No Limit Holdem Tournament • 2 Players

$6.85+$0.15

Although probably most people disagree, I like the turn barrel for thin value against flush draws and overcards.
However, on the river there's hardly any reason for betting because it's neither value (no Ace-high is calling a river bet imo), nor bluff (your small betsizing will not fold out 4x).
 
When having a tough decision about betting the river IP, you need to figure out, depending on your opponent, whether:
a) you're attempting a thin value bet
b) you're attempting a thin bluff.
 
Keep in mind that there will always be at most one of these two cases. If you find out you're in situation:
-a => only bet if his range contains more combinations of better hands than worse calling hands (yes, please DO count them!)
-b => only bluff x% of the pot if the ratio of better folding hands and better calling hands is greater than x%.
-none of the above (i.e. way ahead/way behind type of river) => never bet.
 
You can do some simple math yourself and arrive at the same conclusions.

I find monotone boards players tend to play pretty fit or fold on. 
In the sense that they will continue with a pair, a flush or a FD. 
*Note this comes with the caveat that most players I play against (3.5-15 level) are weak tight fish and play fit or fold on the flop regardless of board texture.
 

It makes them great boards to cbet when checked to in position with your bluffs because they will take the pot down with a high frequency. 
With bottom pair, you will only get value from passively played FDs. 
 
When you cbet here, what's your plan vs a c/r? 
Will you flat and hope villain shuts down? 
Will you fold? 
 
I think whether you bet here for value or not depends on how confident you are villain will play his draws passively and that he will play very straight forwardly on later streets if he doesn't make his draw. That is, by betting here, if villain continues, you have tough turn and river decisions. 
 
Personally (not sure if it's right or wrong?), in these spots where you aren't getting much value from villain's continuing range and you have showdown value which you don't want to have to fold if villain c/r (or starts betting on later streets), I prefer to check back and bluff catch the turn then play the river in position depending on villain's bet sizing and the board texture. 
 
I think you're overplaying your hand going for 3 streets of value with bottom pair on these type of boards. 
Especially the 3rd barrel.
There is basically nothing that calls a bet which you're ahead of.