House Rules

Grazing Damage

If an attack roll misses, it can still potentially do some grazing damage at the discretion of the GM.  If a player's attack roll is less than the enemy's AC but greater than half an enemy's AC, the attack can still do 1d4 damage.  If the attack roll is less than half the enemy's AC but greater than 5, it can still do 1 damage.

This damage won't stack with the Graze Weapon Mastery property, which would always hit.

Graze (D&D rules)

If your attack roll with this weapon misses a creature, you can deal damage to that creature equal to the ability modifier you used to make the attack roll. This damage is the same type dealt by the weapon, and the damage can be increased only by increasing the ability modifier.

Heroic Inspiration

Players can gain a charge of heroic inspiration in a number of ways, usually at the discretion of the GM when they do something awesome or particularly well.  It's also possible to obtain heroic inspiration through story means.

The charge of heroic inspiration can be used to increase any d20 roll up to a 20.  The roll will not function as a natural 20; it simply makes up the difference after a player rolls, whatever it is, if they decide they want to use their charge in order to have as good a chance as possible to succeed at their task as they can have.

The charge of heroic inspiration can also be used according to standard D&D rules:

Heroic Inspiration (D&D rules)

If you (a player character) have Heroic Inspiration, you can expend it to reroll any die immediately after rolling it, and you must use the new roll.

Thieves tools and lockpicks

Thieves tools can be used to pick locks or disarm traps.  They let you add proficiency to the trap disarming or lock picking.

Lockpicks can be used to pick locks, but do not add proficiency to the pick attempt.

Both things are destroyed if the attempt fails.  If your roll is less than half the requirement to pick the lock, then your tool breaks in the lock, and it cannot be attempted again.  Otherwise, so long as you have enough picks or tools, you can keep trying.  Both locks and traps require straight dex checks, unless you have some feat or skill that adds proficiency.

If you have neither a lockpick or thieves tools, you can improvise something to pick a lock, but must roll with disadvantage.