I’m thinking of one graph in particular, that a pro posted when he retired from online. I believe the graph only represents high stakes play. He runs above EV from his 400 thousand hand mark, until the 1.3 million mark when he retired. I was under the impression that AI EV was not based on skill?

BTW I think this entire sample is HUPLO but I could be wrong there might be a little 6MAX too. Does AI EV differ in HU?

As far as i know AI EV does not consider card removal. A good player can consider card removal. I.e. AK vs JJ has different Equity in reality when players have already folded Aces or Kings.

If you play 1 hand and win 100% of the pot, when you had 80% equity, then you ran above EV for one hand, while your opponent ran below EV. You were "lucky" that the best hand held, and villain was "unlucky" not to suck out.
A "career" is made up of thousands of such hands. If you generally do better in races than expected, you'll be above EV for life. If you are less lucky than average, you'll be below EV.
It doesn't matter what sample size you look at. Roughly half of all players are luckier than average in all in races, and half are unluckier than average. For any particular player, it doesn't "even out" in the long run. You could be 10 buy-ins above EV after 10,000 hands, and then run exactly according to EV for 10 million hands. You'd still be +10 BI above.

As an aside, if we could get access to the lifetime graphs of famous tourney players, I'm sure that the majority of them have run exceptionally well in coinflips and have essentially run above EV for their entire lives. Running well in flips can sustain entire careers of so-so regs.

Expectation for all future hands is to be at EV. So, once you are above EV, in the future you should remain above it.

That is true but the relative difference will tend to zero as the sample size increases. If you examine the OP graph, at about 520,000 hands the pro experienced some big lucky wins for +600,000 over expectation. At that time his winnings were 2.2m so the relative “luck” factor was about 0.6/2.2 = 27.3%, wow!

Now look at the end of the graph, at 2,280,00 hands, He is still at about 600,000 above expectation, but with total winnings at about 6.5m, his relative luck is 9.2%, 1/3 of what it was earlier.

This is just another way of stating what the above two posters commented on.

If the database were filtered, to remove all-ins that occur via a 2-bet, 3-bets etc., then the AIEV line would be closer to the green line.

So, it would only be hands with a 1-bet shove before the river, that was called.

Pros are better at playing optimally on streets with 2-b, 3-b, jam raises.

-Rob

EDIT: The database does not take this into account.

It's 50/50. Either you run above EV or you don't.

I don't think this is necessarily true. Someone could run above EV with pre-flop all ins, but below EV in post-flop races. Or vice versa.
Or be like me and run below EV in every ****ing situation. :/

Its scary to think that the graph implies that there could also be some player out there who, for a lifetime of 1 million hands, is running way below below EV expectation. ugh

I don’t understand how this is. Can someone explain this to me like I’m in 5th grade? How do past results have any bearing on future results, or am I misunderstanding

His redline also dips near the end, idk how u can maintain the same slope in green line and decrease in red

It's exactly because past results have no bearing that this is true. At any given point, your future AIEV expectation is 0. So if over the past month, you are up, say, 100 BI in AIEV, if your future expectation is zero, then your sum total of expectation is last month + future = 100 + 0 = 100.

Your AIEV per unit of time or hands will trend to zero, because 100/1 month = 100/month but 100/100 months=1/month and 100/1000 months=.1/mo and 100/10000 months = .01/mo and so forth.

In real life your future results won't be exactly even, but your future *expetation* is

Imagine a graph of a players first 1,000,000 hands where his AI winnings were $600,000 over expectation. Pretty lucky guy! Then imagine a graph for his next 1,000,000 hands where his AI winnings are $5,000 under expectation. Not lucky at all, He's practically normal!. Now, what happens when you combine those two graphs into one giant 2,000,000 hand graph? Is he lucky or normal?

Thnx for the explanations, that makes sense. Even though it’s obvious it kind of surprises me, because I always assumed that over a large enough sample AI EV and green line would converge

The second poster mentioned that AI EVdoesn’t account for card removal, so a talented players EV line will express the edge he gets from factoring removal. Is this one aspect of EV that is skill based?

In reality that might not be the case because a player may be forced to quit due to capital/bankroll issues long before that player would reach that mark.

Basically it's easier to keep playing when you're running really well than it is when you're running really bad.

Probably true. After just 100,000 hands of running well below Expected Value I wouldn't want to even see a card deck again.


(I guess its possible that the excess winnings on non-all-in hands could balance out the all-in losses and keep someone going in poker.)

As others have said, while it may or may not converge in an absolute sense - +$600,000 is a lot of money! - it will probably converge in a relative sense - +$600,000 over 10 billion hands is a rounding error.

At the point where the redline started levelling off, the blue line started going more steeply upwards. It could be due to a change in playing style, or a change in game format (e.g. a switch to more ring games and less heads up).
The winnings can only come from two things though: winning without showdowns (red) or winning at showdown (blue). In this context, Blue + Red = Green.

These are good replies I wish I had learned this stuff earlier, I have never really payed attention to the EV line

Can we talk about card removal. The second poster mentioned that AI EVdoesn’t account for card removal, so a talented players EV line will express the edge he gets from factoring removal. Is this one aspect of EV that is skill based?

Running above/below EV is not skill based. It is more an inaccuracy of the AIEV line.

It’s literally 50/50. You have no control over how well you run.

I’m not sure how many high level players account for the type of card removal referenced anyway. It almost never enters my thought process personally. In case it’s not clear, he’s not talking about blockers, which AIEV does account for, but about the interaction of ranges where one players range blocks parts of another, allowing us to weight certain combos slightly.

I suppose it could happen but it just seems so much more likely the All in EV would be so mu higher since your investment and your reward are typically so muc larger than non-allin confrontations.

The deck itself accounts for card removal. It does not contain two of the same cards.

I think there can be a small allin ev edge (compared to the calculations of HEM and PT) by the good player having reads.
I'll give a example.
Say a really good player with reads on the opponents
Hero BB: AhKh
utg limps
utg+1 over limps,
sb raises
Hero in BB: 3 bets
gets called only by sb.

On the turn the board is: Kc 4h 8h 7d

sb goes allin and Hero calls.

Now as far as the trackers are concerned the hand is AhKh vs Ks8d on board:Kc 4h 8h 7d so Hero has 27.273% equity according to the tracker and this is used to appoint the all-in ev.

But the good player knows that utg ang utg+1 only play this way with low/mid pairs.
This extra knowledge means that Hero's 'true' equity is with 4 dead cards of nature 6c6d, 5h5s, and this gives an equity of 27.5%. This is slightly better than the equity given/used by the trackers and so in practice this good player appears to gain a little on all-in ev. It is not much but it is possible with very good reads to appear lucky over a very large sample.

I am not 100% sure of the above but I think it is even less likely good reads could give an all-in edge if the game is always HU, so maybe this player was just lucky along this 1.2 million hand path.

Would a similar all-in edge be possible for a great HU player? Perhaps on multi-street hands reads can have some effect, I don't think so but I don't really know. On the example above the edge really comes from 'knowing' some dead cards and the good player calling wider using this knowledge.

As an example, AK is more likely to have the full completent of 6 overcard outs vs QQ in a BvB stack off situation if the prior action was folded to the SB. AK is less likely to have 6-outs if the action was UTG opens QQ, MP 3-bets (with a range containing many Ax hands), hero in the BB cold 4-bets AK, UTG 5-bet jams QQ, MP folds.
HEM would think AK has 43% equity vs QQ, but if MP's range contains a lot of Axs 3b/folds, then there will be fewer aces left in the deck, and AK will lose more often than 'expected'.
I'm not sure how significant in terms of the EV line these card removal effects would be. Probably not much at all in the grand scheme of things, and it would be pretty much impossible to utilize "skill" in utilizing such knowledge. What you gain from removal effects in one spot, you'd lose when you're in the opposite situation.