3a. If the runner has 5 cards, they need to fail all three traces to flatline. So the corp must outspend what the runner has possible to spend three times. If the runner has X credits, the corp needs X credits for the first sub to succeed (trace1+x canât be beaten by X credits and 0 link). Corp needs X-1 credits for the second trace to fire, and X-2 credits for the third trace to fire.
Assuming Making News still has access to its two recurring credits, it has functionally 22 creds for the traces. So 22 must be greater than or equal to X + (X-1) + (X-2), or 3x-3. 25 >=3x, which means the runner needs 9 credits to survive. This of course assumes the runner doesnât have access to the bad pub from rezzing Shinobi, in which case they only need 8 credits (plus the bad pub) to survive.
3b. This is a much worse situation for the runner, obviously. The runner now must guarantee that a trace doesnât fire by outspending what the corp can afford. If the runner has fewer credits than or equal credits to what the corp can spend (22), then they will flatline. If the runner had 22 credits, for example, and spent them optimally to avoid flatlining, they would spend all 22 on the first trace, since itâs the easiest one to beat and credits lose value when theyâre competing repeatedly against base link strength. If they spend 22, however, the corp would spend all 22 as well and win by 1, and then automatically win the second and third trace because the runner has no credits to compete. So the runner needs at least 23 credits to guarantee they wonât die, and would have to spend them all on the first trace. With more credits the runner could choose to beat the second or third sub instead of the first, thereby saving themselves some more cards (but probably not money, sadly). Bad pub changes this by one again.