Cash Game: AK all-in preflop everytime, you can't lose.

Okay, for some math...rufus, someone correct me, I know I'm wrong.

One opponent, given that you have AK, has:

C(3,2) + C(3,2) = 3 + 3 = 6 ways to get AA or KK out of C(50,2) = 1225 possible hands.

So, the probability he has AA or KK is 6/1225 = 0.004898.

With no other information, the probability he has AA or KK is (C(4,2) + C(4,2)) / C(52,2) = 0.009050.

So, the fact that you have AK decreases the chances he has AA or KK from 0.9050% to 0.4898%.

That the probablility that ONE opponent has AA/KK, but what's the probability that one of nine opponents has AA/KK including the times you have AK, and one opponent has AA and another KK?

What I was trying to figure out was, if you went all in preflop everytime you had AK suited or not, would it be profitable, and at what number of BB would you have to have to be profitable?

For instance, if opponents only called preflop allins with AA/KK, this is how I see it:

Assuming you move all in with 25bb, and opponents call only with AA/KK you will win 95% of the time uncontested and pick up (on average) the blinds, plus one limper, so 2.5bb (a complete guess, maybe someone could be more complete). Out of 100 hands, you will win 95 times uncontested for 237.5 bb. You will be called 5% of the time by AA/KK and lose 80.0% of the time for a loss of 100bb. On average, you expect to win 1.375bb per all in.

Correct???

You do have to consider that people calling your all-ins with no hand but AA or KK is a pretty hefty assumption -- if you're just going all-in with no provocation, your overbet might get someone to call with hands like QQ or even JJ/TT, against which you're also a dog (albeit a small one). It's also possible that you might face hands like AQ or AJ, which you dominate about 80%.

There's nothing wrong with making this play occasionally, but I really don't like raising all-in with it preflop, as you don't extract maximum equity out of your hand. Maybe I try to be too tricky, but when I get this hand, I'll raise if no one else has, and try to extract more if I hit the flop, thus saving a few bucks if I miss completely.

Pardon me if I took your post completely out of context -- I just thought the consideration would make an interesting point that poker isn't necessarily just pure math.

Considering the strigent calling requirements (most people aren't this tight), consider the following:

KK+, AKo VERSUS

AA 84.670% to win Six different ways.
AA, AKs 66.818% to win Ten different ways.
KK+ 64.551% to win Twelve different ways.
KK+, AKs 58.258% to win Sixteen different ways.
AA, AKo 51.856% to win Sixteen different ways.
QQ+ 51.570% to win Eighteen different ways.
KK+, AKo 50.000% to win Twenty four different ways.
QQ+, AKs 49.672% to win Twenty two different ways.
AA, AKs, AKo 49.465% to win Twenty two different ways.
KK+, AKs, AKo 48.374% to win Twenty eight different ways.
QQ+, AKo 46.055% to win Thirty different ways.
QQ+, AKs, AKo 45.270% to win Thirty four different ways.
22+ 39.457% to win Seventy eight different ways

AA can come in six different ways
KK can come in six different ways
AKo can come in twelve different ways

You would be moving all in 1 in 55.25 hands.

Considering the above, is this an "unbeatable" strategy? By that I mean, with the hands that show a profit in win rate, you don't get them often enough to show a profit, and those with lower win rates lose in the long run anyway.

(And as a reply to the above comment, I realize that poker isn't all math, but its fun for me [img]/images/graemlins/grin.gif[/img])

[AaronBrown]

Without arguing the details of your calculation, I'm sure you are correct that you will make money on average going all-in with AK, unless your stack is very large relative to the blinds.

However, you could make more positive EV by playing this hand. Also, that would increase the deception value of the other hands you play.

If you only steal the blinds with your best hands, and lose everything every time you have a good hand and someone has better, you won't win in the long run.