Probability of Getting Pocket Aces Twice in Texas Hold’em
Question: Have you ever wondered what your approximate odds are of getting dealt pocket Aces not just once, but twice in a single Texas Hold’em session? That sounds like hitting the jackpot. In fact, there is a particular number for how likely you are to get pocket aces twice. In a single Texas Hold’em game, the probability of getting pocket Aces is 1/221 (or about 0.45%). So, what if we wanted to get them one after the other? Let’s do the math.
In a regular cash game, if we play enough to experience every possible starting hand an equal number of times, the chances of getting pocket Aces each time is 0.45%. Well, two games in a row? Especially since each occurrence is a standalone event, we must multiply it. So, the chance of getting pocket aces two hands in a row is 0.45% * 0.45%, which gives us about 0.002025%. That is almost astronomical inhumanity. That’s roughly 1/49,000.
Probability of Getting Pocket Aces Twice in Online Poker
How about hitting pocket aces twice back-to-back in an online poker game? That sounds so unlikely, but let’s see what is the actual chance. Every game of online poker, the odds are 1 in 221 (0.45%) that you will be dealt pocket aces. Now, we just need to multiply these two probabilities for both consecutive occurrences, as every instance is independent. Thus, the likelihood of being dealt pocket aces two hands in succession is 0.45% * 0.45%, or 0.002025%. This means about 1/49,000.
Real online poker games can see you play hundreds of hands per day. At a 0.002025% probability, and if you play, say, well, I don’t know, maybe around hundreds of hands daily, it would take you over almost a year of playing at least on average per day to experience such an episode. Naturally, this is a best-case calculation—actual cases may be different.
Probability of Getting Pocket Aces Twice in High-Stakes Games
How infrequent is it to deal A-A twice in a row playing high-stakes poker? Let’s analyze it closely. The likelihood of a dealt hand in Texas Hold’em being one pair is 1/221 or about 0.45%, and it does not get any more common than getting pocket Aces. Well, how about in important games? You may still only win any given hand 0.45% of the time. Therefore, the chance of getting pocket aces in consecutive hands would be 0.45% * 0.45%, or just north of 0.002025%. That is to say, 1 in about 49,000.
This means that some hands could potentially be for a lot of chips in high-stakes games. Let us say that you are a new player to a high-stakes cash game and you deal approximately 30 hands an hour. That equates to roughly 1,633 hours, or 68 days of non-stop poker you would need just for one single opportunity at running aces twice in a row. It should be noted that this model is based on each hand being derived independently, as opposed to player strategy and gameplay, which can absolutely affect the outcome.
Probability of Getting Pocket Aces Twice in Multi-Player Games
How likely am I to get pocket aces more than once in a multiway game? It’s a curious question. So first up, the probability. Pocket aces is 1/221 or about 0.45% in Texas Hold’em. Since we want it to occur twice consecutively, the probabilities need to be multiplied together for two events in a row, and thus this corresponds to the probability of obtaining pocket rockets followed by another pair, which is 0.45% * 0.45%, that lets only slightly over 0.002025% or more or less 1 in 49,000.
Multi-Player Games: Conversely, the addition of more participants in games can increase complexity as well. Imagine you are playing in a game of ten players where one hand takes about 10 minutes and that the casino offers mini-tournaments lasting half an hour. So if you play daily for around five hours, it may take 490 days, or longer than a year, to see something like this. That is a mathematical way to look at it and does not necessarily describe how the live game will play out.
Probability of Getting Pocket Aces Twice in Poker Tournaments
What are the odds that you receive pocket aces back to back in a poker tournament? How rare is that? Let’s analyze closely. That gives us a likelihood of roughly 1 in 221 (0.45%) in any Texas Hold’em game that you will have pocket Aces dealt to your hand! As we need this to happen for 2 hands in a row, these probabilities multiply together, and the overall probability is 0.45% * 0.45%, which works out at something like 0.002025%. That’s about 1/49,000.
But what does this probability impact in a game of a poker tournament? If you are playing a big field tournament, let’s say about 30 hands an hour, it would then take you 1,633 hours, or 68 days of continuous play to have one crack at receiving pocket aces twice in succession. Of course, this is all under the assumption that each hand is dealt as an independent showdown (as in 100% player-strategy-invulnerable play result).