
You hold AsKs, and the board on the turn is Kh7h7c8c. You bet the flop and turn, and your opponent calls. The river comes the 9s, so that the board reads 



. Your opponent checks. Do you bet, and if so, how much?
A typical argument against betting might be something like this:
"The board is too scary. Our opponent could have three sevens, or a full house, and now there's three to a straight on the board. Anyway, our opponent could well just have a busted flush draw, so there is no point betting."
To check here, however, potentially misses value from the hand. We have top pair, top kicker, and there are still a number of hands that we can beat which our opponent would find difficult to fold. These hands include KQ,KJ,K10,QQ,JJ,1010, or indeed a hand like 
which was drawing to the flush, but has now hit the second pair on the end. I recommend a small value bet, of between 30% and 50% of the pot.
A value bet is a reasonably small bet made on the river when you hold a good, but marginal hand. It relies on the fact that your opponent may have to call with a number of weaker hands. Getting the most from your winning hands with the correct value bet is one of the most important skills in the game.
Let's see what is wrong with the argument, for not value betting on the river in this pot.
Our opponent could have three sevens or a full house.
This remains a slim possibility, but if our opponent does hold a big hand and back-raise here, we should be able to get away from our hand. However, it is unlikely that our opponent hit three sevens on the flop because of the way he has played the hand. Some players would re-raise on the flop with three of a kind, most would wait to the turn and then check-raise. Very few would play such a strong hand by just calling twice, and then checking on the river. Indeed, the check on the river almost surely tells us that our opponent has a marginal hand, and we can beat a marginal hand.
There are three to a straight on board.
There are many boards where you should worry the possibility of a straight, but this is most definately not one of them. The straightening cards have come "runner-runner" (on the turn and river). It would be almost impossible that our opponent has a hand like J10 or 65 for the straight, given that he has called on the flop. The only feasible explanation would be that our opponent has 
or 
; his flush draw missed, but turned into a runner-runner straight. However, this is a remote possibility, and should not concern you enough to check.
Our opponent has a busted flush draw.
This is very possible, but it has no influence at all on whether we should bet or not. If our opponent has a busted flush, he will not be calling any bet, and so this hand is not relevant at all; it is a void scenario.
Logic says that we only need to think about two groups of hands:
1) The hands that we can beat, and may call us.
2) The hands that have us beat.
The hands that we can beat, but with which our opponent cannot possibly call, are not relevant to our decision.
In this scenario, we have eliminated most hands in category 2) from being a likely possibility, but there are enough hands in category 1) to justify a value bet. In any case where category 1) outweighs category 2) significantly, do not miss the value bet.
Examples - do you value bet or not?
You hold 
, and the board comes 



. Your opponent calls twice, and now checks to you on the end. The second eight on the end is not great news, and there is a possibility that your opponent has just outdrawn you. However, this is reduced by the fact he has now checked; many players would bet with three eights. There are still many hands in category 1) (e.g.99,77,A10,K10,Q10,J10,A2, 76) which you have beat and may pay you off for a small bet. Make a small value bet.
You hold 
, and the board comes 



. Your opponent calls twice, and now checks to you on the end. The queen has of course put an overcard to your pocket pair on the board. However, it should not be of too much of a worry; there are not many hands that include a queen that your opponent could be playing, given his calls on the flop on turn. Far more likely, he is playing a hand in category 1) like A7,76,33,44,55,88,99 or1010, and will call another value bet.
You hold 
and the board comes 



. Your opponent calls twice, and now checks to you on the end. Do not value-bet, check behind on the end. There are now two many hands in category 2), which have us beat (e.g.A10,K10,Q10,J10,A8,98,109 ,QJ,J7,76)
The biggest argument against value betting
Let us go back to the first example, where we hold 
on the board of 



. We have said that our opponent's check on the end could well be made with nothing but a busted flush draw. What if we bet and our opponent decides to come back over the top with a raise? We may then make a horrible mistake, and lay down the best hand.
This argument means it could be worth avoiding some value bets against very aggressive players, who you have seen make this move as a bluff.
Realistically, however, this is a move that you rarely see; more often someone would choose to bluff by betting out on the river, rather than check raising.
This worry of being check-raised stops many players achieving value bets, and winning chips that should be theirs. Sniff out every opportunity of getting the maximum number of chips into the pot with your winning hands, and you are well on the way to being a winning player.
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