new characters can be really enjoyable, especially in regards to being able to mix up a party dynamic that has gotten a little too comfortable.
On Failure
Something that may help in regards to non-death failures would be to consider that weaknesses are quite possibly the most interesting part of any character. It gets boring to watch a character always succeed at things. We even have a name for such a character: the Mary Sue. How, then, do we get used to the fact that our characters aren't always capable of everything they want to do? A tactic I like to use is to take gambles where it's more-likely-than-not that I'll fail. This serves two purposes: it gives my characters a depth that failure can cultivate, and it helps me get used to the idea of my characters failing. That way, when I engage in an action that I actually expect to succeed at, and I fail, I can adopt the mentality I've become accustomed to before, and continue on without bad feelings.
Some systems actually encourage this kind of risk taking, and might be worth looking into. One I personally have experience in is Anima: Beyond Fantasy, which rewards you with XP at the end of sessions where you succeeded on skill checks you were likely to fail (therefore encouraging you to take risks to earn that bonus XP).