I'm BB with Jh3s.

Cepheus raises button. I call.

Flop: 9h10hJx.

I check, he bets, I raise, he calls.

Turn: 8x. I check, he bets, I call.

River: Brick (can't remember. I write down HH during next hand. site provides no HH)

I check. He checks back K6.

Good turn check and call.
Good check on river-to catch any bluffs.

Mostly confused About his turn bet.

I think it's a good example of betting with a dominating draw, which I've been thinking about a lot lately. I made a post about it here:

http://forumserver.twoplustwo.com/22...-draw-1525414/

Cepheus says you should mostly be leading the turn. He will also be checking it back fairly often depending on which K6 he has. He'll also go for another barrel on the river sometimes. http://poker.srv.ualberta.ca/strategy

I don't see what's so confusing about it. I'd lead the turn for sure.

For leading with Jh3s, it actually depends on which 8x falls on turn. On 8s it barrels 82% but on 8d it barrels 57%. For all other combinations, it barrels much less than 50%. I don't know how significant this is honestly, J3 is probably a borderline hand and there could be many different ways to mix frequencies and obtain equilibrium.

Actually I like both lines, I would play the same too,

I am testing my solver vs Cepheus a bit lately so I've run this hand as well. I removed flop donk to make it a bit faster and solved to 0.45mb/hand (Cepheus is 1mb/hand overall).
It looks like you played optimally with your turn call being worth 0.04bb comparing to a fold:
http://i.imgur.com/ZIqyo6d.png

It would be nice to know what the blank is but it seems the bluffing range is geared towards low pair (to block some random 2 pairs which got there on the river like for example J3 on 3 river) and A-highs (to block A7) as your calling range on the river looks like this:
http://i.imgur.com/We4CCX7.png

So the bluffing range looks like this:
http://i.imgur.com/pwl6zhC.png

(again, apparently to block A7o combos and J3 combos but also J5/J4/J2)

It seems the mixing isn't that random. I compared some solutions to Cepheus and mixing frequencies on "insignificant" hands are amazingly close. For example see those for c/r flop range:

http://i.imgur.com/3z4To7v.png
http://i.imgur.com/pzrjXd8.png

This is different algorithm than they use and better accuracy but still the frequencies match almost exactly even for hands like Js3c and Js3d.

There is apparently a reason why Ks3c check-raises more than Kd3c

Don't see anything unusual about the way hand played out.