I made a gunslinger in an Iron Gods game specifically so I'd be targeting touch AC and my dice would have a harder time screwing me over. They do still find a way though; I had a night where I rolled a 1 for a misfire 3 times in a single combat.
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Casters.
It's entirely possible to make a wizard that doesn't roll dice in combat. You can cast spells which don't require attack rolls or don't directly target the enemy, or casting buffs, etc.
In fact the old "god wizard" build does exactly that sort of thing. With a smart spell selection you don't ever have to roll for your spells.*
Maybe some exceptions for spell resistance, but if you know an enemy has SR you can choose other spells.
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A cleric or bard. Just sit back and buff your teammates. No dice needed except for the occasional heal.
Indeed, support characters are the way to go. You serve to amplify the abilities of the entire party, leaving very little actual attack rolling on your end.
I am playing one of these kinds of characters in an Iron Gods campaign, a Skald VMC Bard, using a reach weapon and combat reflexes. I'll also be channeling energy at level 5, and be the main source of healing in the campaign, being VERY effective at the in-combat kind of healing.
But, if you aren't interested in being a support character, think about using the Warpriest (Calamity Caller). You get an at-will ranged attack ability, that only requires a saving throw (no attack roll).
I'm actually working on a luck based shaman...channel to let allies reroll a attack, and later misfortune...gm typically hates misfortune. But as other mentioned spellcasters would make the gm roll..unless he/she have hot dice.
A cleric or bard. Just sit back and buff your teammates. No dice needed except for the occasional heal.
Currently running an oracle/paladin with Inspiring Blade of Iomede & Dazzling/Motivating Display. Inspiring Blade has no die roll, Dazzling Display is usually a trivial die roll.
Warsight lets me have more control over initiative.
Divine Aura on a charisma build = very rarely fail saves.
High AC sword & board, with full plate. Not afraid to stand on the front line.
LoL at kill the healer first, she's the highest AC and best saves in the party and always has a way to contribute, vanguard or rearguard.
A cleric or bard.
Seriously though, a character who buffs allies and debuffs enemies (by forcing them to roll a save) is going to roll very few dice.
Volkard Abendroth has a good idea (the post above this one). Paladin's have great defences, and it's not just a bonus to saves, it's immunity to some debilitating conditions (natural-1's getting you down? Try ignoring the roll entirely!).
Another thing to look at would be abilities that let you re-roll your dice x/day, or roll twice and take the higher result. I'm playing a gnome alchemist in carrion crown, and I took the "Eternal Hope" alternate racial trait. I passed 3 saves in the first 3 days of adventuring because of that trait. Literally a life-saver.
Lessons of Chaldiera, reroll a failed save once per day. Best trait ever lol.
A commoner can take 10 for the vast majority of their life.
For a more off-the-wall idea, consider a Firebrand Gunslinger. Dragon's Breath rounds do not roll for attacks at all, and even the save is for half damage so you have guaranteed damage every round. It'll be low against a single target and the fact that you only deal fire damage is a pretty serious issue but certainly an interesting thing to think about.
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Here's a 1 point build Evangelist Cleric who summons who is quite effective despite both awful dice rolls and awful attributes.
This character serves primarily as a force multiplier for allies, so personal die rolls don't matter.
Inspire Courage works with no dice rolls.
Clerical spells will never be offensive, so dice rolls don't matter.
Bad attack die rolls will prevent summoned monsters from inflicting much damage. That's not their purpose. Summoned Monsters are mostly to absorb damage that would otherwise go to a PC: pre-healing. Summoned monsters still absorb damage and take up space on the battlefield even if they don't hit anything.
dead characters generally don't rely on dice rolls anymore... X^|
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dead characters generally don't rely on dice rolls anymore... X^|
@Unbegreiflich: If that was a snarky comment suggesting that the above 1-point-build Evangelist is fragile and will die easily in combat ... that's just wrong. That build actually has pretty strong defenses. The Animal Companion, with 18 Strength, reach, and combat reflexes, provides a strong defensive reach screen that mostly keeps melee foes at a distance. That sort of PC should remain near the squishies, to protect them, rather than on the front line, but is no easy target. Obviously, if you have more than 1 point to spend on attributes, raise your CON. The purpose of that build is to demonstrate how it's possible to be quite effective, both offensively and defensively, with minimal resources.
Apologies in advance if I misunderstood.
Let's assume a player has very bad luck (as in, most attack rolls result in failures, with a bad record of 1s' showing up at the worst moments).
I would experiment with the limits of this 'luck', perhaps aiming to claim the prize for being the first person to prove the existence of the paranormal.
For example, you could have this person bet small amounts on the roulette table. When he bets on red, you bet on black, and you bet ten times as much. If he is genuinely unlucky, you should turn a consistent profit.
Witches. They make other people roll dice.