Wednesday, 6 October 2010

On the redline

Most serious STT players obsess over their redline. This is a measure of how "lucky" they've been with allins. If you win an allin, you gain over your expectation; if you lose it, you lose what you expected. In case that's not clear, imagine you shove 63, and are called by KT. You now expect to win 33% of the time. If you do win, you won 66% more of the pot than you expected, and when you lose, you lose 33% more than you expected. The gap between what you expected and what you got is important to STT players, because they can tell themselves they were unlucky if expectation is a lot higher than results.

I will note straight away that for most typical nitty 2p2 types, particularly those who do not shove enough, expectation will very much be higher than results. That's partly because you so often get it in with the best hand, and obviously, when you lose in that case, what you lose is further below expectation than winning would be above. It's also, as I discuss below, perversely because you tend to do the opposite later in the game and get it in worse when the equity involved is higher.

But there are other components to luck. I was thinking about this the other day. I lost 9ish buyins and I had about the unluckiest day I could remember. But when I checked my expected results, I should have lost even more! I had actually run good in allin EV. How was that even possible?

Well, here are a few things that most players don't even think about.

Take that 63 hand. If you make KT fold, and you often do, you gain his equity in the hand for free. You don't consider yourself lucky, but think. If I had KK, shoved and he showed AA, I'm not going to be unlucky when he wins (he's a 4/1 favourite), but I sure am unlucky that he had the only hand ahead of me preflop! I don't have the maths to hand how often I can expect that, but it's not often. If it happens to more than a time or two in a set, you are running bad. But your allin EV doesn't consider that. The same goes for the times you threebet the LAGtard who is raising half his hands and this time he has a monster. He may have raised 20 times in a tournament, and the one time you went for it, he had you beat. He may well have not had a better hand every other time.

But I am focusing on how lucky you are to get away with shoves. HEM will credit you with a gain because you took the blinds and your equity increased, but it doesn't credit you for folding out better. But villain will often make a Sklansky mistake (should have called if he could see what you had).

We all know it's unlucky to shove AA, get called by JJ and then watch in horror when a J flops, or to get it in on the flop and watch JJ turn his miracle card. But when you raise AA, flop rags, get it in and are shown a set, you are not considered unlucky by HEM. Your expectation then is very low and you usually get nothing. But he flopped a set! 7/8 times that won't happen but this time it did. Effectively you were as unlucky as with the JJ hand where you got it in pre. But if he flops it for a raise, you weren't very unlucky at all according to your redline.

The same obviously goes for the times you raise AK, get called by A8, flop comes A83r and you get stacked. Again, you are not accounted unlucky preflop where you would be if you shoved.

Nor does it account for longer-term patterns that we would also consider "lucky". You're supposed to flop a set one in eight times, roughly. But you can call 20 raises with small pairs and hit nothing. Or you can hit your set and no one else has a piece, so you have had your "luck" in hitting, but you gain nothing from it. Of course, you can also hit and then get sucked out on. This should all even out in the long run, but the long run is not a day, a week or even a month. If I have a day where I play a hundred games and hit 30 sets in the early levels, getting paid off with every one, do I think I'm lucky? Well, it doesn't show in my redline, does it? (I don't know how often I get dealt pairs or hit flops, but that strikes me as hella lucky!)

Also, your redline is skewed by high-equity spots. If I shove the first hand of an 11 with JJ, and get called by AK and lose, I lose 5ish bucks; but if I shove that 63 on the bubble with 4K chips and get called by KT and lose, I lose more dollars (I'm not sure how many, but say I have $23 equity, I would lose 33% of that, which is about 7.50 or so). I am "unluckier" to get caught when shoving with a worse hand than I was to get caught with the better hand. Sure, I gain a ton when I win, but losing is worse than winning (you lose more equity when you lose than you win when you win because of the structure of STTs: note that I'm not saying that you lose more when you lose with 63 than you win! I am saying that the downside when you shove is always bigger than the upside unless you're heads up, so that proportionately winning twice when a 66% favourite does not make up for losing once). So we tend to lose out both ways! We get it in better when equity is low, and if we run bad, our losses take many similar spots to recoup; and we tend to have the worst hand at high equity, so we lose more in dollars even if we run as expected.


Alex said...

Nice article, I take my redline with a large dash of salt due to the reasons you've stated.


blah said...

I might not see eye to eye with you in strat but this might be one of the best worded pieces I've seen in a while. I've for a long time tried to explain to SNG players with little success that LAGs will run above EV and nits will run below EV, I might just link them to this blog post to save my breath.

Thrash370 said...

PS that was Thrash370 posting that comment, for some reason google wants to show up as blah, testing to see if I fixed that.

kvaughan said...

I really don't understand the first part of this post. Getting it in with the best hand more often does not make your results run higher than expectations.

In any case, you are obviously correct that the redline is not a way to remove luck from poker. I don't think anyone worth arguing with disagrees with you.

What it does do, is give you better information quicker than results alone. According to work done by Juk, a set of results that are ev-adjusted are equivalent to a sample size of 3.7 times a set of results that aren't ev-adjusted. So, if you look at your redline after 1000 games you have the same level of information as if you had played 3700 games.

That is an extremely valuable piece of information and I have been able to make some very sound poker decisions based on the redline that I wouldn't have been able to make otherwise.

Anonymous said...

K, the idea of the first part is, trivially, that you are going to lose more equity than you win if you get it in as a big favourite.

It needs explaining why nits "run bad" all the time but LAGs (and in general regs in regular speed games) do not. As you know, I'm not a very maths-oriented type, so I look for plain explanations that make sense.

Thanks for your comment. I appreciate it.

kvaughan said...

Let's say I get it in with AA against KK. If I win, the difference between my equity and my expected equity is small, if I lose, the difference is huge. I get and agree with that.

The flawed jump is to then conclude, that if you get it in ahead all the time, you will run below expectation. It doesn't work like that.

Also, I'm not sure why you think "nits run bad all the time". If it's from talking to people, keep in mind that there are huge self-reporting biases which might skew the results. I wouldn't accept that as fact.

One area where the redline is flawed, however, is that it uses ICM. As I think we both know, ICM is merely a proxy for equity and there are plenty of situations where good players exploit flaws in the ICM model to make better plays than a pure ICM perspective would dictate. For example, shoving looser UTG. If it's true that LAG players run above expectation, it might be because they run plays that have low expectations according to ICM but good actual expectations (because ICM gets it wrong).

But, assuming no flaws in ICM, then definitionally, everyone has the same chance to run above or below expectation.