Odds & Outs advanced

Introduction

In this Article

• Odds and outs
  
• The Odds - Sheet
  
• Discounted Outs and Implied Odds
  

The Flop

The most important street in Hold’em is the flop. 5/7 of all information is now available and you can make serious considerations of how good your winning chances are. The flop is the right moment for a critical stock-taking. Hands which have been very strong pre-flop can be worthless on the flop. It is a question of how good your hole cars work together with the community cards.

The absolute value of your hand

You can classify your hand into the following categories in hierarchical order:

Trash
Drawing Hands (you still need to improve)
Made Hands (1 pair or better)
The Nuts (the best possible hand)

It is a little bit more complicated if a strong drawing hand is more valuable than a made hand, but in most cases, the order above fits. Of course a made hand is getting better the closer this hand is at the nuts.

The relative value of your hand

The relative value of your hand is way more important than the absolute value. You have to beat your opponents. The second best hand does not bring anything, even if it’s a nice straight. The opposite is the case. It is the most expensive hand.
It is hard to evaluate the relative value of your hand because you don’t know the hands your opponents hold. For that reason you try to analyse your opponents (called “educated guess”). The information this assumption is based upon consists of the following parts:

If there is a pre-flop raiser, there are justified chances that your opponent already holds a strong made hand (high pocket pair).

(see above)

If you are playing against one player, ace high can be a strong hand on the flop. But if you’re pit against 5 opponents, even an overpair (like aces) might not be enough to be ahead. There is quite a chance that an opponent holds two pair or better.

If opponents raise and reraise, you should hold a very strong hand if you want to continue.

Drawing Hands (Draws)

The meaning of drawing hands on the flop is pretty simple: You don’t even hold a pair. For this consideration we are always behind.

Explanation: If you play heads-up, you will often win with ace-high. In this case you should assume that hands like AK are a made hand even if you did not improve on the flop. If you hold a middle pair in a multiway pot, you are behind in most cases and have to treat this hand as a drawing hand.

Chance-Risk-Relationship

Supposed you evaluate your hand as a drawing hand, what do you have to do?
In general, you have to evaluate your chances of winning the hand in relation to the pot-size. This reflection will give the necessary information if you should go to the turn.

The decisive question is: Is the expected value higher than the money you have to invest in the average?

If you want to calculate the chance-risk-relationship, you have to compare two different values with each other: The pot-odds and your winning chances (also expressed in odds). The key to this calculation is called “outs” and will be explained now.

The Outs

An out is a card which will improve your hand to a probable winning hand.
Example: Let’s assume you hold 7 6 on the button, 5 opponents are in the hand and the flop shows 8 4 A . Your gutshot draw gives you four outs: the four fives. Against this number of players, the sixes and sevens are not serious outs. It is not impossible, but very unlikely, to win the pot with a one pair hand on the turn.

The probability to win

Probability shows the chance that an event might happen. It is expressed with a number between 0 and 1, whereas 1 would be 100% chance and 0 would be no chance at all. In the gutshot-example there are 4 cards which will help to improve your hand. How high is the probability that one of these cards will show up on the turn? To calculate the probability, you have to divide the favourable cases by the number of all cases.

Requirements: The deck includes 52 cards. You know 5 of them on the flop and 47 are still unknown. As for the unknown cards, 4 will help you.

Calculation: 4 over 47 = 0.0851. The probability that you improve your hand on the turn is 0.0851 = 8.51%.

The Odds

In contrast to probability, odds express the chance of an event not to happen. They describe the situation in a kind of negative way. Displaying odds is more handy at poker. Odds are expressed as a weighing of favorable against unfavorable cases. In our example there are 47 possible turn cards. Out of these 47 turn cards there are 4 favorable and 43 unfavorable. So the odds are 43:4. For a better transparency, we reduce this value in order to display a 1 on the right side (we divide 43 over 4). The result would be 10.75:1. The bigger number is on the left side, because it expresses the chance of the event not to happen. The event “improving the gutshot draw to a straight” would be the 1. The event “not improving the gutshot draw to a straight” would be displayed by the 10.75. To simplify the calculation, we round off the 10.75 to 11, so the simplified odds are 11:1. That means: In 12 cases we will improve our hand once and do not improve 11 times. To be clear: The probability to improve our hand on the turn is 1/12, not 1/11! The odds display 12 events (11 + 1). The events are divided into favourable and unfavourable. Using odds instead of probability has two advantages: 1. it gives a better overview and 2. it is compatible with the pot-odds (see below).

The conversion of odds to probability is calculated like this:
p to q = q/(p + q)
For this example: 11 to 1 = 1/(11+1)

As you have seen above, odds are a confrontation of favourable and unfavourable cards. But there is also another method:
1. You divide the number of unknown cards by the number of outs: 47/4 = 11.75
2. You subtract a 1 to express the odds: 11.75 – 1 = 10.75. Your odds are 10.75 to 1.

The Pot Odds

Pot Odds describe the relation between expected profit (the size of the pot) and expected investment (how much do I have to pay to see the next card). The past does not concern this action at all. Forget what you have already put in the pot – it is not your money anymore. Just start thinking about what you might put into the pot in the future!

Example:
You have to pay $1 to see the next card; the pot already consists of $10. As a result, you get pot odds of 10 to 1 (10:1)

Final Calculation

At the end you only have to compare the pot odds with the winning(chances)-odds. If the relation is positive you should stay in the hand. With a negative result, you should fold.

We go back to our gutshot example. 6 players (you included) called pre flop (6 SB small bets). The small blind bets the flop. All other players call. The pot size is now 11 small bets. You have to spend 1 SB to see the turn card. The pot odds are 11:1 and so are the profit odds. The relation is balanced, an easy call. It would be even better if the pot odds were 20:1. The situation would be very profitable. In average, you would lose $1 11 times and win $20 once. To calculate your average gain, the difference of $9 can be divided among the 12 events (9/12 = 0.75). You would make an average profit of $0.75 per event. Your call would have had an expectation value of $0.75.
It would be a totally different situation if the pot odds would be 5:1. You would lose $1 11 times and win $5 once. All in all, that would be -$6 over 12 events (-6/12 = -0.5). My call would have an expectation value of -$0.5. Thus, calling would be a mistake.

The Expected Value

At poker, everything revolves round the expected value. In general, you have three options: Call, raise or fold. It is your duty as a poker player to choose the action with the best expected value. But this is not always that simple, as a lot of unknown parameters affect the decision. But there are also simple ones. You just don’t play gutshots with pot odds of 5 to 1. But you will find a lot of players making these mistakes. These players cause you to win money.

The whole Process

1. Calculate the pot odds
2. Count the outs
3. Calculate from outs to profit odds
4. Compare pot odds and profit odds

Or you can choose this way:

1. Count the outs
2. Calculate from outs to profit odds
3. Use following formula: Call if odds x costs are smaller / equal pot, otherwise fold (You multiply the odds with the cost for a call and compare this with the pot size. (If it is smaller or equal you can call)

The Odds - Sheet

It is not necessary to calculate from outs to odds on your own. You won’t have time for it anyways, especially if you are multi tabling. The solution: You just have to memorize a handful of numbers. In the beginning, you can use a chart that can be put on your desk. Doing so, you could look the odds up easily whenever necessary. After a while, you will get familiar with these numbers anyways and won’t need the chart anymore.

Download as Excel-Table

Explanations:

This sheet shows the chances of drawing hands to improve with the next card. The outs are not discounted and show the optimum. Overcards will be treated as “live” outs, so this sheet always works with the assumption that you win the hand in case you improve this way. The harsh reality shows something else. Especially in multiway pots, you will not win with only holding top pair in general. This sheet should be treated as a calculative basis.

Draws with 4 or less outs are called Weak Draws (red)

Strong Draws are draws with 8 outs and more orange). Under normal conditions you can go to the river with these draws.

Monster Draws are draws with 14 outs and they are “even money” (yellow), that means that you have winning chances of 50%.

A flopped set is both a fullhouse and a quads draw as. You will always go to the river with this hand. The 17 outs you can find in the sheet is the result of both streets added (7 outs on the flop and 10 outs on the turn)

With 8 or more outs, you pretty much always go to the turn. So only longshot-outs (7 and less) are to really interesting at the flop. We rounded the results, as the number beyond the dot is not that important.

Strategical Implications

The following chart shows the effect of mathematics on strategical decisions:

Hold’em is a tough game. So it’s no wonder that there are more things to be aware of and to be calculated:

Discounted Outs

Outs are the number of cards that improve your hand. But what you need to know is: How many cards will improve your hand to a winning hand? Not every turn card which improves your hand means that the pot is yours for the taking. Therefore, not all outs have the same value, so they need to be discounted if they are weak. To get a realistic result, you have to include discounted outs into your calculation.

Example:
You got A K , the board shows Q 7 5 .. Without a pair, you are probably behind against multiple opponents. Still, you got 6 outs (3 Aces and 3 Kings). But A and K are scary, as they would bring a 3-flush draw onto the board. If one of these cards will show on the turn, your hand will be improved but possibly an opponents hand could be improved even more by this 3-flush draw.
Other dangers: If the turn shows an Ace, you might be losing to someone holding A7 because he would have improved to 2 pair. Plus, you could still lose against a set. You see, there are a lot of dangers out there. As a consequence, an overcard draw with AK is not a strong hand. Against two other players, you need to discount three outs. If there are 3 or more players, you need to discount even more.

Hands drawing to the nuts sometimes have to be discounted, too. For instance, a one card straight draw usually needs to be discounted.

Example:
The board shows KQT and you got A8s. Your jack-outs do not have a big value because you would have to share the pot with every other player holding an ace

Implied Odds

Now you should realise that discounted outs have a major impact on the expected value. Fortunately, there is another positive factor called implied odds. If you hold a strong hand, guaranteeing your victory, you can calculate with implied odds, too. Those implied odds include possible profit on the turn and river.

Without this consideration, you would only be able to call a gutshot if you the pot size mounts up to 10.75 times the money you have to invest. But in case you improve your hand, you will gain additional profit on the turn and on the river. This means that you can call a gutshot against 2 or more players with pot odds of only 1 to 8. You expect to win at least 3 bets on the turn and river. It is still possible that you will lose your hand anyways. This might happen because of tainted outs and redraws.

Redraws: A redraw is given if you hold a gutshot, but some opponent got a flush draw or fullhouse draw. This may lead to the point where you will improve on the turn, but get beaten on the river. You can calculate with normal odds, but not with implied odds. Usually, you should discount your odds as well.

Tainted Outs: This is an out which will improve your hand, but that will be even better for your opponent’s hand. For instance, you hold an OESD and your opponent has a flush draw. There are two cards that will improve your hand to a straight and complete the opponent’s flush, as well.

A rule of thumb: Discounted outs and implied outs neutralize each other. This a simplification. It is supposed to help beginners to come along on there first steps without making any big mistake. As an intermediate, you should play more versatile.

The contrary of implied odds is called reverse implied odds. Poker is a zero-sum game, every advantage on the one side will be a disadvantage on the other. Implied odds have a favourable effect when you have a strong draw, but the same way they have an unfavourable effect on (weak) vulnerable made hands.
If your gutshot draw materializes on the turn, a top pair hand usually will pay you off. If you miss your gutshot on the turn, you usually won’t invest any more money. Implied odds usually cause drawing hands to lose small bets on the flop, but to win big bets on the turn and river. For that reason, you should protect your vulnerable made hands as aggressive as possible.

Relative Position

To estimate the pot odds, you need a good overview of how much you have to pay to see the next card. Your position relative to the betters/raisers affects the value of a weak draw. Hands with weak draws are profitable for one, but usually unprofitable for two bets. Assume you are holding a gutshot and sit right to the better’s left hand side. 3 players are yet to act after your call. The pot size is 8 times your expected investment, so you could play the hand after calculating the implied odds (as we figured out, a gutshot might be playable with pot odds of 8:1). But what happens if there is a raise coming up after you acted? This hand would instantly become unprofitable, because you would have to spend twice as much to see the next card. Thus, the hand becomes unplayable in this situation. When the better/raiser is on your immediate left, your call closes the action. That way you are guaranteed to see the next street for just one bet.
The higher the chance of a raise behind, the less value your weak draw has. If the chance if a raise still to come is too big, you need far better odds – you could call it a security-margin – than you would if you’d spend only one bet in any case.

Equity

Equity is the portion of the pot entitled to you according to your chances of winning. A straight flush draw has 15 Outs on the flop and an equity of 54.12 percent if you continue to the river. Even though, you do not have a made hand, a straight flush draw holder owns more than 50% of the pot (It has to be a nut draw). So you have to enlarge the pot as much as possible, as it increases your equity, as well and prepares a bluff on the turn at the same time in those cases the turn card does not help.
The following situation, because it happens frequently, is even important. You have a nut flush or straight draw and three opponents. With 9 Outs, you have an equity of 34.97% (odds of 2:1 to improve to the river). You also should bet for value here. You just put 25% of the money in the pot, but own 34.97%. (Statistically, you win around 10 Cent of every Dollar put into the pot).