The table below shows the odds of each hand winning in typical all-in match ups in Texas Holdem. The percentage chance of winning assumes that both players are all-in and that all 5 community cards will be dealt to determine a winner. The table also assumes that there are no other players in the hand, although the results should be very similar.
All-in hands probability odds chart.
- Sep 15, 2011 Solution to problem 2.32 in Miller - calculates the probabilities of all possible five card hands in poker.
- The probability of being dealt a royal flush is the number of royal flushes divided by the total number of poker hands. We now carry out the division and see that a royal flush is rare indeed. There is only a probability of 4/2,598,960 = 1/649,740 = 0.00015% of being dealt this hand.
- You are dealt a 5 card poker hand. What is the probability that all are of the same suit (all hearts, all clubs, all spades, or all diamonds)?
If the turn is also not a 2, your poker odds of hitting it on the river are again 22:1 (4%). However, the combined hand odds of hitting a 2 on the turn or river is 12:1 (8%). For mathematical reasons, only use combined odds (two card odds) when you are in a possible all-in situation. All In Match Up Odds. The table below shows the odds of each hand winning in typical all-in match ups in Texas Holdem.The percentage chance of winning assumes that both players are all-in and that all 5 community cards will be dealt to determine a winner. Interestingly, most, if not all, standard poker games like Texas Holdem make use of a single 52-card deck so it would be possible to compute for your exact probability of getting each hand. But we won’t bore you with the math behind it. Apr 18, 2017 All Long-Shot Odds in Poker. Below we've listed all odds and probabilities mentioned in this article. Below each scenario we have provided the mathematical formula for how to calculate the probability. Keep in mind that all probabilities assume that each player stays in the hand until the mentioned scenario can no longer be reached.
Typical Match Up | Hand 1 | Hand 2 | ||
---|---|---|---|---|
Under Pair vs. Overcards | T T | 57% | 43% | A K |
Overpair vs. Pair | K K | 80% | 20% | 9 9 |
2 Overcards vs. 2 Undercards | A Q | 63% | 37% | 5 7 |
Dominated Hand | A J | 79% | 21% | J T |
Very Dominated Hand | Q Q | 89% | 11% | Q J |
Overcard vs. Dominated Kicker | A 9 | 29% | 71% | 9 9 |
Pair vs. 1 Overcard | 8 8 | 69% | 31% | A 5 |
1 Overcard vs. 2 Middle Cards | J 4 | 57% | 43% | 6 8 |
How to use the all in match-ups odds chart.
The table can be used to estimate your chances of winning in common all-in situations, however, the table does not highlight the exact probabilities for the certain match-ups in general.
For example: in the pair v overcards match-up, 2 2 would be a 53% favourite against A K instead of being a slightly stronger favourite like T T with a 57% chance of winning. The is due to other factors such as the increased probability that two overpairs will appear on the board creating a higher two-pair with a better kicker for the player holding A K.
All in match up odds evaluation.
As you can see from the table, some of the match-ups are closer than you might expect them to be. For example, if you have another player dominated with a hand like A J against J T, your opponent will win the pot 1 time in 4. Therefore you should be careful not to become overly excited when cards like these are turned over in an all-in situation, because your opponent is not always as far behind as you think.
Another interesting all-in match up is the very common AK versus an under pair. The table shows that although the odds are fairly even, the under-pair will usually have the slight advantage.
This means that it is always better to be pushing all-in rather than calling an all-in with AK if necessary, because to call with AK against an under pair is a losing play in the long run. By pushing all-in with AK you give your opponent the opportunity to fold for fear of an overpair, which will improve your expectation in the long run.
Go back to the poker odds charts.
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Please enable JavaScript to view the comments powered by Disqus.DeucesCracked, for the last 5 months I've made more money playing
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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?
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%.
List Of All Poker Hands
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.
The good news is that there is a simple system, with powerful shortcuts & rules, that you can begin using this week. Rooted in GTO, but simplified so that you can implement it at the tables, The One Percent gives you the ultimate gameplan.
The good news is that there is a simple system, with powerful shortcuts & rules, that you can begin using this week. Rooted in GTO, but simplified so that you can implement it at the tables, The One Percent gives you the ultimate gameplan.
This 7+ hour course gives you applicable rules for continuation betting, barreling, raising, and easy ratios so that you ALWAYS have the right number of bluffing combos. Take the guesswork out of your strategy, and begin playing like the top-1%.
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.
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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.
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