Odds

Odds Introduction

Like it of not – odds are the basis for every single decision you make at the poker table. If you want to become good at poker you need a good understanding and feeling for how to use odds to make the right decisions. If you want to become great at poker you need to become really good at estimating odds. Examples of when you might be using odds (whether you think about it that way or not) are:

  • Decide to draw with a gutshot draw to a straight based on the odds for how much you will win in average when you hit compared to the odds of making the straight
  • Decide to call a bet on the river based on the odds from the pot and the odds of you having the best hand
  • Decide to raise opponents bet on river with a trash hand based on the money you are risking compared to the money you will win when he fold and the odds of him folding
  • Decide to call an opponents all-in bet preflop with your AJs at a late stage in the tournament based the odds from the pot and the odds of your hand winning against his range

As you might know odds are just a different way of expressing probability. Probability tells you how often an event will occur – odds tells you how often an event will not occur.

Let me give you an example:

Board:

Your hand:

You have a flush draw on the turn. There is $100 in the pot and opponent bets $50. Your opponent is very conservative and you believe he has a good hand. You are quite sure you will win if you hit your flush and lose if you miss. You are also quite sure he won’t pay you anything extra if the flush card hits.

Should you call or fold?

This is the kind of decisions we are making all the time at the poker table. And odds are what helps us make the profitable choices instead of the long term losing decisions. In this example you should fold. You get 3:1 odds on your money and the odds of hitting your flush is 4:1 which is worse than the pot odds. Put in a different way you have a 20% probability of making your flush and the needed win percentage based on the money in the pot and the money to call is 25% which means you should fold.

Odds are written in the format occasions when it will not happen versus occasions when it will happen. For example, the odds of rolling a 6 on a six-sided dice are written as 5:1. 5 times out of 6 you will roll another number. If we look at the odds of throwing heads with a coin it will be 1:1. This is how we look at things in the very long run.

Pot Odds

Pot Odds are the odds that you are getting from the money that is in the pot right now based on how much you have to pay to call (or bet or raise). For example, there is $100 in the pot and your opponent bets $50. Your pot odds would then be 3:1 (read “three to one”) based on that there will be $150 in the pot and you would risk $50 to get a chance of winning those $150. This means that if you win more than one time out of four (25%) it will be profitable to call.

An example of when to use this is when your opponent bet $50 in a $150 pot on the river.

Board:

Your hand:

You have pocket aces. You believe your opponent has made a flush or he is bluffing. If you believe he is bluffing more than 25% (1 time out of 4 is 25%) of the time you will be correct to call (if your assumptions are correct). Pot odds are used in poker when there will be no more betting. If there might be more betting you need to use Implied odds (see below).

In Texas Hold’em and Omaha you are normally using Pot Odds in the following scenarios:

  • When opponent has gone all-in
  • When opponent bets on the river
  • When you consider betting or raising as a pure bluff
  • When opponent is very conservative and won’t put more money in the pot even if he has the chance (rare)

Pot Odds are calculated by dividing the total amount of money in the pot (including opponents bet) with the amount you have to call. If the pot is $10 and opponent bets $10 the total amount in the pot is $20 and it will cost you $10 to call.

In this case we get Pot Odds = 20 / 10 => 2/1 which is normally written as 2:1.

The amount that can be won is on the left side and the amount you risk is on the right side. 2:1 (or 2 to 1) means you will risk 1 for the chance of winning 2. If you win you will get back the 1 you risked plus the 2 you won. Most of the time calculations are easier if you use 1 on the right side. For example 7:2 can be written as 3.5:1 which is the same thing.

Let’s look at some more examples:

When opponent is all-in

Your hand:

You have AJ of clubs in the Big Blind with $1 and you have 3-bet one of your opponents who is now all-in with $30. Everyone else has folded and you are far from the money or in a cash game (otherwise you need to consider something called Bubble Factor). Should you call? 

It depends on the range of cards you are expecting your opponent to play. But let us first take a look at the odds. Small blind is $0.5, Big Blind is $1. Opponent opened with $3 and you raised to $9 and opponent went all in with remaining stack to a total of $30. This means there is $39.5 in the pot (small blind 0.5 + your money $9 + opponents $30). 

When you decide to call or fold in this situation you only consider the odds, not that you have already invested money. If the odds tell you to fold that is what is business is considered a “sunk cost”. Never waste good money after bad.

AJs has odds of better than 2:1 for all ranges broader than 5% which means you should call if you estimate that your opponent is on a wider range than top 5% (AA, KK, QQ, JJ, TT, 99, AKs, AKo, AQs, AQo).

Board:

Your hand:

You have a flush draw on the flop. Your opponent goes all-in with $20 in a pot of $30. You are fairly sure he has a better hand than you right now and that you will have the best hand if you hit your flush draw. Should you call? 

The Pot Odds are: (20 + 30) / 20 = 5/2 => 5:2. This is the same as 2.5:1.
The odds of you making the flush with two cards to come are about 2:1 which makes this an easy call. See information about outs and  odds below for explanation of how you estimate the odds of hitting the flush.

When opponent bets on the river

Board:

Your hand:

You have QQ as an overpair on the river and your opponent bets $30 into a $50 pot on the river. Should you call or fold? You estimate the following distribution of hands for your opponent:

  • 1/3 of the time opponent will have worse pair or be on a bluff
  • 1/3 of the time opponent will have a higher overpair or three-of-a-kind
  • 1/3 of the time opponent will have a straight

Your hand is best one time out of three. This means the odds of you having the best hand is 2:1. The odds you are getting on your call is higher than the odds against you winning which means that you should call and expect a profit in the long run.

When you consider betting or raising as a pure bluff

Your opponent bets $4 into a $10 pot on the river. You estimate the following hand range distribution for your opponent:

  • 1/3 of the time opponent will have a weak pair or worse hand.
  • 1/3 of the time opponent will have a strong pair or three-of-a-kind.
  • 1/3 of a time opponent will have a straight.

You consider raising to $14 with your worthless hand. You predict opponent will fold with the weak pair or worse hands and call or raise with the rest. You expect to always lose when you are called. Should you make this bluff raise? Again we have to turn to the odds to find the answer. You will risk $14 for the chance of winning what is already in the pot, $14. This means that the Pot Odds are 1:1. Your opponent will fold one time out of three, this means the odds are 2:1. The Pot Odds are clearly worse than your win odds which means it is clearly a very bad raising decision.

When opponent is conservative

Your opponent is very conservative and won’t put any more money in the pot if a flush card hits. You are on a flush draw on the turn. The pot is $60 and opponent bets $20. Should you call?

The odds of hitting a flush draw is 4:1. This means that this is what is called a break-even decision in poker. In the long run you will neither win nor lose money on calling. It doesn’t matter what choice you make.

Implied odds
Pot odds does not take into account that there might be further action in the hand. For example, there can be opponents behind that might get involved or you could be on a draw that could make you extra money when you make it. Implied odds is the best guess of what your odds would be at the end of the hand in these situations. It is a vital concept in especially no-limit poker and is used even more than pot odds.
Let’s say for example that you are on a straight draw. The pot is $10, your opponent bets $5. You think that you will win an extra $15 in average if you hit your draw on the next card. No one else is involved in the hand and the next card is the last. Then you will pay $5 to get a chance of  winning $30, i.e. your implied odds are 6:1. The odds of hitting the straight draw is 5:1 so this is not a fold (it might be a raise or a call).
To make the best decision in poker you must definitely consider raising in many situations when a call is profitable and even when a call is unprofitable (see raising as bluff in the Pot Odds discussion). When bluffing with decent hands exact calculations become very difficult since you might have a decent chance of winning even if opponent does not fold immediately and most players base such decisions on experience and feel for the game and  opponents rather than exact calculations. The difference compared to Pot odds is that you add the extra money that you expect to win to the pot.

It is very important that you think about the average extra win, not the good case. If you hit that well concealed straight draw you will sometimes win your opponents entire stack. But the important question is, how much will you win in average? For example, sometimes you will think your opponent is on a good hand, but it will turn out that he has bluffed. It is VERY important that when you estimate the extra money you think about what you will gain extra in average, not in best case. In many cases opponent might shut down when you hit your draw and many players heavily overestimate their implied odds.

Since there is betting left to be done implied odds are quite complex, both to learn to roughly calculate but also to make the right assumptions. If your guess is wrong on your opponents handrange you might draw to a losing hand or may not get any additional money when opponent has air. Beginners often overestimate implied odds, so it is better to be a bit cautious if you are new to this. But it is a key part of no-limit poker so if you want to become good you have to practice this.

Implied odds are fundamental to situations where you consider calling to get the best hand.  Implied Odds should also be considered when you are likely to face another bet when you have a mediocre hand (sometimes this is called Effective Odds). If you for example have a pair with a poor kicker on the flop and a conservative opponent bets into you you might look at the Pot Odds and say the probability of you having the best hand justifies a call. But in this scenario your hand is unlikely to improve and your opponent might well bet again at the turn and you need to fold.

Implied Odds are most commonly used when you are on a draw, but they are also used for some preflop decisions. When deciding whether to call with a decent hand like a small pocket pair against a tight early position raiser you should consider Implied Odds to make the right decision. The odds of hitting a set (three-of-a-kind based on your pocket pair) on the flop is 7.5:1. To make a call a good play in this scenario (if we assume no one else will enter the pot) you need an average expected total win from what’s in the pot right now plus the extra money you will win when you hit to be higher than 7.5:1.

Example:

You are playing Full Ring $1/2 No-limit Texas Hold’em and a tight and an aggressive opponent has raised to $3. You are on the Button with a 33 pocket pair and everyone else has folded. The blinds are conservative and unlikely to become involved in this scenario. You have played many times against this player and he normally only raises with the top 5% best hands from this position. Should you call?

Your odds of hitting the set are 7.5:1. To estimate your Implied Odds we need to consider Opponents range of cards and what might happen later in the hand.  A common 5% range contains 6 * 6 high pair combinations and 32 high card combinations. It means the chance of opponent holding a high pair is over 50%. There is $4.5 in the pot. You will risk $3 to see the flop. If you expect your average extra win to be be more than 7.5 * 3 = 23 you should call. Your opponent has seen you call with small pairs and small suited connector in this spot and he knows you aren’t bluffing that often. He is fairly careful. You expect to him to bet 2/3 of the pot on flop and turn if you call and call a 1/3 pot on the river in most scenarios when he has a pocket pair.

Opponent has pocket pair:

You expect him to slow down quite a bit on scary boards so you adjust this down to $28 to be realistic.

Opponent has two high cards:

You expect to win a continuation bet on the flop when he misses and you expect to win a flop bet and a turn bet when he hits a pair. 2/3 of the time he will miss the flop and 1/3 of the time he will hit one pair.

This calculation show that we need to win an average of $23 for a call to be correct but we only expect to win $20 which means we should fold. In reality it is even more complex than this, we might for example win without hitting the set sometimes and we might be winning by bluffing sometimes. In general we should have quite favorable conditions to call with a small pocket pair against this kind of early position raiser with the main idea of winning a great pot when hitting a set. But if you are playing against poor opponents who are overly aggressive with a good pair or when multiple opponents are involved the situation changes completely of course.

Playing a Draw

When you believe that you currently don’t have the best hand this is considered to be a “draw” or “drawing hand”. You might for example be drawing to a straight or flush. This is a common situation when you need to look at the odds to make good decisions. If you learn the odds of hitting the draw for some very common drawing situations and how to calculate your implied odds to compare with you are on a good way to learn some real poker!

  • Flush – 4:1
  • Open ended straight draw – 5:1
  • Two overcards hitting a pair – 8:1
  • Gutshot straight draw 10:1
  • Two overcards to a pair 7:1

For example, you are on a gutshot straight draw against a very aggressive opponent. He has 3-bet you before flop and you believe that he has a strong pair or two high cards often. There is currently $150 in the pot on the turn and opponent bets $50. You put your opponent on the following hand distribution:

  • Half the time a strong pair
  • Half the time a pure bluff or two high cards

You expect to win the rest of opponents stack in the first scenario if you hit your draw. He has $250 left.
You expect to win an extra 1/2 pot size bet on the river half of the time in the second scenario and half of the time nothing extra. This means that half of the time you hit your straight you will win an extra $250 and half the time you will in average win extra 1/2 * 125 = 62.5.
The total average extra win is then 0.5 * 250 + 0.5 * 62.5 = 156.
You total implied odds are Total amount in pot + Extra / Amount to call = $200 + 156 / $50 = 7:1. You need 10:1 for a gutshot straight draw so it is clearly not a call (it might be a raise if opponent will fold often enough, which in this case is unlikely).

The explanation behind the odds for hitting draws is that we have a certain number that will help our hands and a certain number of cards that won’t help us. For example if we have a flush draw on the flop we are seeing 5 cards, there are 47 cards left in the deck. Of those 47 cards 9 will give us the flush and 38 won’t help us. We have odds of 38 to 9 to hit a flush – this is close to 4:1. You can calculate the other examples in the same way. But an easier way to do this is to use the rule of 4 and 2 (see below).

You have to be careful so you don’t overestimate your chances of winning when you are drawing. You need to take into account that sometimes you will hit your draw, but opponent will have a better hand. Sometimes you might also get the best hand on the turn but opponent will improve on the river. This is extra important when you are drawing to hands like this:

  • Two overcards to hit a pair
  • The lower end of a straight (called idiots end because you can lose a lot of money with these straights
  • A weak flush when opponent might have high cards

Break Even Percentage

In poker we are often thinking in percentage of chance of winning a hand. For example, if we call a bet of $5 for the chance of winning $15 we need to win the hand at least 25% of the time for that to be a profitable call. This is our Break-even percentage. If you think about it is makes sense. If we play four rounds and we in average will win one and lose three then we will lose 3 * 5 = 15 and we will win 1 * 15 = 15. That’s break-even, we lose as much as we win. And winning one out of four is the same as 25%. We calculate Break-even percentage by dividing the amount for calling with what is in the pot + opponents bet + amount to call (which is same opponents bet) and multiply with 100 to get the percentage.

Some more examples:
Opponent bet $10 in $10 pot. Break-even percentage 33%. Calculated by Amount to call / (Pot + Bet + Bet) = 10 / (10 + 10 + 10) = 10 / 30 which is 33% (multiply with 100 to get percent).

Opponent bet $10 in $30 pot. Break-even percentage 20%.

Remember that it is enough to get it roughly right, there are a lot of unknowns anyway. But if you get it completely wrong, or don’t get it at all you are going to leave a lot of money at the table.

The above examples are based on scenarios when no more money will go into the Pot (compare with Pot Odds). If there might be more money added to the pot we need to consider those as well (compare with Implied Odds).

The above examples are based on scenarios when no more money will go into the Pot (compare with Pot Odds). If there might be more money added to the pot we need to consider those as well (compare with Implied Odds).

Pot is what is in the pot after opponents bet has been added.

Let’s take two examples to see how you can quickly estimate your Break-even percentage.

Pot is $20, opponent bet $20, you expect to win an additional $40 on next street half of the time if you hit your draw. This means your average expected extra win is $20.

And the easier way to calculate is by looking at odds against. We risk $20 to win $40 (pot + bet) + $20 (average extra). That is, we risk $20 for winning $60. This yields odds against of 60/20 => 3:1 which converts to 25%

Outs – The rule of 4 and 2

Break Even Percentage is extra helpful together with the rule of 4 and 2. An out is a card that will help you get a hand that you believe is stronger than your opponents. For example if you have an open ended straight draw (you have 4 consecutive cards) there are 8 cards that will help you make your straight – 4 on each end. These cards are called outs. There is a rule of thumb for Texas Hold Em and Omaha that is accurate enough in most cases which says that each out give you 2% chance of making your hand with one card to come and 4% chance of making your hand with two cards to come.

Example: 
You are on an open ended straight draw. The pot is $10, your opponent bets $10. You think that you will win an extra $20 in average if you hit your draw on the next card. No one else is involved and next card is the last. You will pay $10 to get a chance of winning $40, i.e. your implied odds are 4:1 and your Break-even percentage (see Implied Odds exercise) is 20%. An open ended straight draw gives you 8 outs, i.e. 16% chance and you should not call (but you should consider raising since opponent might fold or you might win a big pot if you hit your draw).

Most of the time you will be using the rule of 2 since if you call on the flop, you don’t know what your opponent will bet on the turn when you miss your draw. Most of the time you will have to pay more to see the river. But you do use the rule of 4 when you consider all-in situations on the flop. If you call an all-in on the flop you will see both cards and you will multiply your outs with 4 and compare that with your Break-even percentage.

Let’s say for example that you are on a draw to the nut flush. The pot is $20 and opponent goes all-in for $20. Will a call be correct?
We have 9 cards that will make our flush, that’s 9 outs. If we multiply 9 with 4 we get our chance to make the flush, 36%. The Break-even percentage is:

This is the same as 2 / 6 which is equal to 1 /3 which is 33%. So it is correct to call since our chance of making the flush (36%) is higher than our Break-even percentage.

It is quite often correct to go all-in yourself in the flop when you have good outs. If you in the above example think your opponent might have a good hand and you had acted before he went all-in you could add his fold-equity to your 36% of making the flush. One of the trickier things when deciding to call based on implied odds is that you sometimes can’t be sure if you will have the best hand even if you hit your draw. Your opponent might for example get a higher flush when you hit yours. 

Let’s say for example that you are on a straight draw and there is a possible flush draw on the board. If your opponent has the flush draw you can’t count the cards that make your straight that are of the flush draw color as outs. This is called discounted outs. Since it can be a bit tricky to get used to thinking about outs and implied odds for beginners it is probably best to be a bit pessimistic when you judge your number of outs if you are uncertain.

Here is a list of commonly used situations where you look at your outs:

  • Gutshot straight draw: 4 outs
  • Two overcards: 6 outs
  • Straight draw: 8 outs
  • Flush draw: 9 outs
  • Straight draw with one overcard: 11 outs
  • Flush draw with one overcard: 12 outs

You have to be a bit careful when you consider calling based on your outs. Often you can’t be a 100% sure your hand will win even if you improve to your drawing hand. For example, you might improve to your queen high flush, but your opponent has a king high flush and you lose a lot of money. Some players use the concept Discounted outs to partially count outs based on their probability. Since it is hard to make exact calculations I normally just adjust the decision. If the decision is close based on the odds and there is a fair risk that opponent might win even if I improve I will not call.

Another concept can weigh close decisions in favor of the call instead. It is backdoor draws. This means that there are 2 cards missing to a straight or flush.

Board:

Your hand:

Let’s say for example you have the hand above. If both the turn and river is a spade you will have the nut flush. The probability of this happening isn’t great, but sometimes it is enough to tip the close decisions in favor of playing. The odds of hitting a backdoor flush draw is 23:1 or 4%. It is similar for straights so it makes sense to sometimes count backdoors as 1 extra out which is sometimes enough to weigh a decision. Don’t overestimate them though. You need to be able to see two cards for them to be valuable and sometimes opponent will make a large bet on the turn so you will have to fold even if you hit the first card you needed.

Odds and Probability Tables
OddsProbability
1:150%
1.5:1 (or 3:2)40%
3:125%
4:120%
5:117%
6:114%
7:112%
9:110%
10:19%

Playing a draw with outs table

Draw Outs Probability Odds
Flush + gutshot 12 24% 3:1
Flush 9 18% 4:1
Open ended straight 8 16% 5:1
Two overcards 6 12% 7:1
Gutshot straight 4 8% 11:1

If there are two cards to come you multiply probabilities with 2 (or divide odds with 2). This is normally only used in all-in situations on the flop.