[Nick C]

The range I'm about to assign to BB may be too tight, but let's say it's AA-TT and AK. In that case, there are 12 hand combinations you're beating, 18 combinations you're losing to, and 1 you're tied with. Start throwing in hands like 99-77 and AQs and AJs and maybe AQ, and things get murkier, since we can't be sure which hands to add. Anyway, since you say he's predictable, I'm thinking maybe the AA-TT plus AK range may be about right.

All right, so that's a starting point, but I'm not sure where to go with it.

With JJ/TT, there's a good chance he'll fold to a flop bet. If so, this isn't necessarily such a tragedy, because we're going to have trouble winning many more bets from those hands anyway, and we'd rather not give infinite odds if he's not putting any more money in unimproved. Also, if we check behind on the turn, will BB bet the turn with JJ/TT often enough for us to actually call? I don't know. He might bet JJ/TT rarely enough that a turn call is unprofitable.

Hmm. I think I like a flop bet. If checkraised, I'd fold.

If he calls the flop bet, I'm worried, but is our straightforward opponent slowplaying? Does he have top pair while also fearing a set? I think I'm with Cold Cash and DMBFan23 on checking behind on a turn blank, given the chance. I don't really expect to be bet into, but if I was, I guess maybe it's a fold?

After that, the play on a river blank is difficult. I think I'd follow Cold Cash's plan and call a bet, after my show of weakness on the turn. What I'd worry about though is simply giving back the bet I saved by not walking into (and folding to) a turn checkraise. At the same time, though, checking behind on the turn does invite BB to take a stab at the river. Edit: Ugh. But how often would he still be in the hand with something you beat, on that board, after your flop bet and preflop cap? I don't know. In any case, though, I'm pretty sure what I'd actually do is call.