I think what’s being called “TFTWF” here is what some other places call “Tit for Two Tats”, that is, it defects in response to two defections in a row.
But wouldn’t the sequence then look like this?
D/C → D/C → D/D → C/D → D/C
and continue like this forever.
Why does TFTWF defect against C? What’s the forgiveness there?
Yeah, I think you’re right.* So it actually looks the same as the “TFTWF accidentally defects” case.
*assuming we specify TFTWF as “defect against DD, cooperate otherwise”. I don’t see a reasonable alternate definition. I think you’re right that defecting against DC is bad, and if we go to 3-memory, defecting against DDC while cooperating with DCD seems bad too.** Sarah can’t be assuming the latter, anyway, because the “TFTWF accidentally defects” case would look different.
**there might be some fairly reasonably-behaved variant that’s like “defect if >=2 of 3 past moves were D”, but that seems like a) probably bad since I just made it up and b) not what’s being discussed here.