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Pot odds and odds of improvement
Introduction to pot odds
Basic, but essential poker concepts include knowing and understanding the pot odds and the odds of improving your hand
To play a winning poker hand over the long term, you need to have several skills, one of which is the knowledge of the pot odds. It is with this knowledge that one can determine the profitability or otherwise of a call bet in a given pot. If the notion is still a little fuzzy for you, after reading the lines that follow, everything will be much clearer
But what do we mean by pot odds?
The notion of odds expresses a probability that something will happen, for example, that your colour flop draw will complete on the bend or the river.
For example, you have Jh-Th on a flop 2h-3h-7s. Jack-ten in heart, on a flop that includes 2 hearts. Your opponent bets a sum X in a pot Y and knowing the odds of the pot will tell you whether calling your opponent's bet will be profitable or not, knowing that you will complete your hand in a proportion Z.
Let's add some detail to our example to clarify our definition
An example
You're in BB position with your Jh-Th and you've called a pre-flop raise for the player on the button.
You are heads-up on the flop.
The pot is $6.
Your opponent bets $4 on the flop
You must therefore invest $4 in a $10 pot (the $6 pot before the flop + the $4 bet at the flop) if you want to see the turn
Do you have the odds to continue? The odds will be expressed in several ways. One of them is 4:1. In other words, with a colour flop print, on one street only (here, the turn to come), on 5 occurrences, 4 times we will miss our colour print and 1 time we will touch it, hence the expression 4:1. We'll say we have a 4:1 odds
In other words, to have the correct odds to call the flop bet, the bet will have to be 4 times smaller than the size of the pot. Since the bet is 40% of the total pot size, it will be said that I don't have the odds to continue. In order to evaluate the profitability of a call, I have to relate the size of the bet to call to the size of the pot. I then compare the result to my chances of improving my hand. In a simple way, I will know that I am not paying a bet that is twice the size of the pot if I complete my draw only one out of five times
So much for the basic idea. But a lot more needs to be said to fully grasp the concept
Let's stay with our example of the colour print. We know that our odds are 4:1 if we rely on a street just to hit our print (here, the turn). We calculate it that way because if we call the flop bet and the turn is a brick, we can bet that our bad guy will bet on the turn again and we won't be able to see the river for free
As for the odds of completing our draw on the turn and the river, the odds are 2:1, i.e. out of 3 occurrences, 2 times the draw will not be completed and 1 time it will be completed (it is important to specify this because we could think that a 2:1 odds indicates that an event will occur 1 time out of 2 when it is more like 1 time out of 3)
Knowing our odds = Helping us estimate the profitability of a call bet
If we modify our example above, let's assume that the pot at the flop is $80 and our opponent makes an all-in bet at the flop of $20. Given our odds (on 2 streets, 2:1), we'll say we have the odds to continue. Let's detail the example
2 times we'll lose $20 (2*20 = $40)
1 time we'll win $100 ($80 already in the pot + the $20 bet)
Win ($80) - Lose ($40) = $40 profitable call over the long run
Odds therefore show the profitability of a call over the long term by taking into account the current size of the pot and the size of the bet to call
Our odds are never more than an estimate
This odds is obviously an estimate because I never know exactly how many outs (an out is a card that can help me) I really have. Since poker is a game of incomplete information, I try as best I can to estimate the odds with the information I have
In the above example of Jh-Th, we say we have 9 outs because we are counting the 9 hole cards still in the deck, but it's still theoretical. I could have far fewer outs than expected if all the players at the table have already received core cards, but since I have no way of knowing this, I assume they are still in the deck. And I might also have more outs than I expected. The key word is estimate
If, for example, my opponent has a small pair in his hand, not only will the hearts give me a flush, but in addition, all tens and jacks will give me top pair, for the best hand, so I will have not 9, but 12 outs. But without full information, I remain cautious and only consider my outs for the flush draw
Odds vs. Odds
So far we've been talking about the odds of the pot expressed as 4:1. But this notation can also be transformed into probabilities
An odds of 4:1 is also a 20% probability. It is important to be familiar with both ratings because each will have its own usefulness
To the mind, a flop odds of 4:1 is a bit abstract. I'd rather know that I will hit my colour print on the turn 20% of the time. It's easier for the spirit to understand. But when I'm facing a bet, this notation is less useful
Knowing that my odds are 4:1 will tell me that I can pay a $1 in $4 flop bet to hit my colour print on the turn, but not a $2 in $4 bet. It makes it easier to compare. If I have a 4:1 odds on my print, I know I can pay a $1 bet in $4. Illustrated 4:1, I know that the pot will have to be 4 times bigger than the bet I call for my call to be break-even or profitable in this situation
How to calculate your pot odds in the heat of the action
In order to properly calculate the profitability of a call at the flop for example, you will need to know this information:
1- How many outs do you have?
2- How much do I have to call?
3- What is the size of the pot after my opponent's bet?
4- What is my opponent's range?
The information 1-2 and 3 are essential, while the information 4 is complementary, but still very useful. Other information may also be useful, but for the sake of brevity, let's go with this basic information
For the calculation of outs or cards that can help you, it is important to practice well and to know them by heart
Here's a little reminder you'll find useful to remember:
The number of outs in different situations
15 outs. Score of 2:1 (33%) on 1 street or 1:1 (50%) on 2 streets. Colour print + straight print. Example 7h-8h over 5h-6h-2s.
9 outs. Odds of 4:1 (20%) on 1 street or 2:1 (33%) on 2 streets. Colour print. Example Jh-Th over 2h-3h-7s.
8 outs. 5:1 (16%) on 1 street or 2:1 (33%) on 2 streets. Open-ended straight draw. Example, 7x-8y on 5-6-K.
5 outs. Odds of 8:1 (11%) on 1 street or 4:1 (20%) on 2 streets. A simple pair that you want to improve to a three or two pairs. Example A-5 on 2-5-J.
4 outs. Score of 11:1 (8%) on 1 street or 5:1 (16%) on 2 streets. Gutshot. Example, 7-8 on 4-5-J (here, the 6 and only the 6 will give us the sequence)
Other elements come into play when you calculate the profitability of a call. Here are a few questions to ask yourself when studying a specific situation
1- If I call on the flop, will my opponent often bet on the turn? Will he bet big?
2- If I hit my draw, what are the chances that my opponent will pay me?
3- Is it possible that my opponent has a better draw than me?
Working with the odds and probabilities calculator
Let's take our example from above.
Jh-Th on a flop 2h-3h-7s
To help us with our calculations, we'll use the pot odds and probabilities calculator at the top of the page
We are always heads-up and our opponent bets $2 in a $9 pot. Since our odds to improve our hand on a street is 4:1, we must call a maximum bet that is four times smaller than the total pot. Using the above mentioned calculator, we find that we have a pot odds of 18.18% (about 4:1). This figure is obtained by dividing the bet to call ($2) by the total of the pot AFTER the naughty bet (naughty bet $2 in a $9 pot, so $11). This makes $2/$11 = 18.18%
From this number, we know that if we improve our hand with a probability greater than 18.18%, we have the right odds to call. Here we learn that our colour will complete 19.15% of the time on the turn and 34.97% of the time if we count turn + river. It is therefore a favourable call
Thanks to the calculator, we can check the profitability of a call in any situation. Simply enter the size of the pot BEFORE your opponent's bet, your opponent's bet, and select the draw you have. You will quickly know if this call is good or not
Small trick
The pot odds calculator is an excellent tool to get familiar with the pot odds and to get accurate numbers. However, during a casino tournament, it may not always be possible to use such software. So here's a trick to help you estimate your pot odds. Let's take our example again and again
Jh-Th on a flop 2h-3h-7s. We said earlier that we have 9 outs. We take this number and we multiply it by 2 if we want to know our chances of improving our hand on one street (the turn) and we multiply it by 4 if we want to know our chances of improving our hand on 2 streets (turn + river). We can do the same thing with any draw when we know our number of outs
So, on one street, we say 9 outs x 2 = 18% of the time we'll improve our hand. By consulting the calculator, we learn that the exact figure is 19.15%, which is not too far from our estimate. So I know that I can call a flop bet that is 18% or less of the pot size to be profitable. It saves me from making the mistakes that you will see too often in your games and calling $10 bets for example in $12 pots
Feel free to review your played hands using the calculator. With practice, the pot odds will become second nature to you