Overbetting

This is only an issue in no-limit Hold'Em ; in Limit Hold'Em you bet size is limitted to be so small that you are almost always *under-betting*, that is betting less that you ideally would if you could control your bet size.  This makes it impossible for you to chase out draws in limit-hold'em, so there will generally be a lot more callers to the river.

Overbetting essentially turns a marginal hand into a terrible one.  That is, it puts you in a situation where you are simply bluffing instead of betting for value.  Right-size betting, or calling, are generally more +EV.  Of course, in some situations a bluff is the right move, you simply have to be aware that by over-betting you are turning your hand into a bluff.  This is sort of based on a simple Bayesian poker idea - your opponent may have some distribution of hands before you bet, eg. 20% good hands, 50% marginal, 30% poor, now if you bet a lot and he calls, that conditional probability means that the hands he will call you with are only the very good hands, so now you are facing much better hands, like maybe 70% good, 30% marginal.

Let's look at some examples; say you have A3 and you limp in from the button.  The blinds call you and the flop comes A26.  Both blinds check and you bet 3 times the pot size.  What kind of hands will call?  Well, they must assume you have a pair of aces or better, so they will only call if they can beat that.  Any other pair of aces will beat you, since you kicker is the lowest possible (A2 has two pair!).  So, anyone who calls you has you beat badly.  That means you're just bluffing.  Now, that doesn't inherently make this a bad play, but two other factors do make it a bad play - 1) hands they would fold are nearly drawing dead, so it doesn't hurt you much to let them stay in, and 2) you have a good bluff-catcher hand, if they don't have a pair of aces and make a play at the pot you can call and make much more money that way.  By bluffing and winning you are picking up only the blinds, if you can get them to bluff, you take many more chips.  The fact that there's no good draw out (assuming a rainbow flop) makes it safe to slow-play even your very weak pair of aces.  If they have folding hands, the best they can have is a low pair (5 outs) or a gutshot (4 outs), so letting them see one free card is unlikely to hurt you, and you can also see it on the board if something in the 2-6 range comes.

The problem with overbetting is that you're risking a lot of chips to win a few.  You will win small pots and lose big ones.  A lot of beginners and bad players overbet top pair, and you can make a lot of money from someone making that mistake.  It seems like a good play to beginners because they frequently win the pot and get to rake in the chips.  What they don't realize is that it's a small pot, and they're putting themselves at great risk.  As mentioned before, the overbet has turned their hand into a bluff, so this play has all the danger of a big bluff.  It would be foolish to make consistent big bluffs, but because they have something marginal like a pair, they feel like it's not a bluff.  Note that this is very different than a "semi-bluff" or a "bet on the come", in which case you have a legitimate draw.  A pair is not a decent draw, so if you're behind you have very few outs to come back.  The good thing about a proper semi-bluff is that when you get caught by a real hand, you still have a chance of winning.

You can see all this in terms of EV's.  When you overbet, it's simply a large bluff.  You might win the blinds (3 chips) 70% of the time, but when you're called, you're beat, and you lose 10 more of your own chips.  So, your EV for this play is : 0.7 * 3 - 0.3 * 10 = - 0.9 ; each time you make this play you're losing roughly one chip on average, even though you win 70% of the hands.  This also shows you how this bad play could turn into a good play - if your opponents are too tight, you might be able to risk less, say 5 chips instead of 10, and still get the same amount of folding from them.  If you can do that, your EV is now 0.7 *3 - 0.3*5 = 0.6 chips.  This is simply an illustration of the idea that right-sized bluffs are very good plays against opponents that are mistakenly playing too tight.

If you a playing against a consistent overbetter, you need to simply wait for a big hand.  Try to see cheap flops and hit something like two pair, trips, or more.  When you do hit it, you can get paid off well.  Let them take the blinds, you'll make it up many times over when they overbet with top pair or when you have a big hand preflop.  Once you do this, you can also use the large re-raise bluff.  If they are overbetting with marginal hands like top pair, if you come over the top for a huge raise, they will have to fold (assuming they are a good player), especially if you've been playing tight and showing them big beats (as you should).

One of the worst possible over-bets you can make is to go all-in preflop with a big stack when there are only blinds in the pot.  This is never *ever* a good play.  If you have a good hand, you'll probably just win the blinds, and you're giving up a lot of value.  If you don't have a big hand, you will often win the blinds when your opponents fold, but you will lose your whole stack when they do call you.  One exception is that it may be +EV to make this move in the long run if you can set your opponents up to think that you go all-in preflop with junk.

A lot of beginners have trouble with the concept of sizing your bet.  If you are a favorite, why not put all your chips in the middle?  You have to think about more than just your chance of winning - you have to think about all the cards he may have and what he may do with them, and what the final result will be in all those cases.  This is the "ev tree" that we've talked about before.  If you have a very big hand, you probably don't want to bet too big, because you want to sucker him into getting more of his chips in the pot; if you have a mediocre hand that you think is probably best, you should generally bet it, but you shouldn't risk too many chips just in case he does have a very big hand.

Underbetting

Underbetting is the opposite mistake, not betting enough.  Basically the problem with under-betting is it makes it very good for your opponents to call you when they are drawing.  You're giving them very good pot odds, which makes them happy to call, which is bad for you.  Note that underbetting can only be a problem with hands that are weak or need to defend.  Marginal hands that are currently the best are greatly improved if you can reduce the number of people drawing.  It's crucial to know that being up against fewer players *severely* increases your chances of holding up.  For example, let's say you have top pair, and there are 3 other people in.  You might bet 3 chips and get one caller, or you might bet 1 chip and get 3 callers.  In either case, you've got the same amount of opponent's money in the pot, but in the first case you are *much* more likely to win (assuming your hand is currently winning).  For example, with top pair you might have a 70% of holding up vs. one caller.  Against 3 callers you have only a (0.7^3) = 0.34 = 34 % chance of holding up !!  Basically by under-betting, you allow lots of people to see cheap cards and make hands that will beat you.  If you consistenly underbet you will find that draws keep making it against you, and it's your fault!

You need to right-size your bet so that draws will not have the right pot-odds to call you.  If they do then call you anyway, you make money in the long run.  If they fold, which is the correct play for them, you're still happy because you picked up the pot.  Depending on the kind of mistakes your opponent makes, you should bias your bets one way or the other.  For example, if they tend to call too often even when they have bad odds, you should bet more, allowing them to make that mistake.  The reason that you don't just always overbet the pot-odds has been discussed in the previous section on overbetting.

If you are playing against someone who's often underbetting (which many beginners and online players do), you should simply correctly chase your draws.  They probably have a pair, so you simply call with your weak pair, your straight and flush draws, and you try to make a big hand.  Beware drawing to things that will also make them a big hand (eg. drawing to two pair or trips).  They are giving you great odds to draw, so just take it.

Note that in Limit Hold'Em you are often forced to under-bet.  In order to get a sufficiently large bet in, you have to use a check-raise or similar tactic.  Still, most bets in multi-way limit pots will be under-bets, which makes it correct for draws to chase.  This is simply life in limit hold'em, and simple pairs won't win many multi-way pots.

One interesting concept in poker is that you can "turn a good hand into a weaker one" by playing it strangely.  What we mean by that is that you may as well have had the weaker hand because of how you played it, that you threw away the advantage of the hand actually being better.  The classic case of this is when you way over-bet with a marginal hand.  You have essentially turned that marginal hand into pure junk - you are now on a pure bluff and can't beat any hand that would call.  Another example of this is if you just limp with a high pocket pair trying to make a set.  Say you limp with TT, it's very likely there will be overcards on the flop; you played it the way you would play 22, not the way you should play QQ; if you're only going to play it strongly when a T comes on the flop, then you have turned your TT into 22.