# Math - AK or AKs vs AA or QQ

• Bronze
Joined: 02.02.2009
Why is there such an equity difference between AK and AKs vs AA compared to AK and AKs vs QQ?

eg.

Vs AA

AKs 12%
AKo 7%

Vs QQ (no shared suits)

AKs 46%
AKo 42%

Ok not a massive difference but why does AKs have 1% more equity vs AA than it does vs QQ?
• 14 replies
• Bronze
Joined: 17.01.2011
i think it's something along the way of that one of the only ways for AK to beat AA is by spiking a flush.
vs QQ you'll just always have more outs in general...
• Bronze
Joined: 28.01.2012
Originally posted by Hackett77
Why is there such an equity difference between AK and AKs vs AA compared to AK and AKs vs QQ?

eg.

Vs AA

AKs 12%
AKo 7%

Vs QQ (no shared suits)

AKs 46%
AKo 42%

Ok not a massive difference but why does AKs have 1% more equity vs AA than it does vs QQ?
I would assume the 1% equity against AA is because the queens are blockers to the broadway straight, whereas the aces are not.
• Super Moderator
Super Moderator
Joined: 02.09.2010
to win vs AA w/ AKo, you need a straight, two more kings (at least) or 4 cards of the same suit as whichever of your cards is of a different suit than the aces.

With AKs, you have all of the above possibilities, but you only need 3 more cards of the same suit.

No A will help you w/ AKo -- unless it is part of the 4-flush that matches your king.

vs QQ, any K or any A helps too.
• Bronze
Joined: 02.02.2009
Thanks metza, that makes sense.

VorpalF2F and Tomaloc, its the opposite, The equity difference is 1% better vs AA than QQ.
• Bronze
Joined: 17.01.2011
that doesn't go against what we are saying

in relative terms having suited cards makes much more of a difference against AA than against QQ. this is the point that we're making
• Bronze
Joined: 02.02.2009
Originally posted by Tomaloc
that doesn't go against what we are saying

in relative terms having suited cards makes much more of a difference against AA than against QQ. this is the point that we're making
Yes I know that Suited cards do better than the non suited equivalent of the same hand vs XX but thats irrelevant to this question.
• Silver
Joined: 18.03.2008
The only way AK wins vs AA is with a flush, so being suited matters more than AK vs QQ, how are u not getting this
• Bronze
Joined: 02.02.2009
Originally posted by ihufa
The only way AK wins vs AA is with a flush, so being suited matters more than AK vs QQ, how are u not getting this
who isnt getting what?

maybe im wrong but last time I checked 3 or 4 kings plus 9TJQ also beats AA?
• Gold
Joined: 02.01.2009
The reason AKs makes less of a difference when up against QQ is that some of the time you make a flush with AKs you would have won by making a pair anyway, so those boards dont contribute any extra equity compared with AKo. Vs AA its much less likely when you make a flush you would have won anyway, so the suitedness of AK adds more equity.

We can show this with a simple calculation

the chance of hitting a flush is ~5% higher with suited cards which means suited AKs adds roughly 5% equity vs AA. Against QQ we need to take away all the times we hit a flush but also hit an A or K with the other two cards. Given a board that is xx there is 1-(41/47)*(40/46) ~ 25% chance that at least one of the two other cards is an A or K. So the equity added vs QQ is roughly 0.75*5% ~ 4%.

To do it properly we need a much bigger calculation since we need to take straights and stuff into account, but thats what the equilator is for ^^
• Bronze
Joined: 25.10.2008
It's actually because when you hold AKs, AA will never have any of your flush outs taken out while QQ will.
• Gold
Joined: 02.01.2009
Originally posted by NightFrostaSS
It's actually because when you hold AKs, AA will never have any of your flush outs taken out while QQ will.
True but AhKh has only 0.3% more equity vs QsQc than QhQc, so its not a huge effect.
• Bronze
Joined: 17.01.2012
How about winning vs AA on straight or set of Kings?
• Bronze
Joined: 25.10.2008
Originally posted by Jan217
Originally posted by NightFrostaSS
It's actually because when you hold AKs, AA will never have any of your flush outs taken out while QQ will.
True but AhKh has only 0.3% more equity vs QsQc than QhQc, so its not a huge effect.
The other part then must come from AKo being able to make two 1 card flushes vs QQ that are almost always good while AA can be blocking one of them by making a higher flush.

I'm rly too lazy to look it up on stove, but it's pretty obv it's all about the flushes.
• Silver
Joined: 18.03.2008
Originally posted by Hackett77
Originally posted by ihufa
The only way AK wins vs AA is with a flush, so being suited matters more than AK vs QQ, how are u not getting this
who isnt getting what?

maybe im wrong but last time I checked 3 or 4 kings plus 9TJQ also beats AA?
hmm