I know the 88 hand has brought a lot of discussion, so I figured it's worth mentioning why I checked the flop. This post will have a lot of numbers in it. You have been warned. 
I think that we have pretty decent equity on this flop when it comes down, but I'm not sure how awesome our equity is versus his calling range. I don't think it's bad by any stretch, but I think it's not a super-awesome value bet. I gave him this calling range pre:
22-TT,AJs-ATs,KTs+,QTs+,JTs,T9s,98s,87s,76s,65s,AJo,KQo
He's fairly 3-bet happy and off the top of my head I'm pretty sure he likes to 3-bet somewhat depolarized... 3-betting things like AQ.
I think he would likely fast play his two-pair+ range. According to Combonator (check it out in the first video of the series) he has 103 hands in his pre-flop calling range on this board. Two-pair+ is 15 combos, so thats about 15% of the time I'm getting raised for value. He's pretty raise happy so he may also raise me with some bare overs and BDFD type hands. That leaves me getting raised pretty often. Which I'm ok with given that I have 60% equity. If you take some of those hands out, though. Then I start not really getting "value" when he raises.
Board: 7d 6s 5c
Dead:
equity win tie pots won pots tied
Hand 0: 39.692% 38.83% 00.86% 15376 342.00 { 77-55, AcJc, AdJd, AsJs, AcTc, AdTd, AsTs, KcJc, KdJd, KsJs, KcTc, KdTd, KsTs, QcJc, QdJd, QsJs, QcTc, QdTd, QsTs, JcTc, JdTd, JsTs, T9s, 98s, 76s, 65s }
Hand 1: 60.308% 59.44% 00.86% 23540 342.00 { 8c8h }
He's only actually calling me here about 13% of the time (TT-88). Vs that range we have 36% equity.
Board: 7d 6s 5c
Dead:
equity win tie pots won pots tied
Hand 0: 64.462% 59.52% 04.94% 8250 684.50 { TT-88, 87s }
Hand 1: 35.538% 30.60% 04.94% 4241 684.50 { 8c8h }
So, if we just see how our equity is vs the combination of his raising range and his calling range (which isn't super accurate, but helps is get a image of how things look) we get this:
Board: 7d 6s 5c
Dead:
equity win tie pots won pots tied
Hand 0: 46.114% 44.19% 01.92% 23626 1026.50 { TT-55, AcJc, AdJd, AsJs, AcTc, AdTd, AsTs, KcJc, KdJd, KsJs, KcTc, KdTd, KsTs, QcJc, QdJd, QsJs, QcTc, QdTd, QsTs, JcTc, JdTd, JsTs, T9s, 98s, 87s, 76s, 65s }
Hand 1: 53.886% 51.97% 01.92% 27781 1026.50 { 8c8h }
Check out how not-awesome our value is by betting this flop. Sure, our hand is very pretty but we aren't really getting great value. It's also going to be get hard to get paid when we really realize our equity. When we are far ahead he mostly folds and when we're flipping and slightly behind a lot of money starts going in, AND we may even have to fold our equity at some point.
However, if we check I expect this guy to bet almost 100% of his range. Now my equity looks like this.
Board: 7d 6s 5c
Dead:
equity win tie pots won pots tied
Hand 0: 32.000% 30.66% 01.34% 32477 1420.50 { TT-22, AJs-ATs, KTs+, QTs+, JTs, T9s, 98s, 87s, 76s, 65s, AJo, KQo }
Hand 1: 68.000% 66.66% 01.34% 70612 1420.50 { 8c8h }
Now we're building a pot with much greater equity. I'm pumped to c/c this flop, and it's going to be really easy for us to click call again on the turn. We're just building the pot with equity much more often if we check.
Also, think of it from a perceived range standpoint. How many bluffs does really expect me to have when I bet this flop? Sure, I have some straight draws, but not that many really bluffy hands? It's pretty interesting that Combonator says he's folding this flop about 50% of the time, so we could actually bet ATC here. This is an example of a "bad" board to c-bet, but in reality it looks like a pretty good board to bluff. But he won't think that we are bluffing that much because it's a "bad" board to c-bet so we need to start thinking about having a checking range both because he won't call as much and to protect our checking range so we aren't just always folding every time we check.
What do you guys think?