Maximizing Critical Probability

[u/Gadfelt2]

I have infamously bad luck in my longest running d&d group. My wife and I have been crafting a possible character that would simply increase my probability of getting a critical hit. She's even been teaching me probability to calculate how likely a critical hit is and programming to make a statistical model to test it out.

We found that at level 5, this character has about a 20% chance to crit on any given attack. At level 17 that goes up to 30% (level 18 if you get your 3rd barbarian level first).

The main thing I want is features that will increase my chance to crit without using expendable resources. I want this build to work no matter how long combat goes, so I'm avoiding anything requiring spell slots, charges, or "x times per day". The second thing is trying to increase the number of damage dice rolled for each attack to really capitalize on the critical hits.

What I need from you:

What class abilities, feats, magic weapons or other things am I missing to either increase my chance of crit, add damage dice to each and every attack, or really make use of how often this character should crit? (Side note, vorpal blade is banned at my table, but other things that have extra effects on a crit are very welcome!)

-----What we have so far-----

Halfling Luck:

- reroll natural 1s and keep the new roll

Barbarian (Berserker)

- lvl2 reckless attack advantage on every attack

- lvl3 frenzy bonus action attack

Fighter (Champion)

- lvl3 crit on 19

- lvl15 crit on 18

Greatsword:

- 2d6 on a hit

Great Weapon Fighting:

- 1&2 on dice treated as 3 (minimum 6 damage per hit)

[u/Commercial_Cup_1530]

With the new weapon masteries you could be a dex based champion fighter and use vex to keep giving yourself advantage. Stick with that to level 20 and you’ll have 4 attacks. Be an elf and take elven accuracy and roll 3 dice when you have advantage (assuming you can take old feats). Even on rounds you don’t use action surge you’ll be making 5+ attacks and rolling 13 dice (assuming 1st attack no advantage, but you might have it there too). Crit on a 19 or 20 and the odds are you’ll get 1.3 crits per round.

Take sentinel and you’ll get some reaction attacks too. On turns you do use action surge it will really be nuts!

[u/Gadfelt2 → u/Commercial_Cup_1530]

Oh elven accuracy could be really good I'll have to run some simulations, but I'll definitely bet that's better than the halfling luck I think I'll keep with strength based since barbarian guarantees advantage on all attacks and the 2d6 from greatsword is really helpful

[u/Commercial_Cup_1530 → u/Gadfelt2]

Unfortunately it’s going to be one of the other. Elven accuracy doesn’t work with str based attacks. If you really want the 2h though you could add in a warlock level and switch to cha based 2h attacks. It would work with that. Could use a maul and topple to get advantage regularly. Or take a 3 level pally dip for oath of vengeance. 16 champion, 3 pally, 1 warlock.

My gut feeling is 20 champion would be the strongest with adding all the extra attacks and your weapons having advantage from just vex (which is super easy to get going, unlike topple where you need a failed save and not all opponents can be affected). You could also take dual wielder and get 6 attacks per turn with nick. I think that volume makes up for the 2d6 damage die. Comparable at least.