Best Poker Starting Hand Odds
The main underpinning of poker is math – it is essential. For every decision you make, while factors such as psychology have a part to play, math is the key element.
In this lesson we’re going to give an overview of probability and how it relates to poker. This will include the probability of being dealt certain hands and how often they’re likely to win. We’ll also cover how to calculating your odds and outs, in addition to introducing you to the concept of pot odds. And finally we’ll take a look at how an understanding of the math will help you to remain emotional stable at the poker table and why you should focus on decisions, not results.
What is Probability?
Poker hands odds & outs: a crash course-guide on poker odds, pot odds, probabilities & odds charts so you can win at Texas Hold’em at the tables or online. One of the most important things that a poker player should know is what their poker odds are in a given situation. Top 10 Best Starting Poker Hands List. If you ever get lost what the best poker hands to play are, just refer to this starting poker hands list, and you should be good. Choosing the right hands preflop is one of the most important things when starting out, and it can have a huge impact on your win rate.
Probability is the branch of mathematics that deals with the likelihood that one outcome or another will occur. For instance, a coin flip has two possible outcomes: heads or tails. The probability that a flipped coin will land heads is 50% (one outcome out of the two); the same goes for tails.
Probability and Cards
When dealing with a deck of cards the number of possible outcomes is clearly much greater than the coin example. Each poker deck has fifty-two cards, each designated by one of four suits (clubs, diamonds, hearts and spades) and one of thirteen ranks (the numbers two through ten, Jack, Queen, King, and Ace). Therefore, the odds of getting any Ace as your first card are 1 in 13 (7.7%), while the odds of getting any spade as your first card are 1 in 4 (25%).
Unlike coins, cards are said to have “memory”: every card dealt changes the makeup of the deck. For example, if you receive an Ace as your first card, only three other Aces are left among the remaining fifty-one cards. Therefore, the odds of receiving another Ace are 3 in 51 (5.9%), much less than the odds were before you received the first Ace.
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Pre-flop Probabilities: Pocket Pairs
In order to find the odds of getting dealt a pair of Aces, we multiply the probabilities of receiving each card:
(4/52) x (3/51) = (12/2652) = (1/221) ≈ 0.45%.
To put this in perspective, if you’re playing poker at your local casino and are dealt 30 hands per hour, you can expect to receive pocket Aces an average of once every 7.5 hours.
The odds of receiving any of the thirteen possible pocket pairs (twos up to Aces) is:
(13/221) = (1/17) ≈ 5.9%.
In contrast, you can expect to receive any pocket pair once every 35 minutes on average.
Pre-Flop Probabilities: Hand vs. Hand
Players don’t play poker in a vacuum; each player’s hand must measure up against his opponent’s, especially if a player goes all-in before the flop.
Here are some sample probabilities for most pre-flop situations:
Post-Flop Probabilities: Improving Your Hand
Now let’s look at the chances of certain events occurring when playing certain starting hands. The following table lists some interesting and valuable hold’em math:
Many beginners to poker overvalue certain starting hands, such as suited cards. As you can see, suited cards don’t make flushes very often. Likewise, pairs only make a set on the flop 12% of the time, which is why small pairs are not always profitable.
PDF Chart
We have created a poker math and probability PDF chart (link opens in a new window) which lists a variety of probabilities and odds for many of the common events in Texas hold ‘em. This chart includes the two tables above in addition to various starting hand probabilities and common pre-flop match-ups. You’ll need to have Adobe Acrobat installed to be able to view the chart, but this is freely installed on most computers by default. We recommend you print the chart and use it as a source of reference.
Odds and Outs
If you do see a flop, you will also need to know what the odds are of either you or your opponent improving a hand. In poker terminology, an “out” is any card that will improve a player’s hand after the flop.
One common occurrence is when a player holds two suited cards and two cards of the same suit appear on the flop. The player has four cards to a flush and needs one of the remaining nine cards of that suit to complete the hand. In the case of a “four-flush”, the player has nine “outs” to make his flush.
A useful shortcut to calculating the odds of completing a hand from a number of outs is the “rule of four and two”. The player counts the number of cards that will improve his hand, and then multiplies that number by four to calculate his probability of catching that card on either the turn or the river. If the player misses his draw on the turn, he multiplies his outs by two to find his probability of filling his hand on the river.
In the example of the four-flush, the player’s probability of filling the flush is approximately 36% after the flop (9 outs x 4) and 18% after the turn (9 outs x 2).
Pot Odds
Another important concept in calculating odds and probabilities is pot odds. Pot odds are the proportion of the next bet in relation to the size of the pot.
For instance, if the pot is $90 and the player must call a $10 bet to continue playing the hand, he is getting 9 to 1 (90 to 10) pot odds. If he calls, the new pot is now $100 and his $10 call makes up 10% of the new pot.
Experienced players compare the pot odds to the odds of improving their hand. If the pot odds are higher than the odds of improving the hand, the expert player will call the bet; if not, the player will fold. This calculation ties into the concept of expected value, which we will explore in a later lesson.
Bad Beats
A “bad beat” happens when a player completes a hand that started out with a very low probability of success. Experts in probability understand the idea that, just because an event is highly unlikely, the low likelihood does not make it completely impossible.
A measure of a player’s experience and maturity is how he handles bad beats. In fact, many experienced poker players subscribe to the idea that bad beats are the reason that many inferior players stay in the game. Bad poker players often mistake their good fortune for skill and continue to make the same mistakes, which the more capable players use against them.
Decisions, Not Results
One of the most important reasons that novice players should understand how probability functions at the poker table is so that they can make the best decisions during a hand. While fluctuations in probability (luck) will happen from hand to hand, the best poker players understand that skill, discipline and patience are the keys to success at the tables.
A big part of strong decision making is understanding how often you should be betting, raising, and applying pressure.
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Conclusion
A strong knowledge of poker math and probabilities will help you adjust your strategies and tactics during the game, as well as giving you reasonable expectations of potential outcomes and the emotional stability to keep playing intelligent, aggressive poker.
Remember that the foundation upon which to build an imposing knowledge of hold’em starts and ends with the math. I’ll end this lesson by simply saying…. the math is essential.
Related Lessons
By Gerald Hanks
Gerald Hanks is from Houston Texas, and has been playing poker since 2002. He has played cash games and no-limit hold’em tournaments at live venues all over the United States.
Related Lessons
Related Lessons
On This Page
Introduction
Rules
- A single 52-card deck is used. All cards count as its poker value. Aces may be high or low.
- One player is designated as the dealer, usually with a laminated marker. This person does not have to physically
- The player to the dealer's left must make a 'small blind' bet. The player to the left of the small blind must make a 'big blind' bet. The amounts of both blinds should be specified in advance. The purpose of the blinds is to get the ball rolling with some money in the pot.
- Two cards shall be dealt down to each player, starting with the person to the dealer's left.
- The player to the left of the big blind must either call or raise the big blind bet. The play in turn will go around the table according to normal poker rules, which I assume the reader already knows. Table rules will specify any limits on the size or number of allowed raises.
- The small blind may also raise the big blind. If nobody raises the big blind the player making the big blind has the option to raise his own bet. The term for this is the 'big blind option.'
- Three community cards will be dealt face up in the center of the table. This is called the 'flop.'
- Another round of betting will ensue, starting with the player to the dealer's left.
- A fourth community card will be dealt face up in the center of the table. This card is called the 'turn.'
- Another round of betting will ensue, starting with the player to the dealer's left. Generally the minimum bet is double the first two rounds of betting.
- A fifth and final community card will be dealt face up in the center of the table. This card is called the 'river.'
- Another round of betting will ensue, starting with the player to the dealer's left. The minimum bet is generally the same as the previous round.
Each player still in the game at the end will determine the highest poker value among his own two cards and the five community cards. It is NOT a requirement that the player use both of his own cards. The player with the hand of highest poker value shall win. Following are the hand rankings.
- Straight flush: Five consecutive and suited cards. For example 5, 6, 7, 8, 9.
- Four of a kind: Four cards of the same rank, plus any fifth card. For example Q, Q, Q, Q ,4.
- Full house: Three of a kind and a pair. For example 6, 6, 6, J , J.
- Flush: Any five cards of the same suit, except for a higher ranking straight flush. For example A, Q, 8, 4 , 3.
- Straight: Five consecutive cards, except for a higher ranking straight flush. For example 8, 9, 10, J, Q.
- Three of a kind: Three cards of the same rank, plus any other two cards. For example 5, 5, 5, Q ,2 .
- Two pair: Two pairs, plus any fifth card. For example 8, 8, 2, 2 ,Q .
- Pair: A pair and any other three cards. For example 7, 7, 2, 5 ,A .
- ? High: Any five cards that do not form any higher poker hand. A king high hand for example might be K, Q, 7, 5 ,4 .
- If two or more players have poker values of the same rank then the individual cards will be used to break the tie. If necessary all five cards will be considered.
- I get asked a lot whether the two unused cards in a player's hand are used to break a tie. The answer is a firm NO. The two unused cards do not matter.
- If a new player arrives at the table he should either wait for the big blind position or put up an amount equal to the big blind, amounting to a call of the big blind.
- If a bet is made after another player runs out of money, then a separate pot is created. The player that ran out of money is not eligible to win the second pot. If more than one player runs out of money then multiple separate pots can be created.
- In formal games players may not bet with cash or buy chips with cash in the middle of a hand.
- There are numerous rules of etiquette, which I won't get into.
- There house may set the betting rules. There are three main types. A 'structured' game features raises of specified amounts. For example a '3/6 game' would mean that raises after the deal and flop are $3, and after the turn and river are $6. There is usually a limit to the number of raises a player may make, typically three. A 'pot limit' game has structured minimum raises but the maximum raise may be anything up to the amount in the pot at the time the raise is made. A 'no limit' game also has structured minimum raises but there is no maximum raise.
Examples
Example 1
Board: A, 2, 4, 5, 6
Player 1: J, 6
Player 2: 7, Q
Player 1 wins. Both have an ace high flush, so the second highest card is considered. Player 1's jack beats player 2's 7. The only way to have a flush tie is if the flush is entirely on the board and no hole cards are higher than the lowest card on the board in the same suit.
Example 2
Board: J, A, 7, 5, 6
Player 1: 2, J
Player 2: 10, J
Player 2 wins. Both have a pair of jacks so the singletons are considered. High highet singleton in both hands is an ace so the second highest singleton is considered. Player 1's second highest singleton is a 7, compared to player 2's 10. A 10 beats a 7 so player 2 wins.
Example 3
Board: A, A, K, Q, J
Player 1: Q, J
Player 2: Q, 2
Tie. Both have a two pair of aces and queens, with a king singleton. Some people incorrectly believe that in such cases the unused cards are considered, in this case player 1's pair of jacks beating player 2's jack/2. Only the top five cards matter. The jacks and deuce are irrelevant.
One of the most important aspects of Texas Hold'em is the value of each two-card hand before the flop. The decision of how to play your first two cards is something you face every hand, and the value of your first two cards is highly correlated to your probability of winning.
The following table shows my power rating for each initial 2-card hand in a 10-player game. The numbers are on a 0 to 40 scale. Basically, you should only play hands that are dark green, blue, or purple. Of course you should be more be more liberal in late position and picky in early position. If forced I would say you should need 10 points in late position and 19 points in early position to call the big blind. If your table is loose, as if often the case online, you can play a bit looser yourself.
Use the top table if you have a pair, the middle table if your cards are suited, and the bottom table if your cards are unsuited. Except for a pair,look up your high card along the left and your low card along the top.
Following are the links to my tables of the value of each intial hand according to the number of players. The 10-player section explains the methodology for creating the table table.
Best Poker Starting Hand Odds Against
Pot Odds
The following table shows the probability of making various hands after the flop and the correct 'pot odds.' The pot odds are the breakeven ratio of money in the pot to the amount you have to bet for the player to be indifferent about calling, assuming the player would definitely win if he makes the hand (a big if) and there are no additional bets (another big if). This table is a good starting point the player should make mental adjustments for the probability of winning without making the hand, losing with making the hand, and expected future bets. The odds of a two pair improving to a full house are the same as those for four to an inside straight.
Pot Odds — After Flop
| Hand | Probability of Making Hand | Pot Odds |
|---|---|---|
| Four to a flush | 34.97% | 1.86 |
| Four to an outside straight | 31.45% | 2.18 |
| Four to an inside straight | 16.47% | 5.07 |
The next table shows the pot odds after the turn.
Pot Odds — After Turn
| Hand | Probability of Making Hand | Pot Odds |
|---|---|---|
| 4 to a flush | 19.57% | 4.11 |
| 4 to an outside straight | 17.39% | 4.75 |
| 4 to an inside straight | 8.70% | 10.50 |
Best Poker Starting Hand Odds Today
Hand Strength Calculator
I'm proud to present my new and improved Poker Odds Calculator. Enter any situation in Texas Hold 'Em, and it will tell you the probability of each possible outcome.
Poker Tournament Calculator
My Poker Tournament Calculator will determine each player's probability, for up to nine players, of finishing in each place, and his expected share of any prize pool, assuming equal skill among all players. It produces the same results as what is known as the Independent Chip Model.
Internal Links
- Pinapple — Strategy and analysis of which card to discard before the flop.
- Bad Beat Jackpots: What is the Probability of Hitting one?
- Texas Hold 'Em Dominated Hand Probabilities: What is the probability one of your opponents has similar, and better, hole cards than yours?
Written by:Michael Shackleford