Monday, December 17, 2007

Poker Odds - Ace King Off Suit in Texas Hold Em - What Are The Odds

Ace king is a great starting hand in Texas hold em. We will analyze the probability of AK winning a showdown against a number of other hands. This will allow us to see why this preflop hand is so highly regarded.

When up Against Pocket Pairs

The worst situation with this preflop hand is that you are up against pocket kings or pocket aces. In a heads up (2 player) situation, the probability of winning with AK off-suit against pocket aces are approximately:

As Kd vs. Ah Ac - As Kd winning at showdown: 6.67% or 12.7 to 1 (that is 12.7 lost hands to each won hand)

You have the worst of it against poker aces. However against pocket kings, the odds are:

As Kd vs. Kh Kc - As Kd winning at showdown: 29% or 2.4 to 1

As you may hit an ace, the situation is not as bad as with pocket aces, and while you would not want to be in the pot if you knew your opponent had KK, the odds below will show that your 29% chance of win makes this a situation acceptable considering the other starting hands your opposition may have.

To see the odds against an under pair, we will use pocket queens as a case study. The odds are approximately:

As Kd vs. Qh Qc - As Kd winning at showdown: 43.49% or 1.3 to 1

Your starting to approach even money on these odds. The thing about AK against pokets is that while you are an under dog, out of all the possible pre-flop hands (there are 1326 of them), there are only 6 possible preflop hands of any given rank that are pocket pairs (e.g. QcQd, QcQh, QcQs, QdQh, QdQs and QsQh). Over the 13 possible ranks (2 - A) this is only 78 out of 1326 possible preflop hands that you are in with the worst of it.

When up Against Hands that are not Pocket Pairs

Now, how does AK go against other hands that are not pocket pairs. Here we will see where this hand becomes so nice. Assuming you have put in a pre-flop raise and your opponent has called, the odds are good that they might have an ace, in which case you will have them dominated. Against AQ off the odds are approximately:

As Kd vs. Ah Qc - As Kd winning at showdown: 71.3% or 0.36 to 1

As shown here, this is where the odds really shines. Against a suited connector:

As Kd vs. 6h 7h - As Kd winning at showdown: 58.03% or 0.72 to 1

Here you are still a clear favorate, and when your opponent holds two under cards:

As Kd vs. Qh 10c - As Kd winning at showdown: 63.34% or 0.57 to 1

Things are looking good.

Against Varying Numbers of Randomly Dealt Hands

We now want to get some understanding of how AK performs against one verse multiple opponents. In order to do this we will look at AK off-suit against a different number of random hands, assuming all random hands see a showdown. Against one other randomly dealt hand, the odds are approximately:

As Kd vs. 1 random other hand - As Kd winning at showdown: 64.58% or 0.53 to 1

And against 3 randomly dealt hands the odds are approximately:

As Kd vs. 3 random other hands - As Kd winning at showdown: 37.42% or 1.59 to 1

Lets make a few assumptions to look at this: if you put say $10 in the pot pre flop and all random hands call and you are all in, against 1 random hand, you will take $20 with a $10 investment with a 64.58% chance and you will loose this pot with a 35.42% chance. This equates to giving you an expected pot of $12.92 (including your original investment). Under the same assumptions with all 3 opponents with randomly dealt cards who are all in pre-flop, you will take a pot of $40 with a probability of 37.42%, giving you an expected pot of $14.97. So you can see here that while many players like to end up in heads up with such an opening hand, under these assumptions, you are getting a better return against multiple opponents.

So we have just looked at the odds when holding AK off-suit as an starting hand in Texas hold em. As you can see from this study, when you are dealt this starting hand, you are in a very strong position.

Atricle written by B. Callen. This poker calculator was used to calculate these poker odds. Check out this poker odds calculator that attaches to the online poker rooms, or see this party poker deposit bonus code.

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