Doesn't AK and other unpaired hands lose value when all-in in fullring vs a pocket pair? Often somebody has atleast 1 of your outs right?

I think so, in heads up, unpaired hands has slightly more equity allin vs a flip then FR as the deck is stacked with more outs

All cards you don't know (and you aren't able to read) are totally random.
Doesn't matter if some players hold them... if they're in the deck... if they're on the floor... neither do if they're kid's drawing.

The unique case you can "burn outs" (and with not much certainty) is when many players had shown interest on pot. Or when many players don't.

For example:

UTG raises to 3bb,
MP calls,
MP2 calls,
HJ re-raises to 8bb,
CO calls 8bb,
BU calls 8bb,
SB shoves 25bb,

And you are BB, with AQ...

In this situation "probably" there are any ace in other players hands, because "Ace" is the most-played card. And here there are six players who had shown interest on play this hand.

But, this a very uncommon situation (or, call, call, 3b, call, call, shove...), and even here, you wouldn't be sure about their cards.

Additionally, playing full-ring, when and everybody folds to bu, or to sb, the probability of "burned aces" decreases, due to the same reasoning as before: if somebody had received an ace, he probably would have shown interest, limping or raising.

That's less accurate when playing shorthanded; less players: less information available.

So, at the beginning of the hand, when nobody has acted yet, there's absolutely no difference between shorthanded and fullring (even among two, three or any number of players) about our issue.

AK vs. pocket pair is on average 45%/55%. Over a large number of trials for example, there will be situations when you have instead of 6 outs just 2 (the other 4 outs being dealt to the other players ). There will ALSO be situations when none of your outs are dealt to the other players, and you chances of hitting an ace or a king increase ( when all of your 6 outs are in the remaining 34 cards, your chances are higher than 55% ). In the end AK vs. pocket pair is on average 45%/55%.

The way I look at it is the more people fold pre-flop with no action in front of them, the less likely they hold an A. Similarly but less significant with a K.

But if there are several limpers and then I raise with AK and the BB shoves with what I think is a PP then I have to take into consideration that I may not have all 6 outs.

I find this is less important to me than position. When I am out of position I am more likely to want to be all in because it will negate my positional disadvantage.

Also, it matters whether I am the one going all in or not. With fold equity AK may be better than 50% against say 22-99 because people will fold their small pairs some % of the time fearing being dominated.

And just to address the specific question: If i am all-in with AK and the other guy turns over TT and somebody at the table says "I folded an A" it doesn't mean we have worse than 45% odds at that point. Unless we know that some other people with an A or K didn't speak up, the remaining 32 cards in the stub would still have 5 of our outs. So 5/32 is > 6/50 (our outs knowing only our own two cards). Even 4/32 is > 6/50.

I think this may be an error Rick but I'm not 100% sure.

limp ranges can include weaker Ax for sure, even up to AJ in EP, but they can also include a wide proportion of suited connectors smaller pp, etc. however they also include quite a bit of Kxs and KT+.

The fact you haven't seen a raise would imo indicate a slight bias in your favour in terms of remaining aces, but I could get behind the idea that more Ks are removed. AQ may even be a slightly better proposition given that Qxs limps are less likely than Kxs (particularly true if old-timers have limped and still remember Super System).

I don't think you're contemplating folding AK here very often, but it's a real enough decision in late stages satellite and other icm-heavy spots. my tendency would be to treat the deck as random in every situation, but if anyone's done some cold hard number crunching on the distribution of particular cards among limp hands i'd be v interested to see it.

The reason I think limped hands are disproportionately holding an A is because there are a ton of combinations of offsuit hands people won't limp like 72/93/T4/J5/Q6/K2/etc. There are no hands with an unsuited A that people won't limp.

Also, the times I have taken it into consideration are usually when people have limped or cold called raises and after somebody raises/shoves they think long and hard about folding. I am thinking they have PP's or a somewhat large Ax like AQ/AJs.

One hand I remember playing at FW: A UTG raise, I call with AK in MP, 2 callers behind then a short stack SB shove. Original raiser re-shoves. I believed some of my A's were no longer there (I thought UTG had QQ because of my AK) so I folded as did the other two cold callers. SB had JJ, UTG had AK. Both cold callers said they folded AK!