The first thing to know is that there are 169 different two card combinations that a player can have as their hole cards: 13 pocket pairs, 78 unsuited card combos and 78 suited card combos. This might seem low, but you keep in mind that the suits of the cards don't have any value over one another (Hearts have the same odds of appearing as Spades.) After that, we need to roughly rank the 169 hands from top to bottom to be able to figure out what percentage of total hands they encompass. I'm not going to list them out here, because exact math will rarely come into play during an actual game, instead you need to have a good feeling for general ranges. I've listed out some ranges below along with the percentage of total possible hands that is included in the category, followed by the odds of being dealt one of those hands. There are other combinations that can be calculated, but if you're looking for a place to start, the list below will do you well.
- Pocket Pairs
- AA or any specific pair (0.45%)(220 : 1)
- AA, KK, QQ, JJ, or TT (2.26%)(43.2 : 1)
- Suited Cards
- Suited cards, 10 or better (3.02%)(32.2 : 1)
- Suited connectors (3.92%)(24.5 : 1)
- Connected Cards
- Connected cards, 10 or better (4.83%)(19.7 : 1)
- Connected cards, all (15.7%)(5.38 : 1)
- Big Card Combos
- Any 2 cards with rank at least queen (4.98%)(19.1 : 1)
- Any 2 cards with rank at least jack (9.05%)(10.1 : 1)
- Any 2 cards with rank at least 10 (14.3%)(5.98 : 1)
- Any 2 cards with rank at least 9 (20.8%)(3.81 : 1)
So what this means is that you can choose a number of hands that you want to play, and match that up with the number of times that you'll be dealt those hands. If you want to play tight, maybe you will play any 2 cards with a rank of Jack or better. That means you'll be playing about 9% of the hands that you are dealt, or about 1 in every 10 hands. The more hands you're playing, the more the average value of your hands drops.
The next step is understanding the type of player that you're playing against. Again, this isn't rocket science, it's really just deduction and math. If the player is a maniac who is playing 90% of the hands that he is dealt, he isn't the luckiest guy in the world, he's playing a bunch of garbage hands! If you only enter the pot with him when you are playing the top 9% of the hands that you're dealt that means that before the flop, your hand is going to be stronger than his hand 90% of the time. The remaining 10% of the time you're not necessarily beat, but that portion of his range is the same as the cards that you are playing.
Subsequently, if a player is super tight and is only playing 5% of his hands and you're playing 10% of your hands, whenever you two are in the pot together, 50% of the time he will have a better hand than you do.
Bringing the two together
Bringing the two together
So the part that tends to lose people, is trying to answer the question: "How do you know that he doesn't have Aces?" The true answer to that question is: "You don't." What you do know, however, is that there is only a 0.45% chance of someone being dealt Aces, and you know what percentage of their total range includes Aces. If someone is the tightest of the tight, and you know they only play pocket pairs of 10 or better, they are only going to play 2.26% of hands. If you act before them in an unraised pot, you will get them to fold to a bet when you hold any two cards 97.74% of the time. Then, whenever they call or raise your bet, you know that they are holding one of 5 possible hands, and you can play accordingly.
If you are playing against another player where their range is the top 15% of all hands, the odds of them having Aces when they play a hand against you is 3% (0.45/15). Knowing these odds, and being able to characterize the people you are playing against are probably the two most important parts of the foundation for becoming a good player.
Power of Position
There are generally 9 seats at a poker table, assuming the table is full, and the player who is first to act will rotate around the table with each hand. This is very important, because acting later in the hand is far more powerful than acting first. If you are last to act in a hand, you get to see what every person ahead of you does before you have to decide what you want to do. Now this doesn't mean that everytime you act last you're going to win the hand, but it does mean that you should rarely be losing money when you're beat and you should be able to maximize what you gain when you're winning. For example, if you have pocket 9's and you're first to act, you raise the hand, and two people behind you call. The flop comes Q 10 4. Now there are two over cards to your hand on the flop, since you're first to act, if you bet, it's easy for someone with either of those cards to call you and you have no idea what they have. If you check, it's easy for someone with any two cards to bet their hand, and you have no idea what they have. They could easily have a Q or 10 in their hand, or they could have a smaller pocket pair than yours, or even something like KJ. Being able to see what another players interest in the pot is before you have to decide what to do is always going to be better then needing to act first.
Avoid being results oriented
If you've played poker before, I'm sure you've heard someone recant some horrible bad-beat story about how someone beat them in a pot when they had pocket Aces when their opponent only had pocket 7's. So now, to make sure that no one calls them, they always overbet whenever they have a big hand to make sure they get all the "garbage" hands to fold. This type of player is being results oriented, and he's losing a ton of money when he plays like this. You want people to call with worse hands when you have Aces, you've got them beat! You also want to try and get them to put even more money into the pot when they are beat, because this is how you make money! Understand that about 15% of the time, they will win the pot with a smaller pocket pair, that's just the way the odds work. But that means in the long run, you will be ahead whenever you bet with Aces and get called. You have to think of poker over the long-term, not just an individual session.
For more information on probability in Texas Hold'em: http://en.wikipedia.org/wiki/Poker_probability_(Texas_hold_%27em)