I'm new to the game and have been trying to learn poker hand values, have been looking at all kinds charts. The thing I've noticed in quite a few of them is that the A2 specifically doesn't get much love. Why does it do so much worse than other small aces like A3 or A4? Some charts literally prefer K6o over A2s which is just mindblowing to me. Thanks

P.S. The charts I am adding do not show for which positions they are so I believe I am not disrespecting their creators or harming their business.

https://imgur.com/a/ZWi23WK
https://imgur.com/a/rwwzxPg
https://imgur.com/a/JnMt5PJ
https://imgur.com/a/6pc3jn5
https://imgur.com/a/hlhRgLN

Not sure what you are really asking.

Do you believe that A2 wins the same number of deals as A3? (It is pretty clear that A3 wins more deals than A2.)

Which of those charts prefer A2s over K6o? It would be weird if one did. I'm not sure what the color coding means.

A2o gets dominated by all the other Ax which are frequently played so it's hard to make too much money on A-high boards. It can make a rare wheel straight but it's not even to the nuts and continuing postflop with just a non-nut gutter and over to the board is often only going to be marginal at best. K6o has a slightly better kicker which can make middle/top pair sometimes. Both hands suck and should only very rarely be played. When they are played, like BB facing a SB open, they are very, very marginal.

Oops you're right, I misread this chart: https://imgur.com/a/6pc3jn5
Green is for calling, purple is for raising, yellow is for borderline hands that CAN be raises, and in almost all charts they fall under raise or fold but in this case it clearly has to mean raise or call. I've gone through these charts a lot and yellow almost always means raise or fold, so I auto identified the colour yellow with the fold. Sorry

What prompted this question was really the Zenith Poker chart I've seen in one of their videos, this one: https://imgur.com/a/hlhRgLN
I then saw A2 avoided in charts maybe one too many times and thought there was a connection.
Your explanation makes sense, A2 is the only ace that will never dominate any other aces which probably cuts into its EV enough for it to be a near 100% fold in that Zenith chart.

Thank you for the explanation

Yeah I know it's a worse ace than A3, but I thought there would be predictable proportion to how A5-A2 were reducing in value, not a drop off like this: https://imgur.com/a/hlhRgLN

But probably the drop in value for A2 is because it's literally the only ace that will never dominate any other aces.

Thank you for the input

Here's the results of a simulation of 10,000,000 6-max deals where the table shows the tallies of the winning hands.

You can see, as everybody realizes, that there is a slight decline in winning percentages in moving from A5o, A4o, A3o, and A2o.

It's not really a huge drop off. Zenith gives A3o as .02BB EV and A2o as 0BB EV. It just happens that the hands are so close to even that a very small difference results in one being played and one being mostly folded. K6o does get played more often in that chart but it's also 0EV.

Awesome chart, thank you for sharing.
It's exactly the kind of linear proportion that I was expecting.
And perhaps you know of similar simulations or mass hand histories of tens of millions of hands that show the EV of each holding? Rather than equity. If you know what I mean

Oh okay, makes sense. I'm new to this, so it's easy for me to misinterpret information

Zenith gives the EV of these hands in the context of their solve. It's where I got the numbers in my last post. I think you have to sign up but BU/CO/BB charts are free. Note that the EV numbers are only true within the context of their solve. A different solver or a solve with different parameters might give slightly different results, and you'll get different results if you play them.https://preflop.zenith.poker/

They will say A2o is -.5BB EV to call from the SB but I prefer to consider the EV as the difference compared to folding.

At 100bb+ there is a nut weakness of A2 also, obviously the advantage of ace+wheel vs. A6 is being able to make a straight. But the only board that A2 makes a straight on is 543, and 76s is represented heavily in many positions preflop as well. Whereas with A3 you only make a straight on 542 but no one really plays 63s in almost any position.

Fwiw nuttedness is extremely underrated by most players, for example in my sim 100bb SB vs BTN 3bet pot, SB is cbetting extremely often on A high boards but only 2% on A23ss pretty much solely because they have 54s even though we have AA. They have more low sets too but changing the board to A36ss raises it up to a 40% cbet so I'm guessing the presence of 4 combos 54s alone makes a huge deal.

Do solvers consider A2 worse then say middling aces like A6-A8? Don't think they're really a big fan of any of them

There's no essential difference when flopping eg. bottom pair with the small aces or at least the difference is so small that it'll take a lifetime for the difference to converge. The difference, if any comes from the straights. Straights when holding a deuce are bottom straights that might be drawing nearly dead or at least the opponent has more outs against them, when you're ahead.

That said, I've always thought a six to be a sort of special card, since on boards like 2345 you beat an ace that is very unlikely to fold. If you hold a seven and the board is 3456, an ace (including pocket AA) probably doesn't play for stacks. Thus, my theory is that A6 is a better hand than A7 and K6 is a better hand than K7. BUT, in my current database of 470k hands there is no huge difference between those hands, so my theory is probably not meaningful or correct.

Then again, to highlight the variance and the meaninglessness of a 470k hand database, when filtering for A2-A9, The most winning hand for me is actually A2s and the most losing hand is A2o. There is a clear difference between suited and offsuit (suited being up +48,92bb/100, offsuit down -14,21bb/100, though this includes hands where I didn't vpip and lost money from the blinds, when I vpip the offsuit aces are +4,61bb/100), but the size of the kicker doesn't seem to relate to the winnings at all.

Flopping a deuce with A2 is of course worse than flopping a nine with A9, but it's a double edged sword. If eg. your ace is suited and you flop a pair + FD, there's not much real life difference between a deuce and a nine, because if the money goes in and the opponent has something like pocket kings, the EV difference is too small too matter. It matters of course if the opponent has something like pocket 88, but in real life the opponent probably folds his 88 rather than play for stacks, so whether you had a deuce or a nine is irrelevant. And if the action doesn't involve an all in, a deuce has the "advantage" of being easier to fold. If the flop is, say, 972 with no FD for you, you probably don't play a big or even a medium sized pot. The nine can, in real life situations, cost you more money in some situations eg. when the opponent has an overpair or a set.

Poker is a complex game, it isn't automatic that the EV curve between hands is linear in a game that involves a concept like reverse implied odds.

becouse its worse than A3

In real life multi street poker, the values of different hands aren't linear though. Well, the top hands are, ie. AA wins more than KK that wins more than QQ etc. But most players don't lose the most with a hand like 27o simply because they almost never play it and rather lose the most with hands that are "better" than 72o. JTo comes to mind as such a hand. It looks pretty decent, but it's actually very difficult to play because it's difficult to get a nutty hand but quite easy to get a hand like weak top pair.

A3 and A2 are basically the same hand though, as situations where it matters whether you have a pair of deuces or treys are rare AND if you see the showdown the pot is probably quite small with just a small pair for both you and the opponent. Rare small pots aren't something you should think too much of really. And small aces are such hands anyway that you either wanna make a nutty hand or make the opponent fold. You don't really play them to flop one pair and see the showdown as a winner.

Ok went back over some sims and solver does prefer A7 and A8 over A2 as it plays the former 2 in spots where it wouldn't play the latter but seems to treat A2 and A6 with equal disdain even if A6 may technically be better

Outside of solvers, does anyone have any guesses how long it would theoretically take for the difference between seemingly similar hands to converge into a real difference between them in actual won money?

I mean, my current database is about 500k hands and the variance is still so huge that the order of, for example, how much suited aces make money is almost random. AKs, AQs and AJs are about equal in winnings, but after that comes A2s and the rest are quite random. They're all up, except A7s a bit down. Naturally, if you have ace high flush the kicker is quite irrelevant and a high kicker might actually even be harmful, because the nut flush with AKs makes it impossible for anyone to have king high flush which might in some cases mean they don't raise. I did actually check my database for the made flushes (with 3 flush cards on the table) and A2s has made more money than AKs with flushes.

The offsuit aces are way more linear in winnings though.

And yeah I know, I'd rather have 5 million hands in my db instead of 500k. It's large enough to analyze hand groups, but not large enough to really analyze individual hands outside the preflop monsters, which converge a lot faster.