Knowing Your Odds Better Than Your Opponents Do to Create Winning Plays
There are many types of odds in poker. Of all of these, pot odds and implied odds are the most important. Having a solid understanding of the math behind your plays will give you an edge at the tables. You’ll see that these concepts for pot odds and implied odds play out differently pre-flop, and on the flop, turn and river betting rounds. The stakes get higher when you’re playing real money poker, so learn all the concepts you can.
Here are the concepts explained below:
Of all the mathematics behind poker – pot odds are the most fundamental concept to understand.
Every time you consider calling a bet, you are getting a ‘price’ on your call. This is the amount of chips you need to call to stay in the hand, compared to the size of the pot.
Here are some examples:
The reason this is important is that you can compare the price you are paying with your assessment of your chances of winning the hand.
Taking a simple example; after the river is dealt, your opponent bets $50 into a $100 pot. You need to decide whether she is bluffing or has a strong hand. Assuming you beat the bluff and lose to the strong hand, you need to decide on how often each situation occurs. First, you calculate your pot odds. Here you need to call $50 to win $150. This means your odds are 3-to-1. You need to win the pot once for every 3 times you lose to break even. If you win the pot more than 25% of the time, you are making a profit (over the long run).
Based on your experience of playing this individual, you know they bluff frequently. If you think your opponent is bluffing 50% of the time here, then you have an easy call. The price you are getting from the pot is too good to give up. Even though you know you will lose this particular pot half of the time, the odds you are getting mean you have a profitable situation. If this same situation occurred 100’s of times – you would come out a big winner.
Not only will you receive a price on every bet you call – you can offer your opponents prices while playing a hand. Your raise size in any given situation will mean that each opponent has pot odds to remain in the hand.
Note that this concept covers calling bets. When the stacks are deep, you have the option to re-raise. This means that instead of receiving odds, you are offering them to your opponent.
When you have a draw to a flush or straight, you are unlikely to hold the best hand at the time you make the initial call (for example on the flop). This is where the concept of ‘Outs’ comes in.
In simple terms, outs are cards that are still in the deck which will improve your hand. For example, you hold the ace and queen of hearts. The flop comes all low cards, with two hearts. There are 13 cards of each suit in the deck. You hold two of these, and there are two on the board. This leaves 9 hearts (which we can assume will give you the best hand) in the deck.
With 5 cards seen out of 52 in total, there are 47 unseen cards on the flop. 9 of these are hearts, meaning you will hit a heart on the turn approximately one time in 5.
When you understand pot odds, you can compare the price you are being offered by the chances of improving to the best hand – and make your decision accordingly. It is possible that you will see both the turn and river, which improves your chances significantly.
A quick way to calculate your chances of improving to the best hand with a flush draw or open-ended straight draw is to use the ‘rule of 4 and 2’. Here is how it works:
When you are trying to improve to the best hand, not every card you think of as an out will be ‘clean’. An example involves the same flush draw covered above. If one of your hearts would improve your opponent to a full-house or quads, then obviously you would not win the pot.
On the bright side, your opponent might hold an over-pair to the board – for example tens on a nine-high flop. In this case, an ace or a queen might also be outs!
One big factor yet to be including into the discussion on pot odds involves spots where there is more money in each player’s stack.
Returning to the flush draw example; if you call a bet getting 3/1 on the flop, when you really need 4/1 to make this call profitable in terms of the immediate pot odds, this might be a mistake. What you need to factor in is that you might win many times the bet you called after the turn when you do make your flush.
The concept of winning more money on later betting rounds is known as your ‘implied odds’. Calling bets when the pot is small, and the stacks are deep, means you have plenty of opportunity to win money later in the hand – giving you big implied odds to continue.
Here is an example of how to use implied odds before the flop. You are in late position, holding a small pair like 5-5. A tight opponent raises from early position. From your history with this ‘nit’, you know he has a high pair – probably queens or better.
Obviously, your small pair is not in good shape against this range. You still have a good case for making the call, based on your implied odds. If you call a small bet of 3x the big blind, and hit a 5 on the flop, you are likely to win a huge pot (people who are super-tight are often reluctant to fold on ‘safe’ looking flops). Your implied odds in this spot are big.
You can calculate whether it is worth making a call by comparing your chances of making a set of 5’s with the price you are paying. That chance is around 1 in 8. You will miss the flop 7 times and hit it once in this situation on average. That means 7 times you will fold to your opponent’s continuation bet, and once you will re-raise and win a lot more chips.
If you both have 100x the big blind, and you assume you will win this amount when you hit (you will not always win, and not always double through – more on that below). Here is the maths:
As you can see, this is a very profitable play. You win 79 big blinds over the 8 times = almost 10x every time the hand occurs.
You can use this math to make sure that you have at least 8x the price you are paying still to play. If you call with less than this, you can’t win in the long run.
Next, you need to factor in the fact that your opponent will also improve to a set (which beats yours) sometimes. He will also hit a flush or straight on occasion. Sometimes, this player will fold before you get the chips in the middle. To keep these factors in mind, you need to bump up the stack-depth to make this play profitable. Pros recommend at least 12x the bet you call left behind.
This example used a small pair. You can also use suited connectors or suited ace-x hands for their implied odds value. Since these hands make the nuts less often than pairs, I recommend you have at least 25x the bet you are calling to make them profitable.
By the time you reach later betting rounds, your pot odds and implied odds will be easy to calculate. What is not so easy to factor in is whether you will be paid off if you do make your hands. If you do make a flush, it will be obvious to other players that there are 3 suited cards on the board. You might find opponents folding to you later bets – particularly if you have tight table image.
You should also factor in the chance that your opponent also missed the flop. In the above example, you might find an opponent continuation bets the flop with ace-high, then gives up on the river – allowing you to steal the pot even when you did not improve.
Straights have better implied odds than flushes in many cases. When you hit your straight (assuming there are not four cards to a straight on the board), then your opponents will find it harder to give you credit for the exact hand you hold. This means you have a much better chance of getting paid off than with a flush.
During the later stages of poker tournaments, extra factors come into play which affect the pot odds and implied odds. For a start, stack sizes can be varied. Many players will have shallow stacks in relation to the size of the big blind. This means implied odds for hands like small pairs and suited aces are not available.
Prize pool distribution also needs to be accounted for. In the later stages of tournaments or the bubble of sit n goes – chips you win have a decreasing value in terms of the extra prize money you can win. To factor this in, you need to have better express odds and implied odds to make a call than you would in the early stages. If your opponents know about this, they will be less inclined to call big bets. This means that when they fight back in a pot, you can put them on a stronger range of hands than you would in a cash game or during the early stages of a tournament.