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We have already seen how the relative strength of a poker hand can increase or decrease as flop, turn and river is dealt. For example is a big favourite against pre-flop, but becomes a huge underdog if the flop comes .

If you have a hand that is probably behind, but has the potential to improve to a winner, you need to decide whether it is worth continuing with it through the various streets, and how much you are prepared to pay to do so.

This article explains the calculations required to make the right decision about "drawing hands", ie, hands that will need to connect with later community cards to win.

In short, you need to identify the cards that will improve your hand (known as "outs"), and then determine how significant an advantage you will have. Finally you will need to calculate your odds of winning and whether the pot size makes the whole process worthwhile.

You need to use some basic mathematics to help you make correct decisions.

"Outs" are the cards left in the deck that improve your hand and hopefully win the pot at showdown.

There are 13 cards of each suit in the deck. You hold two of them, and another two are on the board. Four of the 13 hearts have therefore already been dealt, meaning that there are still nine hearts left in the deck. This means you have nine outs.

You have and the flop is . Now any ace or nine will complete your straight. There are four aces and four nines in the deck, so you have eight outs.

If one card is missing to complete a straight, you have four outs. For example, if your hole cards were and the flop was , your outs would be .

You have , and the board is . One of the four queens in the deck will make you a straight. If your opponent has a middle pocket pair, e.g. , then you have additional outs, as any king or any jack would give you a higher pair.

In this case, the number of your outs would increase to ten (four queens, three kings, and three jacks).

If you hold and hit a set on a board showing , you have a pretty strong hand. But it is not definitely a winner and could already be behind if any of your opponents has two spades in their hands.

However, you still have the chance here of improving your hand even further. There are seven cards that could make you a full house or better (a seven, three remaining twos and three remaining jacks), or the turn and river could be the same rank, which would also give you a full house.

You hold and the board is . You have both an open-ended straight draw and a flush draw. This means you have nine outs to make the flush and eight outs to make the straight. At the same time, you have to consider that two cards are counted twice (in this case the and the ), which have to be subtracted. Therefore you have a total of 15 outs here.

Although the term "out" typically refers to a card that improves your hand, there are also sometimes "hidden outs", which help you because they reduce the value of your opponent's hand.

You hold and your opponent has . The board is . Not only would the three kings and the three aces give you a higher two pair than your opponent, but any six or five would help as well. This is because with a five or six, the board contains two pairs that are both higher than your opponent's pocket threes, meaning that the fifth card, the kicker, would decide the outcome of the hand. Your ace is the best possible kicker.

In this instance, you have 12 outs, six of which are hidden.

Advanced players don't only calculate their own outs when on a draw. They also ask themselves what hand their opponent has, and whether one of the cards they hope to appear might also give the other player an even better hand. Cards like this are known as "discounted outs".

You have and the flop is . You have calculated eight outs so far (four aces and four nines).

But how will your outs change if one your opponents has two hearts e.g. and is therefore drawing to a flush? In this example, two of your outs, i.e. and the , would give your opponent a better hand - even if you hit your straight. This means you have to discount both cards from your outs. You would now only have six outs, which significantly reduces your chances of winning the hand.

In general you should take a pessimistic approach when it comes to discounting outs, as it is better to discount one out too many than one too few!

There are two very simple rules of thumb for calculating the probability of improving your hand using your outs:

**The probability of hitting a draw on the next card is:** *[number of outs] x 2*

**The probability of hitting a draw on the turn and/or river is:** *[number of outs] x 4*

You have a flush draw on the turn (nine outs). The probability of hitting the draw is [number of outs] x 2 = [winning probability in percent]:

9 x 2 = 18%

You have a gutshot straight draw (four outs) on the flop and want to know the probability of making a straight with two cards to come. The rule of thumb is: [number of outs] x 4 = [winning probability in percent]:

4 x 4 = 16%

Probabilities can be displayed as a ratio or odds, which is very helpful when playing poker.

- Odds describe the ratio between the probability of winning and losing.
- The winning probability is calculated as before. The losing probability is therefore:

[Losing probability] = 100% – [winning probability]

It's best to commit the most important odds to memory, instead of having to calculate them again and again..

You are holding on a board of . You've got middle pair. Assume that your opponent has top pair, with for instance.

You have five outs: three aces and two eights. The probability of improving your hand is 10% (5 outs x 2). The probability that your hand doesn't improve is therefore: 100% – 10% = 90%.

The odds are now [losing probability] / [winning probability]

In numbers: 90% / 10%. This can be simplified (both sides divided by 10), with the result being odds of 9:1.

You have on a board of . You assume that your opponent has top pair .

You therefore have ten outs (three kings and three queens for a higher pair and four jacks to make a straight) and your chance of winning is 20% (10 outs x 2). The probability that your hand will not improve is calculated as follows:

100% – 20% = 80%.

The odds therefore [losing probability] / [winning probability] are 80% / 20%, the result being odds of 4:1.

Certain similar situations appear frequently in Texas Hold'em, and you should try to memorise the odds of your hand winning in those instances. The odds that are of particular importance and appear often are highlighted in the chart below.

Download (.pdf)

Calculating the odds of your hand improving is only the first step in deciding whether to continue in a pot. You then need to figure out whether the size of the pot itself is large enough to warrant pressing on.

For instance it would be pointless speculating $500 with a gutshot straight draw if you only stood to win about $50. You know that the odds of hitting your draw are slim, and the financial gain of making your hand are not good enough to make the risk worthwhile.

Most cases are slightly more tricky to calculate, but the principle is the same. You have to calculate what are known as "pot odds" - the ratio between the size of the pot and the bet facing you. Then you compare those odds with the odds of your hand winning.

The size of the pot refers to the chips that are already in the pot, as well as all the bets made in the current betting round. If the pot odds are higher than the odds of you winning, you should call (or in exceptional cases raise). If the pot odds are lower than your odds of winning, you should fold.

You have on a flop of , so you have the nut flush draw. You have nine outs on the flop and currently the pot is $4.

Your opponent bets $1.

There is now $5 in the pot ($4 + $1), and it will cost you $1 to call. The pot odds are therefore 5:1.

According to the table above, your odds of hitting your hand are 4:1. That means that the pot odds are higher than your hand's chances of winning and you should therefore call.

You are paying $1 with a 4:1 chance of winning five times that amount. It is a good call - and some players might even raise here.

You have on a flop of . This is a gutshot straight draw, meaning you have four outs (any six) to make your hand. There is $25 in the pot.

Your opponent bets $5.

There is now $30 in the pot ($25 + $5), and it is $5 to call. Your pot odds are therefore 6:1.

However, according to the table the odds of winning the hand are 10:1. You don't have the right pot odds to continue in this hand and should therefore fold.

You would be forced to pay $5 with a 10:1 chance of winning only six times that amount. It would be a bad call.

If your opponent moves all in on the flop, you can make the same calculations as described above, but this time look at the "Odds Flop to River" column. If your opponent is all-in, you have the advantage that no further bets are possible. If you call, you therefore get to see not only the turn, but also the river without having to risk more chips.

You have on a flop of , which is an open-ended straight draw. You have eight outs on the flop.

There is $50 in the pot and your opponent moves all-in for $25. You therefore have pot odds of 75 to 25 ($50 plus the $25), and is $25 to call. When simplified, the pot odds are 3:1.

If you call you get to see both the turn and the river without any further betting. According to the column "Odds Flop to River" in the odds table, the odds of winning the hand are 2:1, and because the pot odds are higher, you should make the call.

Calculating odds, outs and probabilities can seem difficult and time-consuming, especially if you are a beginner. But the basics are quite simple to understand and the ability to make simple calculations can help you build a very solid foundation for your game. This part of poker is very well worth learning, especially if you intend to progress further in the game.

If you continually play draws without getting the right odds, you will lose money in the long run. There will always be players who don't care about odds and call too often. These players will occasionally get lucky and win a pot, but mostly they will lose and pay for it. On the other hand, you might be folding draws in situations where the odds are favorable.

If you use the strategies in this article consistently, you can avoid mistakes and gain an edge over your opponents.

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