TaiG is currently working on a jailbreak for 8.2/8.3 not 8.1.3. It has already been patched so it's unlikely that they'll proceed with jail breaking it when 8.3 is right around the corner. Also, 8.1.3 was a minor update while 8.3 has many enhancements and fixes security bugs. In my opinion, I'd update to 8.2 in case they decide to release the jailbreak for it
"It seems that the TaiG team is having difficulties breaking down Apple's iOS 8.2, since there are reports that the newest update is still un-jailbreak-able just like the previous 8.1.3 version. However, TaiG hopes that their team would find the vulnerabilities. They would reportedly be teaming up with other notable developers to crack Apple's latest operating system"
Read more: http://www.christiantoday.com/article/ios.8.2.jailbreak.taig.gives.statement.regarding.release.rumors/51579.htm#ixzz3WfhX4bsp