Not exactly. The rules on Working Together in order to give advantage are as follows:
A character can only provide help if the task is one that
he or she could attempt alone. For example, trying to
open a lock requires proficiency with thieves’ tools, so a
character who lacks that proficiency can’t help another character in that task. Moreover, a character can help only
when two or more individuals working together would
actually be productive. Some tasks, such as threading a
needle, are no easier with help.
In other words, his familiar can only help him if the task is one that
a) The familiar is capable of accomplishing by itself, and
b) The task is one where the familiar's help would actually assist the character in completing the task.
It's up to you, of course, to decide if a given task satisfies these requirements. But you certainly shouldn't just let him gain advantage on every check automatically.
Assumptions
I'm going to be making the following assumptions, based on what you've already provided:
- 3rd level (since you get a crit on a 19 or 20)
- 16 Strength (no ASI to bump up to 18)
- Fighting a CR 3 creature (for base math)
- Average damage is 7.50 (4.50 from the die +3 Str mod)
- Average crit damage is 12.00 (4.50 per die +3 Str mod)
- Attack bonus is +5 (+2 prof, +3 Str mod)
- The enemy has AC 13 (per the DMG guidelines on page 274)
- DPR calculations are:
- Crit damage = Crit % x average crit hit damage
- Normal damage = Hit % x average hit damage
- hit % = 100 – [miss %] – [crit %]
Note that any flat modifier to the damage total won't change with a crit, since you only double the dice rolled, not the modifiers added.
Champion Fighter
Per the DMG page 274, a CR3 creature has an average AC 13, meaning you need to roll an 8 or higher.
With Advantage
AnyDice can tell us our miss chance and our crit chance. From there, we know our hit chance.
- A normal roll of 1d20 will have a 35% miss, 10.00% crit (1.20 DPR), and 55.00% normal hit (4.13 DPR) for a total DPR of 5.33
- A roll with advantage will have a 12.25% miss, 19.00% crit (2.28 DPR), and 68.75% normal hit (5.16 DPR) for a total DPR of 7.44
- A roll with your DMs +2 rule will have a 25.00% miss, 10.00% crit (1.20 DPR), and a 65.00% normal hit (4.88 DPR) for a total DPR of 6.08
With Disadvantage
AnyDice can tell us our miss chance and our crit chance. From there, we know our hit chance.
- A normal roll of 1d20 will have a 35% miss, 10.00% crit (1.20 DPR), and 55.00% normal hit (4.13 DPR) for a total DPR of 5.33 (unchanged)
- A roll with disadvantage will have a 42.25% miss, 1.00% crit (0.12 DPR), and 56.75% normal hit (4.26 DPR) for a total DPR of 4.38
- A roll with your DMs -2 rule will have a 45.00% miss, 10.00% crit (1.20 DPR), and a 45.00% normal hit (3.38 DPR) for a total DPR of 4.58
Rogue
How does this change affect other classes, specifically those who rely on bonus damage dice? I'm using a rogue for this example since sneak attack is easy enough to calculate, but a paladin falls under the same heading with their smite spells and the like.
We use the same percentages and base damage (assume Dex and a rapier) for our fighter, but we add sneak attack damage. That's 2d6 at level 3, so with advantage we add +2d6 (7) on a hit and +4d6 (14) on a crit. Attacks without advantage don't get sneak attack damage added in, so the disadvantage numbers from above carry over (I know you can get sneak attack damage without advantage, but we'll ignore that for simplicity).
With Advantage
- A normal roll of 1d20 will have a 35% miss, 5.00% crit (1.30 DPR), and 60.00% normal hit (8.70 DPR) for a total DPR of 10
- A roll with advantage will have a 12.25% miss, 9.75% crit (2.54 DPR), and 78.00% normal hit (11.31 DPR) for a total DPR of 13.85
- A roll with your DMs +2 rule will have a 25.00% miss, 5.00% crit (1.30 DPR), and a 70.00% normal hit (10.15 DPR) for a total DPR of 11.45
With Disadvantage
- A normal roll of 1d20 will have a 35% miss, 5.00% crit (1.30 DPR), and 60.00% normal hit (8.70 DPR) for a total DPR of 10
- A roll with disadvantage will have a 42.25% miss, 1.00% crit (0.12 DPR), and 56.75% normal hit (4.26 DPR) for a total DPR of 4.38 (identical to the fighter, as no advantage means no sneak attack)
- A roll with your DMs -2 rule will have a 45.00% miss, 5.00% crit (1.20 DPR), and a 50.00% normal hit (2.25 DPR) for a total DPR of 3.45
Conclusion
With your DMs proposed houserule, the expected DPR for any class is going to be decreased because of the fact that you're still only rolling 1 die, so the chance of a critical hit will not change. The biggest, well, advantage of rolling with advantage is it almost doubles your chance of a crit: 9.75% vs. 5.00% for a normal 20 crit and 19.00% vs. 10% for a champion fighter crit.
Indeed, that simple change reduces the overall expected damage output of the entire party, especially those classes that rely on burst damage in the form of more dice. As you gain in levels and get the extra attack feature, magic items/spells that add damage dice, and class features that change the damage dice done, the gap will only increase.
Best Answer
No, a Crit Fail doesn't automatically overrule Advantage.
The Advantage and Disadvantage section of the PHB clearly states:
Nothing in there says anything that would suggest rolling a 1 would cancel out Advantage so you would still take the higher of the two rolls.
The Rolling 1 or 20 section states:
So another way to look at it is that the higher of the two rolls becomes the "new" d20 roll for the attack and, so long as you haven't rolled two 1s, doesn't meet the requirements for a Critical Fail.
This is also backed by Mike Mearls (one of the lead designers, though not rules arbiter like Jeremy Crawford, for DnD) on SageAdvice: