Odds and Pot Odds
Before proceeding with this article you have to read “Outs for Dummies”, “Probabilities for Dummies” and “Pot Odds for Dummies” first. Please skip back, if you haven’t read them yet.
Good call, bad call
The pot odds are the ratio of the wager and the pot. The odds are the ratio of win and loss. If the wager is small compared to the potential winnings, your chance of winning can also be small.
A player has to pay 10 to win 100. This ratio is very good; the pot odds are 10:1. That means that his chance of winning can be pretty small, exactly 10:1. 91 % of the time he looses his small wager of 10, but he wins nice 100 in the other 9 %. The payment of 100 is so high compared to the wager that his odds don't have to be very high.
Vice versa: A player has to pay 100 to win 10. This ratio is rather bad and he must be damn sure to win (exactly 91 %).
This is the whole secret: If the odds are better than the pot odds, it's a good bet.
Odds and pot odds in praxis
Supposing, you have a straight draw on the flop with 8 outs. There are 100 in the pot and your opponent is betting 100. What are you doing with this draw? First of all, you calculate the pot odds which are 2:1 (200:100). Then you take a look at the probability of hitting the straight on the turn. 8 x 2 = 16. 84/16 = 5,25. The odds of hitting one of the 8 outs are about 5:1.
Now you simply have to connect the pot odds with the odds. The pot odds are 2:1, while the odds are 5:1. Because of the fact that 5 is bigger than 2, a call would be a bad investment. Let's take a look why:
There are 100 in the pot, the opponent is betting 100 and you have to call 100 to see the turn.16 % of the time you hit the straight and win 200. 84 % of the time you miss and loose 100.
This brings us to the following calculation: 0,16 x 200 + 0,84 x (-100) = - 52. Because of the fact that the result is negative, it would be a bad call which costs a lot of money in the long run.
How many outs do you need to call those 100 on the flop?
Supposing, you now have 12 outs, what gives you about 3:1 odds (12 x 2 = 24, 76/24 = 3). 25 % of the time you hit and win 200. 75 % of the time you miss and loose 100.
0,25 x 200 + 0,75 x (- 100) = - 25
The result is still negative and a call would be bad.
Supposing, you have 17 outs which equal 2:1 in odds.
33 % of the time you hit and 66 % of the time you miss:
0,33 x 200 + 0,66 x (-100) = 0
At this point the so-called break even point is reached. If the odds equal exactly the pot odds (2:1 in this case) the expected value of a call is 0 and it doesn’t matter if you call or fold.
Now you have a flush draw with one over card giving you 12 outs. The player now moves all-in with 1000 chips. There are 500 in the pot. Do you call or fold?
With 12 outs, the odds are about 1:1 (12 x 4 = 48 or almost 50 %):
0,5 x 1500 + 0,5 x (-1000) = 250
That means that you earn an average of 250 with a call, irrespective of the result. (Again, you have to think in the long term!)
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