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Pocket Aces – statistically the best starting hand in Hold’em – are less than a 75% favorite against 2 or more opponents according to my Texas Hold’em hand rankings. If you’ve ever played Texas Hold’em you already know how important starting hand selection is. 2 handed: first player dealt; odds of getting pocket aces = (4/52)x(3/50) =.46% or 1/217 2 handed: second player dealt; odds of getting pocket aces = (4/51)x(3/49) =.48% or 1/209 correct me if I’m wrong but this infers that the greater the number of players and the further in the action you are (closer to the button) the higher the probability of being dealt aces. The odds of being dealt any specific pocket pair, such as aces, is 220-to-1 but the odds of being dealt a pair of aces and then someone at the same table being dealt pocket kings is slightly less as the two aces have been removed from the 52-card deck. This means that the odds of someone being dealt a pair of kings when you have aces is 205-to-1.Understanding Probability In Texas Holdem Is An Essential Aspect Of Profitable Play
– Pre-Flop Probability Guide
Ever wondered how often you will be dealt Aces? Or what the chances of facing an over-pair are when you hold Jack-Jack? This section of the site will give you the probability of certain hands before the flop (this page) and in later pages the chances of certain flops (for example one suit flop probability) and the chances of dominating hands being out there to your ace-x hand (where x is one of several small to medium cards).
We start by looking at how the cards in the deck can be dealt based on a random distribution of the 1326 ways of 2 cards falling and how often you’ll expect to be dealt certain hands. Then we take suitedness into account – since there are less ways of being dealt 2 suited cards. Later articles in this series will continue with the essential poker probability and card distribution stats you need.
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Firstly, where did the number 1326 come from? Well with 52 cards in the deck your first card is 1/52 this is then multiplied by 1/51 and the total divided by 2 (since it does not matter what order your cards are dealt in) giving 1326 combinations of all cards in any suit.
Of course suitedness is not often important, especially for low cards. The next question is then – what is the number of unique starting hands in Texas Holdem, not counting suits? The answer here is 169 unique hands.Pre-Flop Poker Probability - 169 Distinct Starting Hands
Now we are getting somewhere. Next we can use the numbers above to work out what the probability of being dealt AA, KK (or in fact any pair) is. This is a case of taking the total number of possible hands and then seeing how many of these are your pair. We will take a pair of Kings as an example. Of the 1326 possible combinations there are 6 ways of being dealt this hand pre-flop. The 6 combinations possible are Kh-Kd, Kh-Kc, Kh-Ks, Kd-Kc, Kd-Ks and Kc-Ks.
6 / 1326 = 0.00435 or 221-to-1
So the chances of being dealt any specific pair are 221:1 against, in fact with 13 possible pairs the chances of being dealt any pair go up to 16-to-1 (there are 78 pair combinations from 1326 total).
Next we can look at unpaired hands, a specific example is the number of ways of being dealt Ace-king pre-flop. Here we have more possible combinations, since there are 8 cards that can be dealt first and then 3 remaining cards to make this hand (we will ignore suitedness for the moment). This gives 16 ways in which A-K can be dealt out of the 1326 combinations – a probability of 0.0121% or approximately 82-to-1. In fact this is the same for any unpaired hand when you ignore the suits.Pre-Flop Poker Probability - Probability Of Hands Pre-Flop Chart
The reference table below gives probabilities of being dealt specific hands pre-flop: The next article in this series will look at the chances of being dealt hands at the same time as one or more opponent is dealt a higher hand – for example AA vs KK and AK vs QQ.
Pre-flop Hand Odds
AA0.045
Same for any pocket pair
AK (any suits)0.012
Any 2 cards not inc. suits
AK (suited)
0.003
Pair 10-10 or better 0.023
10-10, JJ, QQ, KK or AA
AK, AQ or AJ0.036
Suits not considered
2 Suited Cards 10+ 0.03
Any Suited Connector 0.039
23 suited or better
2 Cards Jack +0.09
Suits not considered
Finally we can look at how combinations of pre-flop hands work, asking the question what is the probability of being dealt a playable hand for each position. We will use arbitary early, middle and late position combinations here to demonstrate – the actually hands you play is up to your personal style!Position Combinations
Early Position
AA to JJ, AKo, AQs4629:1
Early Mid Position
AA to 99, AQo+, AJs18:1
Mid Position
77+, A10o+ A8s+ KQ+1409,5:1
Late Position
55+, A7+, QJo+, 78s+5,5:1
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Want to find out the probabilities of being dealt an ace before the flop in Texas Hold’em? Use the tables below to help you find the different aces odds based on the situation and the number of players at the table.Aces probabilities odds charts.Probability any player is dealt an ace.# Players% Odds218%340%450%559%666%773%878%983%You have an ace, probability another player does.# Players% Odds212%323%432%541%650%757%864%969%You have no ace, probability another player does.# Players% Odds216%329%441%551%660%768%874%980%
Probability of being dealt an ace in any Texas Hold’em game is 15%.How to use aces odds.
These tables are not going to be of much use to you whilst you play, but it is useful information on the probabilities of hands with aces turning up at your table.
The most useful information from these aces odds tables is that the likelihood of a player being dealt an ace increases with the number of players at the table.
The likelihood of another player holding an ace if you hold an ace yourself table (top right) is interesting. There is a fairly high probability that another player at a 9-seater table holds an ace if you do as well. This means that we should be cautious when dealt weak aces and should fold them in early position. There is a chance that we were the only player at the table holding an ace, but we are saving ourselves more money in the long run for when we come up against another player with a better ace than ours.Odds Of Getting Pocket Aces In Texas HoldemPlaying aces in Texas Hold’em.
An ace is the highest ranking card in Texas Hold’em and can be played either high or low. This means that if you are dealt an ace preflop, there is a fair chance that you hold one of the strongest hands at the table. If you are all-in with an opponent and they do not have a pocket pair or a better ace, you are the favorite to win the hand. Odds Of Getting Pocket Aces In Texas Holdem
However, you should be careful to not become overly attached to the hand when you are dealt an Ace, because there is a fair chance that you will lose a sizeable proportion of your stack if you get into a hand with another player that holds a better ace than you (e.g. A9 vs AQ).
Be careful to not overvalue hands with aces, as they can get you in to a lot of trouble if you do not have a good kicker.
For strategy guides on how to play hands with aces, take a look at the rag aces and pocket aces articles.
Go back to the poker odds charts.Texas Holdem Poker Odds Chart
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