In the previous part, we've covered two of the most common in-position plays as the opener: three barreling and river play after delayed c-betting. Today, we'll move on to an often misplayed Bet-Check-Bet line and examine an underlooked but crucial spot when we arrive at the river all the way checked down.
Bet-Check-Bet (BxB)
So you had the option to second barrel but chose not to. Check back on this previous article for reasoning. Once it's checked to you on the river, you have the option to bet again. Let's see what factors matter most when you are in decision-making.
Generally speaking, you would second-barrel with the top of your range, except for some gruesome, draw-completing turns that you opt to check back some sets or two pairs, etc. So, in most cases, you arrive at the river with a medium-strength hand that wasn't good enough to valuebet the turn but had good characteristics to bluffcatch the river or a give-up hand that now you have to reevaluate.
Let's discuss first our middling hands. You arrived at the river with JhTs after range betting the flop and checking back turn on a board of 
K 
T 
2 3 5 . Typically, you look for hands that could call you, and you beat. So, you are not considering turning your hand into a bluff, but instead finding enough combos to thin valuebet against. While the pool leads out most of their Kx combos, it's safe to say you don't have to be afraid of those. The question is, are there enough weaker Tx-s and lower pocket pairs, A2, a floating hand like A5 that picked up a pair, etc., that would pay you off? That depends a lot on how often Villain goes to showdown and how often they won at showdown. Besides that, if your opponent fits into the average category. Some players will be overly passive and have many Kx combos in this spot, which is a catastrophe when you try to valuebet thinly. Other opponents are non-believers or just have a good sense that your range consists of middling hands that are in trouble against pressure. Constantly assess the whole situation, focusing on your opponents' player type and what you can expect from them.
Now, let's say you had K 4 on the same board and used an overbet strategy on the turn, in which K 4 didn't fit. The thought process is similar to the JhTs, but now you have a way better chance of getting paid off. You beat all Tx combos that might want to look you up, and there is less chance that your opponent holds a slow-played top pair. If you face a tough opponent who likes to test you with raises in this spot, your hand is an excellent candidate to bet/call since you block possible two-pairs and straights that might play this way for value.
How about your air hands? First of all, you have to evaluate your showdown value. Let's assume that a reasonable opponent will bet most of their air hands, missed draws, etc., themselves, leaving a condensed range of weak pairs (weak bluffcatchers) and some ace-highs. We can all agree that if you have a 
7 6 on the board above, you have zero showdown value; you don't beat any hands ever. Naturally, you want to bet these hands to fold out better air hands and some weak bluffcatchers. Depending on your opponent, you don't need to size up to make these types of hands anyway and get fantastic risk-reward.
How about when you had an ace high, like 7 ? In this case, you might have some showdown value against weaker players who just give up the option to bluff the river completely, even when they don't have SD value. Besides, if you bluff low hands with no SD value as you are supposed to but also bluff up to your ace highs, you are virtually bluffing with everything, resulting in massive overbluffing. Consider that in a Button versus Big Blind spot, you c-bet range, you've arrived at the river with a 40-50% range (the entire range you opened with). Regarding the few value bets you can have, bluffing all your air hands is a total blunder, even when the pool overfolds a little bit.
Another aspect worth considering is the runout. Overcards and draw-completing cards will favor you and make a river bet more credible. On blank runouts, be prepared to get looked up more often.
Weak opponents can give away many tells about their game if you see inconsistency in their stats, low aggression combined with high folding numbers or a low wtsd. Another reliable tell could be snap acting/checking, which usually means: "I don't have anything worth considering to bet or call; let's hurry to see next hand".
Check-Check-Bet
A fairly uncommon situation, you might say, why care about it so much? Let's say you've opened 2,5bb from the Button, and only the Big Blind called you, so the pot is 5,5bb when you arrive at the river. It seems like a little, but compare giving up all the time to win, let's say, half of the time with a small bet. In the long run, a 1bb difference per hand means 100bb/100 hands (a total buy-in). Believe it or not, these nuances differentiate between winning and breakeven players.
Once again, it would help if you considered factors like your opponent and the runout. Some players don't fight for small pots; they have air and have already moved on. Others like to peel for such a low price (since we are talking about 2-5bb), so you need to identify them. Again, if the runout is a total brick, don't expect the same amount of fold compared to an overcard that you might represent credibly.
When you decide how much to bet, you need to enlist cards your opponent has and could call you with. It's true for both valuebetting and bluffing that you try to target that range. Let's say you made a new top pair. Then, you should find the biggest sizing your opponent could call with most of her one-pair hands. On the contrary, when you are bluffing, you try to size to fold out most of the possible weak bluffcatchers. Sometimes, all the bluffcatchers will call any reasonable sizing, so you must consider overbetting or targeting only air hands you wouldn't beat at a showdown. A 33-40% pot bet works fine in the latter case.
Conclusion
Both BxB and the Check-Check-Bet lines are very Villain and runout-dependent. When you reopen the action, you'll always risk receiving further aggression, which is the last thing you want with a relatively weak, middling range. Moreover, you'll have valuebets that seem very thin and sometimes difficult to find; on the other hand, you'll have so many air combos in these lines that it's natural to overbluff these spots. That's why it's key to understand how your opponents' range (and player type) will react to another bet on the river. Look for hints in their statistics and practice off the table to understand how certain runouts are better to be bluffed or given up. Also, experiment with the borderline hands that can go for thin value; your wallet will be grateful.
Take your time understanding and practising this immense topic! Good luck with implementing the new information!
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