Poker Odds – Starting Hands, Ranges & Calculations
How Different Types of Poker Odds Affect Your Winning Chances in Poker Games
To succeed in poker, you need a solid understanding of the math. While there are many human elements involved in the game – without knowing about the different types of poker odds, you’ll be left guessing much of the time.
This page is an introduction to many different types of poker odds. It covers different situations and game formats, showing how odds affect your decision making. This includes the odds (chances) of different hands winning pre-flop, along with hand matchups on different flops.
Here is what you will find below:
- Odds and Starting Hands
- Introducing Ranges: How Your Hand Fares Against Them
- Introducing Pot Odds and Outs
- Implied Odds
- Reverse Implied Odds
- Factoring in Opponents Tendencies to Odds Calculations
Odds and Starting Hands
Good poker starts with a solid starting hand strategy. There are several elements to this, including your position at the table, playing style and the known tendencies of your opponents.
When you are dealt pocket aces, you know you have the best hand pre-flop. You will be dealt a pair of aces (or any named pair) once every 221 hands. When you have this hand, your odds all-in against any other hand are as follows:
- Aces vs Kings (or any pair) = 81.7%
- Aces vs Ace-King = 92.8%
- Aces vs 2 Suited Cards = 82.53%
- Aces vs Suited Connectors = 76.76%
As you can see, there really is no reason to slow-play with this hand. Your chances against even the best of the hands your opponents could hold are huge.
When your pair is lower, your poker odds pre-flop take a nosedive very quickly. The number of higher cards which can hit the flop to beat you goes up quickly. Let’s take a pair of jacks as an example:
- Jacks vs a Higher Pair = 17.08%
- Jacks vs Ace-King (or Ace-Queen) = 57.09%
- Jacks vs Ace-x (where the side card is 10 or lower) = 71.35%
- Jacks vs a Smaller Pair = 81.03%
Many players get in trouble with Ace-King, playing this passively by calling – instead of as the premium hand that it is. This hand is essentially a coin-flip against a pair Q-Q or lower – and has some decent chances against kings.
Starting Hand Odds vs Ranges
Of course, poker hole-cards are hidden, you will not know what your opponent’s hold until showdown (if at all). For this reason, making simple comparisons with two specific hands is less useful than comparing your hand to a range of hands that your opponents might hold.
A typical middle position raising range in a smaller stakes game might look like this:
7-7+, A-Jo+, K-10s+
This means that the player will raise any pair higher than 7’s, unsuited cards Ace-Jack or better and suited Broadway hands King-10 or better. This is a 9% raising range.
If you are sitting in later position with a mid-strength hand, knowing the poker odds of your hand being better than theirs pre-flop can be useful. To find this information you will need a poker calculator. These have in interface allowing you to select ranges, and then compare how different starting hands do against the entire range.
Here are some examples against the range above:
- A-A = 84.4% Equity
- 10-10 = 53.7% Equity
- 3-3 = 38.7% Equity
- Ace-Queen Suited = 51%
The complexity of poker starts here. You know your opponent will behave differently with different parts of their range. If you re-raise, they will fold the weakest hands, call with the mid-range (and some strong hands), and will often re-raise with the top part of their range.
If you want to improve your poker game, spending time with a calculator and looking at matchups between different hands and ranges is time well spent. This will get you thinking in terms of the poker odds of your hand against a range – rather than the impossible to know single matchups.
Introducing Pot Odds
Every time you call a bet in poker, you should calculate the price you are getting in the form of odds. If you call a half pot bet of $30 (the pot is $60 and someone bets into you), you would need to pay $30 in a pot of $90. This means the price of your call is 3-to-1. If you win more often than this price, your call has a positive expectation over time.
Pot odds alone will often have you guessing. It is hard to know how many times an opponent is betting a strong hand, medium-strength hand or is bluffing. As you gain experience, you will be better at putting opponents on a range of hands – comparing the pot odds you are getting to your real chances of winning.
Closely related to pot odds is the concept of outs. This describes the number of cards still in the deck which could improve you to the best hand. You can have very few (a single over-card in your hand will pair 3 times on the turn and river, out of 47 unseen cards). You can also have a lot of outs, for example with a combined flush and straight draw.
This means that you will improve to make the best hand a certain percentage of the time. By comparing your chances of improving with the pot odds, you can decide whether to call, fold or even to raise as a semi-bluff.
Implied Odds in Poker Games
Pot odds give you a snap-shot of the price you are getting in a poker hand. Most of the time, there will be more money in both your stack and your opponent’s stack. You get immediate odds on your call – though if you improve to the best hand, you can make a lot more money.
The money you could make on future streets is known as your implied odds.
A great example is where you call with a small pair before the flop. You know you do not have the correct price against the kind of hands you opponent would raise with at that point. If you do hit a set, you can win many times that small bet. Here your implied odds are huge. You will win a big pot sometimes, making up for all those times you miss the flop and fold.
Note that you will not always get paid off. You will also lose the hand sometimes (set over set, opponent makes a flush and so on). To account for those situations, you need at least 12x your bet left in your stack to make this implied odds call profitable.
This same concept applies to suited connectors and suited aces.
Reverse Implied Odds
This concept is more advanced – and is the main reason that it is dangerous to play easily dominated hands like Ace-Nine.
The problem with these hands is that when you do hit the flop with a single ace or nine, you will not know whether you are ahead or behind. If you make a pair with the ace, you will sometimes lose a big pot when an opponent shows up with ace-king (for example). If you pair the 9, your opponent(s) could hold a pair of 10’s or higher – putting you in terrible shape.
Those kind of hands are said to have ‘reverse implied odds’. You are calling a bet pre-flop, though you will likely either win a small pot or lose a big one – depending on how things pan out. I recommend avoiding hands which are easily dominated for exactly this reason.
Small suited cards have a similar problem. You will make the best hand sometimes. If the pot gets large after you make your flush, there is a solid chance someone has a bigger flush – giving you reverse implied odds on your initial call.
Poker Odds: How to Factor Opponent Tendencies into the Math
All the examples above assumed a single opponent, and simple match-ups. You should keep in mind that many situations will involve multiple opponents. You could be facing a bet, work out the pot-odds allow you to make the call, only to find a big re-raise from a player yet to act. This shows how powerful acting last in the betting can be in poker – you can calculate the poker odds knowing that you ‘close the action’.
The tendencies of individual opponents also affect your odds.
Some players will raise ‘light’ and continuation bet on almost any flop. This means you can call with a wide range – hoping to take the pot on a later betting round when your opponent gives up. You still have pot-odds to improve to the best hand here. What you should keep in mind is that you have another way to win the hand. You can be a little more flexible with the odds you take (or give to an opponent) depending on the exact situation.
Loose opponents, who will call down your bets all the way to the river with hands like middle pair, have excellent implied odds. This means you can be a more flexible with your calls when the betting is small – confident that you have the implied odds to get paid off when you make your hand.
On the opposite side, tight and aggressive opponents are less likely to pay you off. If you call to make a flush, the board can look scary – a thinking TAG player is unlikely to pay your big river bet. This means that you need to be getting a better price on the initial call to stay in the hand. Some tight players are reluctant to fold high pairs on a safe board. If you come across these players, your small pairs and suited connectors become more valuable.