Lecture Two: Basic Pot Odds
• Why do we need to learn about pot odds?
In Weeks One and Two, the ‘Fundamental Theroem of Poker’ was introduced and explained. We determined that, according to the fundamental theorem of poker, when we are playing poker, in general, “We should be betting in a way which offers our opponents incorrect odds to call when we are winning in a hand, and we should fold whenever we are losing in a hand and our opponent offers us incorrect odds to call.”
Since, according to this definition, pot odds are central to understanding and applying the fundamental theorem of poker, we will therefore need a good understanding of pot odds in order to learn to play profitable poker.
• What are the odds of winning a hand?
All odds are expressed as ratios, for example, 2:1 or 4:1. Odds are often used to calculate your chances of improving in a hand. If you are drawing to the nut flush draw after the flop, your odds of hitting a flush on the next card are 4.1:1. This ratio expresses how many times we will miss our hand for every time we will hit it. So, when we hear that our chances of hitting are 4.1:1, we can think of it like this: For every 1 time we will hit our hand on the next card, we will miss our hand 4.1 times. Conversely, if it is our opponent that is drawing to a flush, we will know that for every 1 time our opponent outdraws us on the next card, we will hold 4.1 times.
Here are some common odds for hitting a hand on the next card:
Open-ended straight draw = 4.8:1
Flush Draw = 4.1:1
Gutshot straight draw = 10.5:12
Overcards = 6.7:1
Set = 22:1
One pair, drawing to two pair or trips = 8.2:1
We can also calculate odds by the number of outs we have. To do this you take the number of cards left in the deck, then minus the number of outs you have. Divide the answer by the number of outs you have to get your odds. The number of cards remaining in the deck is always the number of unseen cards, so you don’t count the cards that have been dealt to opponents as you don’t know what these cards are.
So, for example, if you are drawing to a diamond flush draw on the turn, you take:
52 cards in the deck minus the 2 in your hand, minus the 4 on the board = 46.
The number of outs you are drawing to will be 13 diamonds minus the 2 in your hand, minus the two on the board = 9.
So we take 46 - 9 = 37.
Then divide 37 by 9 = 4.1.
So your odds of hitting are 4.1:1.
In real life, these odds are complicated by a huge variety of factors, such as the fact that sometimes when you hit your hand your opponent will have hit a better hand, or will have a redraw. Or, board texture for drawing to overcards, dominated top pair hands, etc. The list is huge. For now just continue to think about it as if we were playing poker with the hands face-up, as we were when thinking about the fundamental theorem.
• What are pot odds?
Pot odds are odds concerning bets and the amount of money in the pot. To calculate our pot odds, we take the total amount in the pot (including our opponent’s bet) as the first number, and the amount we have to call as the second number, then reduce it down. For example, if there is $100 in the pot and our opponent bets the pot at us, the pot now contains $200 and we have to call $100. So, the pot odds we are being given are 200:100, which reduces to 2:1. Our pot odds in this case are therefore 2:1. These odds are also known as expressed odds. We can also think of this ratio as telling us how much we win for how much we lose. When we lose, we lose $100. When we win, we win $200.
• How can we use these odds?
We need to compare our odds of winning to the odds the pot is giving us in order to see whether we are making good calls and good bets. In order to make a break-even or profitable call, we need our odds of winning to be equal to or greater than the odds the pot is giving us.
Let’s take the example from above where our opponent bets $100 into a $100 pot. Our pot odds are 2:1. Let’s assume that we also have 2:1 odds of winning the hand. Now we know that when we win, we win $200, and when we lose, we lose $100. We also know that we will win 1 time for every 2 times we lose.
So, doing the maths…
We win 1 time x $200 = +$200
We lose 2 times x $100 = -$200
In total over 3 hands we make a profit of $0 on the hand. In order to get our expectation, or expected value of the hand, we divide the total by the number of times we have played, in this case 3. Our expected value from the hand is still $0. It is a break-even call.
Expected value gives you an average profit or loss that you make for each hand. Now, let’s change our odds of winning to 4:1.
Doing the maths on this…
We win 1 time x $200 = +$200
We lose 4 times x $100 = -$400
So our call is now unprofitable. We will expect a total loss of minus $200 for the hand over 5 hands, and an expected value of -$40 on the hand.
Now we can fully understand the role pot odds play in the fundamental theorem of poker. If we call when we are getting incorrect odds to do so, or offer our opponent the correct odds to draw, we are making mistakes and therefore our opponent will gain. If we fold when we are getting incorrect odds to draw, and get our opponent to call with incorrect odds, we will gain.
Read Part Three...
Week One: Introduction
Week Two: Lecture One: Calculating Equity
To ask me a question about the Fundamental Theorem of Poker, please feel free to leave a comment on my profile page or send me a private message.