Pot Odds and Pot Percents
In common poker parlance, "pot odds" refers to the ratio between what you stand to win and what you're putting in. It's a simple way of tracking the idea that the pot gets very large, so that even with a small chance of winning, it's a good move to get to a showdown. As usual, the full correct analysis involves EV and your chance of winning and future actions, etc. and you should try to roughly do those things in your head, but pot odds is a good basic way to get into that.
One thing to be clear on is that "pot odds" is about calling. You're trying to decide whether to participate in the pot or not, to try to get to a showdown. Once you decide that calling is a good move, you may or may not want to raise. Raising depends on various factors unrelated to pot odds.
So, what is pot odds? If the pot is size P and it's C more chips for you to call, the pot is "offering you odds" P:C written in odds. Personally, I find odds very confusing and hard to work with. What's typically more useful is the pot size after you call (P+C) and the "pot percent" C/(P+C). I'll refer to this as the PP (Pot Percent) - it's the percent chance to win which you must have in order for playing in the pot to be profitable. You'll need to learn to count the pot quickly in units of bets. If the pot after you call is N bets, then the pot percent is just PP=1/N. Note again that this all really isn't right, because you need to consider EV's and future action, and what he has; the chance of winning you compare to PP should be the chance of winning against the hand you suspect he may have.
The time when you typically use pot odds is when you're on a draw. If you think you have the best hand, you certain call a bet, and you may raise. So, you think you're beat, and you have some sort of draw to make the best hand. You're basically comparing your chance of making that hand to the Pot Percent offered. If the chance of making your hand is better than the PP, you should call. In the simplest form, you should only consider your chance of making your draw on the next card. For example, on the flop there are two more card to come for you to make your hand, but there may be more betting action on the turn, so you can't simply assume that you have two cards to make your draw and you only have to pay one bet. Instead, just look at your chance of making it in one card, and then do the same thing again on the turn. This does mean that you may be able to call and see one more card on the flop, but you'll have to fold on the turn. Of course this isn't true if you're getting all-in, you now have two cards to make your hand and you don't have to pay any more on the turn. This means that it's actually much easier to call all-in when you're on a draw than it is to call when you're still live (this is the advantage of being short-stacked). For example, if you can get all-in preflop against many players, you can often get something like 5:1 pot odds, and you have a full board of cards to make the best hand!
The basic principle here is that if you are getting equal "money odds" and odds of winning, or equal "pot percent" and chance of winning, then it's an even money proposition. Like if someone offers you an even-money bet on a coin flip, that's a 0 EV proposition. Similarly, if someone offers to flip two coins and pay you 3:1 only if two heads come, that's also even money, since you have a 25% chance of winning, and you win 3 or lose 1, and 3 * 0.25 - 1 * 0.75 = 0. Now, if you can bias either of those things in your favor, you can make money, either by having a better chance of winning than the "pot odds" show you, or by having better pot-odds than your chance of winning.
In poker you will frequently be calling when you're pretty sure you're beat. That doesn't mean it's a bad call if you're getting good money for your call. Calling when you're behind is a part of winning poker - calling when you're behind but getting good odds for your call.
When you're drawing, the common way to compute your rough chance of winning is by counting your "outs". Your outs are the cards that will make you a better hand. For example, if you have a pair, your primary outs are the 2 other cards of the same rank which will make you a set. If you have a 4-flush (four cards of the same suit), then your outs are all the other cards of the same suit (usually 9 more cards), so you have 9 outs. If you have a 4-straight, you have 8 outs (the 4 cards of each rank above and below your 4-straight). When you know your outs, your rough rule of thumb for your chance of making an out on one card is roughly 2*O % for O outs. More accurately, it's O/N for N cards left in the deck. For example, if you have seen your hand and the flop then there are 5 known cards and 47 unknown cards, so the chance is O/47 ; on the turn it's O/46. It's accurate enough just to think of 2*O % (that's O/50). This leads to my rough rule of thumb for calling when you're drawing :
count your outs O
count the pot size, in units of how much it is to call, *after* you call, N
multiply them : O * N (outs * pot)
compare to 50
if the result is 50 or bigger, call. If it's smaller, fold. If this index is anywhere in the range 40-60, it's a marginal decision. You need to use some judgement then, about what the future action is likely to be, whether you can get paid when you make your draw, how much it will cost when you don't make it, etc.
Note that "Outs" is only a very rough estimate of your chance of winding up the winner. To make a proper estimate, you need to think like I describe in "Hole Ranking". Generally what good players do is to start from the rough estimate that Outs gives you. Then you put your opponent on various hole cards and see how those affect your outs. He may also be improved by the card you are chasing, or you may even be drawing dead (eg. if you are drawing to a low flush and you think there's a 10% chance he is also drawing to a flush). You sort of mentally take these into account and adjust your "outs" in your head. Similarly, you have to bias for "implied odds". If you think you will make your hand and get paid well, you can chase more; if you think you might make it and not get paid well, you should chase less. You can account for these by imagining a slightly different pot size when doing the pot odds computation.
Below that is a chart listing the number of outs given a particular drawing hand, and what hands those outs will give if made. (@@ chart is from rgp, so I need to remake it to avoid copyright problem). Be wary of ever thinking in terms of your chance of winning on both the turn & the river. Usually it's best just to think in terms of taking off one card, but we'll discuss that more later.
Chances of making a hand on the turn/river/both
turn turn river river t/r t/r
Outs (%) (X:1) (%) (X:1) (%) (X:1)
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20 42.6 1.35 43.5 1.30 67.5 0.48
19 40.4 1.47 41.3 1.42 65.0 0.54
18 38.3 1.61 39.1 1.56 62.4 0.60
17 36.2 1.77 37.0 1.71 59.8 0.67
16 34.0 1.94 34.8 1.88 57.0 0.76
15 31.9 2.13 32.6 2.07 54.1 0.85
14 29.8 2.36 30.4 2.28 51.2 0.96
13 27.7 2.62 28.3 2.54 48.1 1.08
12 25.5 2.92 26.1 2.83 45.0 1.22
11 23.4 3.27 23.9 3.18 41.7 1.40
10 21.3 3.70 21.7 3.60 38.4 1.61
9 19.1 4.22 19.6 4.11 35.0 1.86
8 17.0 4.88 17.4 4.75 31.5 2.18
7 14.9 5.71 15.2 5.57 27.8 2.59
6 12.8 6.83 13.0 6.67 24.1 3.14
5 10.6 8.40 10.9 8.20 20.4 3.91
4 8.5 10.75 8.7 10.50 16.5 5.07
3 6.4 14.67 6.5 14.33 12.5 7.01
2 4.3 22.50 4.3 22.00 08.4 10.88
1 2.1 46.00 2.2 45.00 04.3 22.50
Number of Outs Given a Particular Hand to Improve
Outs Given In attempt to make
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15 Open Straight Flush Draw Straight, Flush, Straight Flush
12 Inside Straight Flush Draw Straight, Flush, Straight Flush
9 Flush Draw Flush
8 Open Straight Draw Straight
4 Gut Shot Straight Straight
4 2 Pair Full House
2 1 Pair Three of a kind
1 Three of a Kind Four of a kind