AK in No-Limit Holdem to a Raise--What to do??

All this discussion got me to thinking. Is it in fact +EV to re-raise AK in No-Limit Holdem? So, what I'm going to do is basically take information from my post from a few months back about using VP$IP to figure out what your opponents might be holding, and use that information to calculate the EV of AK, suited or offsuit and see how much of an edge you really have.in the situation.

First, I want to define what I'm talking about here. I'm using excession (from BTP)'s criteria to show tight/loose, etc. He defines the traditional categories this way:

Tight: VP$IP < 22%
Semi-Loose: VP$IP 22-35%
Loose: VP$IP > 35%
Extra Loose: VP$IP > 55%

I'm not yet sure, but it may be profitable to look at these players either ths way or by their PFR numbers, or even perhaps by the percentage of hands they raise PF with (If your VP$IP is 20% and your PFR is 5%, your raising percentage is 25%). Either way, the assumption used here is that a player raises with their best hands, not just any random trash.

For the sake of argument, we'll also define the raising percentage statistic (PFR divided by VP$IP), and use these criteria:

Passive Pre-Flop: R% < 25% (VP$IP/PFR pairs like 20/4, 30/5, or 40/6)
Average Pre-Flop: R% 25-35% (VP$IP pairs like 20/7, 30/11, or 40/12)
Aggressive Pre-Flop: R% >35% (VP$IP pairs like 20/10, 30/14, or 40/18)


More assumptions:

1) A player will loosen up as position gets later. Therefore a player's raising percentage may be 25% overall. It may be 10% in EP, and as high as 40% in LP.
2) Regardless, you should always open-raise with AK, suited or not.
3) We're using Sklansky groups to simplify the discussion:

Group 1 Hands: AA, KK, QQ, JJ, and AKs. There are 28 ways to make these 5 hands, 2.11% of the possible hands.
Group 2 Hands: TT, AQs, AJs, KQs, and AK. There are 30 ways to make these 5 hands, 2.26% of the possible hands.
Group 3 Hands: 99, JTs, QJs, KJs, ATs, and AQ. There are 34 ways to make these 6 hands, 2.56% of the possible hands.
Group 4 Hands: T9s, KQ, 88, QTs, 98s, J9s, AJ, and KTs. There are 50 ways to make these 8 hands, 3.77% of the possible hands.
Group 5 Hands: 77, 87s, Q9s, T8s, KJ, QJ, JT, 76s, 97s, Axs, and 65s. There are 98 ways to make these 18 hands, 7.39% of the possible hands.
Group 6 Hands: 66, AT, 55, 86s, KT, QT, 54s, K9s, J8s, and 75s. There are 68 ways to make these 10 hands, 5.13% of the possible hands.
Group 7 Hands: 44, J9, 64s, T9, 53s, 33, 98, 43s, 22, Kxs, T7s, and Q8s. There are 106 ways to make these 20 hands, 7.99% of the possible hands.
Group 8 Hands: 87, A9, Q9, 76, 42s, 32s, 96s, 85s, J8, J7s, 65, 54, 74s, K9, and T8. There are 132 ways to make these 15 hands, 9.95% of possible hands.

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Now, for the real stuff...
Situation 1: You're in LP, 3 off the button. A player in MP raises to 5 BB, an average raise for the table. You look down and see AKs. What do you do?
If the player is tight and aggressive, you have to think about the top 10% of hands. This includes all the Sklansky Group I and II hands, and the "better" Group III hands. Using Pokerstove, you get that AKs is about a 54-46 favorite over this grouping of hands. AKo, however, has a smaller edge, only 52-48. Poker, and specifically no limit holdem, is about exploiting any small edge you may have. However, is it enough of an edge to push more chips into the pot on what is essentially a coin flip?

Situation 2: Same as above, only the player is very LAGgy and likes to raise a lot of hands. Say he raises his pocket pairs, and his paint cards first in a pot...When the possibility of weaker holdings comes into the picture, your edge with AKs becomes larger--61-39. AKo is a 59-41 favorite here.

You knew there was a table coming, didn't you?

Raisor will Raise with Hands to Group #	PFR%	Edge for AKs	Edge for AKo
Group 1	2-3%	40-60 Underdog	36-64 Underdog
Group 2	3-7%	59-41 Favorite	56-44 Favorite
Group 3	7-11%	62-38 Favorite	60-40 Favorite
Group 4	11-13%	64-36 Favorite	62-38 Favorite
Group 5	13-20%	66-34 Favorite	64-36 Favorite
Group 6	20-25%	67-33 Favorite (2-to-1)	65-35 Favorite
Group 7	25-33%	63-34 Favorite	61-39 Favorite
Group 8	>33%	64-36 Favorite	62-38 Favorite

What does this tell you? It tells you that you are a significant favorite over most hands, but to be extremely wary against hands you may be dominated against. What is dominant over AK? AA or KK--the hands most likely to be raised and re-raised. If you raise first in with AK, and you get re-raised, it becomes decision time, especially if your re-raisor is a tight player. If you assume you are an underdog, or even a coin flip, you must be aware of the pot odds you have to call this re-raise, and you must also be ready to let go of this dangerous yet potent drawing hand. Also remember that as the number of players to a flop increases, the chances you will be able to win unimproved decreases. AK is a fantastic hand, but one you should play similarly to TT or JJ. If a flop comes Q-high and you're bet into, you're most likely beaten and need to muck it.

Meanwhile, if your raisor is anything but tight, re-raising with AK is a +EV move, especially if you don't believe they have AA or KK. You are no worse than a 55-45 underdog to any hand other than AA or KK. My advice again, however, is to know when to let go.