# Odds

**Odds Introduction**

Like it or 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 of how to use odds to make the right decisions. You might be using odds (whether you think about it that way or not) when you:

- Decide to draw with a gutshot.
- Decide to call a bet on the river.
- Decide to raise opponents bet on river with a trash hand.
- Decide to call an opponent’s all-in bet preflop with AJs at a late stage in the tournament.

Odds are just a different way of expressing probability. Probability tells us how often an event will occur, while odds tell us the opposite.

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 will not pay you anything extra if the flush card hits. Should you call or fold?

This is one of the decisions we make all the time at the poker table. Odds help us make profitable choices instead of long-term losing choices. 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. You have a 20% probability of making your flush, and the needed win percentage is 25%. This 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.

**Pot Odds**

Pot Odds are the odds that you get from the money that is in the pot right now, based on how much you must pay to call. If there is $100 in the pot and your opponent bets $50, your pot odds are 3:1. There will be $150 in the pot, and you would risk $50 to get a chance of winning $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 a flush or that 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. 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.

Pot Odds are calculated by dividing the total amount of money in the pot (including opponent’s 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 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 us look at some more examples:

**When opponent is all-in preflop**

**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. Small blind is $0.5, Big Blind is $1. Opponent opened with $3, and you raised to $9. 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.

Pot Odds = Total amount in Pot / Amount to call = 39.5 / 21 => 1.88. This is close to 2:1 odds.

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).

**When opponent is all-in on the flop**

**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 are 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.

Pot Odds = Total amount in Pot / Amount to call = $80 / $30 = 2.7 => odds are 2.7:1.

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 the time opponent will have a straight.

You consider raising to $14 with your worthless hand. You predict your 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? 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. This means it is clearly a bad raising decision.

**Implied odds**

It is important that you think about the * average* extra win, not the good case. If you hit that well concealed straight draw, you will win your opponent’s entire stack sometimes. In many cases your opponent will shut down when you hit your draw. Many players overestimate their implied odds.

**Playing a Draw**

When you believe that you currently do not have the best hand, this is considered to be a drawing hand. You might 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 common drawing scenarios, and how to calculate your implied odds you are on your way to learn some real poker! Here are some examples:

- 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.

Let us say that you are on a gutshot straight draw against an aggressive opponent. He has 3-bet before the 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 your opponent’s 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 when 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.

**Break-even Percentage**

In poker we are often thinking in of our chance of winning a hand in percentage. 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 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 is 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 of calling with what is in the pot + opponents bet + amount to call, and multiply with 100 to get the percentage. Break-even = 100 * 5 / (10 + 5 + 5) = 500 / 20 = 25%.

The example above is 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 opponent’s bet has been added. 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. Break-even percentage = 20 / (20 + 20 + 20 + 20) * 100. This is the same as 2 / 8 = 1 / 4 = 25%. 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 opponent’s. If you have an open-ended straight draw 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 that is accurate enough in most cases. It 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:**

Most of the time you will be using the rule of 2, since if you call on the flop, you do not 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 us say 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, which is 9 outs. If we multiply 9 with 4 we get our chance to make the flush, 36%. The break-even percentage is = 100 * Amount to call / (Pot Bet + Bet) BEP = 20 / (40 + 20) * 100. This is the same as 2 / 6 which is equal to 1 /3 which is 33%. It is correct to call, since our chance of making the flush (36%) is higher than our break-even percentage.

Here is a list of common situations when 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 cannot be a 100% sure your hand will win, even if you improve. 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 your opponent might win even if you improve you should 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:**

If both the turn and river is a spade you will have the nut flush. The probability of this happening is not great, but sometimes it is enough to tip a close decision. The odds of hitting a backdoor flush draw is 23:1 or 4%. It is similar for straights. It makes sense to sometimes count backdoors as 1 extra out, which is sometimes enough to weigh a decision.

**Odds and Probability Tables**

**Playing a draw with outs table**

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.

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