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I'm making a game that uses a dice pool rolling system (for my purpose it's always a d12 and no other dice), and I wanted to figure out if making a 'critical hit' mechanic was possible, that is rewarding rolls roughly 5% of the time.

Playing with anydice this set up:

output 1d12 >11
output 2d12 >21
output 3d12 >29
output 4d12 >37
output 5d12 >45

Gets this output for 'criticals':

I admit with one die, of less that 20 sides, 5% is impossible. But the others are close and seem to fight a pattern of getting over the maximum results (12, 24, etc) - some number (1,3,7,11,15) (possibly \$(n-1)\times4-1\$ for all but the first).

But I cannot say this is the easiest to calculate as you need to sum all dice faces (and so, as your dice pool goes up so does the total sum).

Is there a way to simulate this without summing all dice faces?

The answer needn't use anydice, but I have and might be relevant.

I'm making a game that uses a dice pool rolling system (for my purpose it's always a d12 and no other dice), and I wanted to figure out if making a 'critical hit' mechanic was possible, that is rewarding rolls roughly 5% of the time.

Playing with anydice this set up:

output 1d12 >11
output 2d12 >21
output 3d12 >29
output 4d12 >37
output 5d12 >45

Gets this output for 'criticals':

I admit with one die of less that 20 sides 5% is impossible. But the others are close and seem to fight a pattern of getting over the maximum results (12, 24, etc) - some number (1,3,7,11,15) (possibly \$(n-1)\times4-1\$ for all but the first).

I cannot say this is the easiest to calculate as you need to sum all dice faces and as your dice pool goes up, so does the total sum.

Is there a way to simulate this without summing all dice faces?

The answer needn't use anydice, but I have and might be relevant.

I'm making a game that uses a dice pool rolling system, and I wanted to figure out if making a 'critical hit' mechanic was possible, that is rewarding rolls roughly 5% of the time.

Playing with anydice this set up:

output 1d12 >11
output 2d12 >21
output 3d12 >29
output 4d12 >37
output 5d12 >45

Gets this output for 'criticals':

I admit with one die, of less that 20 sides, 5% is impossible. But the others are close and seem to fight a pattern of getting over the maximum results (12, 24, etc) - some number (1,3,7,11,15) (possibly \$(n-1)\times4-1\$ for all but the first).

But I cannot say this is the easiest to calculate as you need to sum all dice faces (and so, as your dice pool goes up so does the total sum).

Is there a way to simulate this without summing all dice faces?

The answer needn't use anydice, but I have and might be relevant.

I'm making a game that uses a dice pool rolling system (for my purpose it's always a d12 and no other dice), and I wanted to figure out if making a 'critical hit' mechanic was possible, that is rewarding rolls roughly 5% of the time.

Playing with anydice this set up:

output 1d12 >11
output 2d12 >21
output 3d12 >29
output 4d12 >37
output 5d12 >45

Gets this output for 'criticals':

I admit with one die, of less that 20 sides, 5% is impossible. But the others are close and seem to fight a pattern of getting over the maximum results (12, 24, etc) - some number (1,3,7,11,15) (possibly \$(n-1)\times4-1\$ for all but the first).

But I cannot say this is the easiest to calculate as you need to sum all dice faces (and so, as your dice pool goes up so does the total sum).

Is there a way to simulate this without summing all dice faces?

The answer needn't use anydice, but I have and might be relevant.

I'm making a game that uses a dice pool rolling system, and I wanted to figure out if making a 'critical hit' mechanic was possible, that is rewarding rolls roughly 5% of the time.

Playing with anydice this set up:

output 1d12 >11
output 2d12 >21
output 3d12 >29
output 4d12 >37
output 5d12 >45

Gets this output for 'criticals':

I admit with one die, of less that 20 sides, 5% is impossible. But the others are close and seem to fight a pattern of getting over the maximum results (12, 24, etc) - some number (1,3,7,11,15) (possibly $(n-1)*4-1$ for all but the first).

But I cannot say this is the easiest to calculate as you need to sum all dice faces (and so, as your dice pool goes up so does the total sum).

Is there a way to simulate this without summing all dice faces?

The answer needn't use anydice, but I have and might be relevant.

I'm making a game that uses a dice pool rolling system, and I wanted to figure out if making a 'critical hit' mechanic was possible, that is rewarding rolls roughly 5% of the time.

Playing with anydice this set up:

output 1d12 >11
output 2d12 >21
output 3d12 >29
output 4d12 >37
output 5d12 >45

Gets this output for 'criticals':

I admit with one die, of less that 20 sides, 5% is impossible. But the others are close and seem to fight a pattern of getting over the maximum results (12, 24, etc) - some number (1,3,7,11,15) (possibly \$(n-1)\times4-1\$ for all but the first).

But I cannot say this is the easiest to calculate as you need to sum all dice faces (and so, as your dice pool goes up so does the total sum).

Is there a way to simulate this without summing all dice faces?

The answer needn't use anydice, but I have and might be relevant.