Yesterday, I noted here that Justice Kagan had recused herself from two state-prisoner habeas cases even though the Solicitor General had not filed an amicus brief. Tony Mauro has this post at BLT clearing up the reason.  It was the SG's decision not to participate, made by Ms. Kagan herself, that prompted the recusals.

In answers to questions from Sen. Jeff Sessions, R-Ala. about her recusal plans, Kagan forecast her actions when she said she would not participate in cases in which she approved or denied amicus participation. "If I personally reviewed a draft pleading or participated in discussions to formulate the government's litigating position, then I would recuse myself from a case," she wrote to Sessions.

It is unlikely that Justice Kagan's recusal will make a major difference in either case. I don't see her casting the fifth vote to reverse in either one.  Conceivably she might have been the fifth vote to affirm.  In that case, her recusal would make the difference between (1) an opinion favoring the habeas petitioner and setting a Supreme Court precedent and (2) a decision to let the grant of habeas relief stand in the individual case without setting a Supreme Court precedent (although the case would still be Ninth Circuit precedent).  Even that chance if remote, though, in my estimation. I expect a majority of the remaining eight to vote to reverse in both cases.