To be successful at poker, you must know about probability. You don't have to be good at mathematics since most important probabilities in poker can be learned. However, you need to understand what probability is and how it is expressed.
The Odds (or probability) of something happening may be described in a number of different ways. For example, consider the probability/odds of rolling a six with a dice.
- The probabilty of getting a six may be described as 1/6 (one sixth). This is obviously because if you role a dice a large number of times, you will get a 6 one sixth of the time.
- This probability may also be described as 5-1 ("five to one"). This means you will fail to get a six 5 times for every 1 time you do get a six.
- The probability may also be described as 16.67%, because you will get a six 16.67 percent of the time.
Thus: 1/6 ("one sixth"), 5-1 ("five to one") and 16.67% are all ways of saying exactly the same thing.
The first probabilities you need to be aware of in Texas Hold 'Em are the odds of getting particular starting cards (your hole cards).
There are 1326 unique starting hands in Hold 'Em. There are six ways to get a pair of aces. The probability of getting dealt a pair of aces is therefore 6/1326 which equals 1/221 or 220 to 1. In English, this means you will, on average, get a pair of aces once in every 221 hands. You will also get a pair or Kings once in every 221 hands, a pair of queens once in every 221 hands and so on.
You will get a pair of some sort once in every 17 hands.
There are 16 ways to get AK (Ace-King) and so you will get this hand much more often than, for example, AA. You will get AK approximiately once in every 83 hands.
The top hands in Hold 'Em are often considered to be AA, KK, QQ, JJ, AK and TT (Ten,Ten). You will, on average, get one of these hands approximately once in every 29 hands. So you can see that you usually won't have to wait long before a decent hand comes along - all the more reason, therefore, not to play with rubbish hands.
Of course, these probabilities tell you what will happen on average in the long run. In reality, pairs of aces are like buses - you can wait a long time for one and then two come along one after the other.
You now need to know about drawing odds. i.e. You need to know how likely it is that your hand will improve as additional cards are dealt.
Here are some of the most important odds you need to know for the flop.
If you start with a pair, you will get three of a kind on the flop nearly 11% of the time.
If you start without a pair, you will pair one of your hole cards about 27% of the time.
If you start with 2 suited cards, you will get four cards to a flush about 11% of the time.
If you start with medium connected card (such as 67, 78, 89 or 9T), you will get 4 cards to a straight nearly 26% of the time., but often this will be an inside straight draw (e.g. 4 5 7 8, where only a 6 will give you a straight) rather than an open-ended straight draw (such as 6 7 8 9 which is better because either a 5 or a Ten will give you a straight).
Amazingly, these are pretty much the only probabilities you actually need to know for the flop. The odds of getting other hands such as flopping a full house, a straight, a flush or even pairing both your hole cards are just so small as to be not really worth considering. If you get them, count yourself lucky, but you can't play a hand simply on the extremely unlikely off-chance that you might flop these hands.
Now you need to know about your chances of improving your hand on the turn and the river.
On the turn and the river, it is best to think of probabilities in terms of "outs." An "out" is a single card that you believe will give you the winning hand. For example, if you have the Ace and King of diamonds in your hand and there are two diamonds on the flop, then another diamond will probably give you the winning hand.
There are thirteen diamonds in the deck and you already have four of them, so there are nine diamonds left. Therefore you have 9 "outs." As another example, suppose the flop shows 2 10 J and you have Q K. You believe your only opponent has a pair of Jacks. Therefore, a Q or K will give you a better pair and an A or 9 will give you a straight. You therefore have four 9s, four As, three Qs and Three Ks to aim at, so you have a total of 14 outs.
Note that "outs" refers to when you only need one card to make your hand. If you need two cards to make your hand (e.g. you need two hearts to make a flush) then you can usually forget about it - it's just too unlikely!
You can get tables that show you the exact probabilities of improving your hand given a certain number of outs. Fortunately, there is an easy way to estimate these odds without having to remember them all.
You just need to remember this: You have a 2% chance for each "out" on the turn, and a 2% chance for each out on the river. You have a 4% chance for making each out on either the turn or the river.
So , for example, suppose you have four cards to a flush on the flop.
You have 9 "outs."
9x2=18 so you can estimate that you wil get your flush on the turn about 18% of the time.
9x4=36 so you can estimate that you wil get your flush by the river about 36% of the time.
(The true odds are approximately 20% and 35%, but your estimate will be close enough in the vast majority of circumstances!)
Finally, you need to know how starting hands play against each other when played to the end.
This is particularly useful in tournaments, since players will often go "all-in" before the flop, especially towards the end of a tournament. (If all the players in a hand are "all-in", their cards will usually be turned over before the flop, turn and river - for dramatic effect, I suppose!)
There isn't really that much to remember here either.
People will usually go all-in with either a pair or two high cards (especially hands like AK and AQ)
If a pair is all in against two overcards (two cards higher than the pair), the pair is almost always a slight favourite to win (but only by a few percent). Commentators often refer to it as a "coin-flip" since each hand has approximately a 50% chance of winning. This match up of pair against overcards is the classic match up in tournament play and is usually responsible for the elimination of a large proportion of players.
If a pair is up against a higher pair, the higher pair will be a very big favourite and will win about 80% of the time. i.e. It is a 4-1 favourite and will win the hand four times out of five. The lower hand may be referred to as a "big dog" (a term used for a hand that has only a very small chance of winning)
If a big pair is up against two lower cards (not a pair) the pair, again, is a big favourite to win - it depends on the exact cards, but typically about a 4-1 favourite.
If two cards (not a pair) are up against two higher cards, the higher cards are favourite, typically a 2-1 favourite, but less of a favourite against hands like suited-connectors (two sequential cards of the same suite). E.g.
The concept of pot odds is critical to deciding whether to stay in a hand or not. The principle is simple - when deciding whether to stay in a hand you have to consider whether the reward you get when you win the pot is worth the money you must bet in order to stay in the hand.
Imagine that you are playing Hold 'Em and you have 4 Hearts (including an ace in your hand) by the turn.. We have already seen that your chances of you getting a flush on the river are approximately 4-1. Suppose again that there is $2 in the pot and that you must put another $1 in the pot to stay in the hand. You would be betting $1 to win $2. We say that the pot odds are 2-1.
If the odds of you getting your hand are higher than the pot odds, it may be best to fold your hand. Here's why: Suppose that you play this same hand 5 times. On average you will only get your flush once. If you get the flush, you will almost certainly win the hand. If you do not get the flush, you will almost certainly lose the hand. Therefore, you must make enough money in the one hand you do make your flush to pay for the four times you do not make the flush.
The pot odds are 2-1. On the one occasion you win the hand, you will win the $2 in the pot. On the other four occasions you will lose the $1 that you had to bet to stay in the hand. So clearly, over the course of 5 hands, you will lose a total of $4 when you lose and only win $2 in the hand you win. You are making a net loss of $2. On average, therefore, this hand is not usually worth playing. With pot odds of only 2-1, you should seriously consider folding your flush draw.
On the other hand, let us suppose that there is $7 in the pot and you must bet $1 to stay in the hand. The pot odds are now 7-1. On the one occasion out of 5 that you win the hand, you will win $7. On the four occasions you lose, you will lose a total of $4. Thus you are making a net profit of $3. On this occasion, it is worth you staying in the hand because the pot odds are so good.
The principle of pot odds, therefore, is that you must compare the odds of you getting a winning hand with the pot odds the pot is offering you.
Implied Odds
There is one complication to the idea of pot odds to consider here and it is this: Sometimes you should make a call even when the pot odds are slighly unfavourable. The reason for this is that when you do make your hand, you might be confident that you can bet and get a call. This extra proft when you win the hand might make it a profitable call in the long run. This concept is known as "implied odds."
Apart from deciding when you yourself should call, understanding pot odds helps you decide how much to bet. Suppose you have e.g. 2 pair on the turn and you suspect the only other player left in the hand is drawing to a flush. You will want to make a large enough bet to make sure that the pot odds do not justify him calling. If he doesn't call, you win the pot there and then. If he does call, he probably will not make his flush but if he does make his flush, you can be confident that you will get him in the long run since he has called at unfavourable odds.
