Stats

You can't go past it, you need a good statistical knowledge of the game if you want to take the right decisions. How can you decide if you should call an all in with a flush draw if you have no idea what are the odds you will get your flush? Sorry if this gets boring for you, I'll do my best to keep it interesting (most sites will simply give you a chart, no way I will do worst than that!)

Preflop

Most of the difficult preflop decisions will be with a high pair or with 2 overcards (like 99 or AQ), so lets start with 2 overcards:

2 overcards vs a pair: AKo (offsuit) vs QQ has 42% chances of winning, this is just about the worst odds you can have with 2 overcards. Why? First of all, you have offsuited cards, so the odds of getting a flush are low, having suited cards usually boost your odds by about 2%. Now, the straight is also not likely because the only ways you'll get it is with TJQ (and there is already 2 Queen's gone) or with 2345. Best case scenario, the 2 overcards has 52% chances of winning and 2% for splitting, like in 89s vs 22.

1 overcard vs a pair: Now that's bad, like AQ vs KK! Since the only likely way to win this is to get one of the 3 Aces left in the deck, the odds of winning are low... 28%. Every time you only have 3 outs preflop against your opponent, your odds are in the 30% range.

Total domination, overpair! In this case, the overpair has between 77% and 92.5% chances of winning! The worst case (77%) is when you are facing suited connectors and your pair does not include a card that can help him get his straight or flush. The best case would be something like AA vs A6o, in which case he really needs a miracle to win.

Draws

You really should be reading my article about draws for that matter, but I'll give you a quick summary here. If you have a flush draw on the flop, you have 35% chances of getting your flush. Open ended straight draw has little lower odds, 32%. You can simply consider that you will get any of the 2 draws 1 time out of 3, that level of precision is more than enough! An inside straight draw has, of course, half the odds of an open ended straight draw.

2 overcards on the flop

Most of the time, when facing a difficult decision on the flop with 2 overcards, you will be against 1 pair, better know what are your odds of winning! You odds are going to be around 22%. You will have better odds if you have some kind of draw on top of that and you will have lower odds if your opponent has a draw on top of that.

You will also often face a draw. Most of the time, when people bets the flop with a draw, it will be a flush draw or an open ended straight draw. They both have similar odds, so I'll only tell you the worst of them: against a flush draw, your 2 overcards have 45% chances of winning. Yes, it's true, even though you have Ace high and your opponent has nothing, he is favored to the pot with his flush draw.

The powerful holdem hand, the set on the flop!

Unless you are facing an over set or some very lucky straight flush, you have at least 35% chances of winning the pot with a set on the flop. Yes, even against a flush or a straight, you still have 35% chances of winning because you can get a full house on the turn or river. Against an open ended straight flush draw, you have 58% chances of winning. Against anything else, you usually have at least 75% chances of winning the pot (like against a flush draw or an open ended straight draw). It's not even worth learning the odds against 2 pairs of lower, your odds are just awesome!

The other odds

Those are the most important odds. You can guess most of the other ones with this, like for example, 1 overcard on the flop has about half the odds as 2 overcards on the flop. Want more? Have a look at this.