Lets say a lvl 1 rogue who has 10 str is using a shortsword that is 19/20 to crit. The rogue goes up against a mob that has ac of 20 or higher and rolls a 19. Does the rogue hit said target?
Increased Threat Range: Sometimes your threat range is greater than 20. That is, you can score a threat on a lower number. In such cases, a roll of lower than 20 is not an automatic hit. Any attack roll that doesn't result in a hit is not a threat.
Only a natural 20 always hits, regardless of AC.
No the rogue misses the target. A natural 20 is the only roll guaranteed to hit the target, no matter what weapon you use.
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From the PFSRD:
Sometimes your threat range is greater than 20. That is, you can score a threat on a lower number. In such cases, a roll of lower than 20 is not an automatic hit. Any attack roll that doesn't result in a hit is not a threat.
Okay tyvm