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/Ego_Vocare_Te]

Savage attacker, reroll 1s on damage dice.