Frightening levels of intelligence/analysis ITT. Good read. Nice work.

p4f,

Running it twice increases your sample size. That is all.

Because you've halved the stakes of each coin flip. I'll use Garick's toy example of a $100 pot w/ 50% equity. Variance is the average squared distance from the mean. Your EV (the mean) is $50 whether you RIT or not. (I hope that's obvious?) So, variance would be the average of how far your result is from $50 squared.

If you don't RIT, you end up with $100 or $0, so your result is always $50 from the mean. $50^2 = 2500.

If you RIT, you get $0 25% of the time, $50 half the time, and $100 25% of the time. The variance would be:
0.25*($0-$50)^2 + 0.5*($50-$50)^2 + 0.25*($100-$50)^2
= 0.25*2500 + 0.5*0 + 0.25*2500
= 1250.

Thus, we've cut variance in half by RIT. When equity isn't 50%, the math won't be quite as easy, but variance will still always be lower. It's the extreme outcomes that drive variance up, and running it twice makes them less likely. (If we could run it more than twice, variance would drop even lower.)

My problem with general theory threads is that nobody defines what they are talking about. It took about 100+ posts before people started realizing they were talking about multiple different things.

While I'm sympathic to those trying to use statistical definitions for analysis, the problem they have is that in real life poker statisitics are not useable. One major assumption in statistics is that the pool from which the samples are pulled is homogeneous. As Mike Caro pointed out years ago, the skill level at your table is going to have a huge effect on your daily results. Longer term, the more you play the same players, the more they learn about you and adjust their play. Your pool changes over time. For example, your results are going to vary considerably if you are playing at a table full of bad whales compared to a table of the top 9 players in your room.

In terms of swinginess, the variable to consider isn't so much tight or loose, but rather how aggressive one is playing. The classic LLSNL player, the loose passive, isn't going to swing very much. They'll play a lot of hands, but mostly will fold on the flop because they missed. Their stack doesn't move much. When they win a hand, it is mostly calling down and having the best hand. A maniac is going to be pushing all hands to the limit. Most of the time, people will just fold from fear of losing their stack. That allows the maniac to build his stack. However, when he loses, he loses big.

Just some thoughts on the matter.

Ok, so it is literally what it is, run it more often would lead you to be closer to realize your EV.

But aren't these extreme outcomes unpredictable by nature, so running it twice or three times aren't going to be large enough sample to get rid of these uncertainties?

It goes back to the other question - so is the result of LAG with a lot more VPIP more reliable than a nit? Because it seems that it would be if running it more leads to lower variance.

Let me present a more practical matter:

If I have 70% equity - wouldn't it be better for me to run the scenario for higher stake than less stake? If that's the case, halving the stake by RIT doesn't seem to benefit someone who has higher equity.

p4f, I know you enjoy playing the argument game, but please stop it. You know very well that 70% of 100 or 70% of 50 plus 70% of 50 are exactly the same thing.

Please stop asking questions you know the answer to in order to make people clarify points. It is an annoying ILCD-ish rhetorical style at the best of times, and particularly so when the point is so obvious.

In the long run, we will all reach (approach within reasonable bounds) our true equity in all situations. Running it twice speeds that up.

That wasn’t the intent of my question.

If we are playing for $1, it wouldn’t make a difference to me whether I am 90% equity favorite or 10%.

I simply don’t understand lowering variance obviously benefits the equity favorite, then why would someone with equity dog want to RIT.

Perhaps you are giving me too much credit or not enough. I am not asking to clarify a simple math probability question.

Intuitively I cannot rationalize why anyone would RIT, other than to bink something if I am a huge underdog.

It doesn't benefit anybody, FFS. It *just* reduces variance, which means that if you want your Vs to be scared money for extra FE, you should be known to deny it, and if you want them to make optimistic calls you should be known to allow it.

As for you personally (rather than its effect on Vs' psyches) you shouldn't give a ****. As long as you are adequately rolled, it makes no difference whatsoever.

Edit: well, my post looks a little odd, given your ninja-edit, but I think it still answers the question. RIT is entirely about psychology, assuming that your BR is large enough not to have a serious risk-of-ruin.

This:

How about because some people dont take big losses very well and they know if they get all in for 150BBs with AA vs KK and lose they know they wont be able to play their A game the rest of the session?

Why not run twice?
The EV is the same overall but you will win both 64%
You'll chop 32%
You'll lose both only 4%

To mitigate the 30% chance that someone else will bink.


If I bet $1M on a 90/10 favorite, I would much rather RIT (or 50 times) than just once. Because if it's that 1 time that I miss, it would suck. Even though me equity hasn't changed.

But since most people dont reach the long run quickly in live poker, running it twice will help get us closer. Which means we are less subject to random variations.

Reducing variance is a good thing in itself, even for the "adequately" bankrolled. The lower the variance, the lower the risk of ruin.

Not sure why you cut out my point that the above applies "assuming that your BR is large enough not to have a serious risk-of-ruin."

Seriously, that applies to all variance. Assuming that we are sufficiently rolled, we shouldn't give a **** about it. The problem only comes in that most poker players aren't sufficiently rolled, and even those of us who are often have mental trouble with the swings, even when we have no logical concerns.

Every finite bankroll has a nonzero risk of ruin. Reducing the risk of ruin is a good thing.

See also: "Kelly Criterion"

I agree it can be self perpetuating. I don't agree that the quoted text is an example of that. There's a line between criticizing someone's argument and being disrespectful, which I acknowledge I have crossed in other posts, but not there.

-----

"Empirics matter to me, too. However, not a single person has posted any empirical evidence on the topic at all. I have asked several times for you to support your argument with evidence, yet you have not come up with any."

I do thank you for your quotes of mpethy. I will skip a semantics argument about what qualifies as "empirical" evidence, and explain why I don't accept this. I believe the claim is that winning Lags have greater confidence in their win-rate than Tags/nits over a given period of time. If this is the claim, mpethy's post is not evidence in support of this claim. Even if you can find him stating this, I would not accept it because an expert opinion is not enough for me to reach any conclusion. Acceptable evidence would be a report on his analysis of the data including details on how the data was gathered and the relevant statistics which his conclusions are based on. This would allow me to reach a conclusion which agrees or disagrees with mpethy's, or possibly point out a flaw in his method.

I feel you're trivializing the argument. I am not arguing about what variance is, or at least that is a very small part of what I am arguing. Jay S summed it up more succinctly than I could, and I agree with him completely. Lags may have a lower standard deviation than Tags, but it is can not be due to playing more hands pre-flop. My argument is not attacking the conclusion, but the reasoning behind it.

If the claim from above is not what you are making, and you are just claiming that "a Lag style is swingier than a Tag style," "Swinginess" is not well-defined enough to argue about. I ask you to formulate an arguable claim.

Sorry, I am not interested in "formulating an arguable claim" if "all other factors being equal, nits and short stackers have greater swings and LAGs have less extreme swings" is not considered one. If you don't find that arguable, sorry, but that is what is actionable in terms of how it impacts players, especially the new folks on short rolls who think they can play a very nitty short-stack game and not have a high risk of ruin.

Also note that the claim is not, as you said above, that LAGs are swingier (that is not what the empirics indicate), nor that LAGs have a greater confidence in their winrate over a shorter period of time (though that could be a corollary of their experiencing less violent swings).

Finally, as multiple posters have stated, the statement above about swinginess has been well known and supported by empirical evidence for about 10 years now. I posted indirect evidence about that because it's as much as I'm willing to do on this argument. You are the one seeking to overturn the dominant paradigm, so the burden of proof is on you.

I will state that saying that someone has not posted any evidence because they haven't posted evidence that you find sufficient is arrogant and condescending. I will also say that re-stating others arguments either with extreme lack of care or intentionally to create strawmen is also problematic.

Does no one have access to player database / stats anymore? That seems to be what browni is after. I'm not sure anyone can reliably replicate mpethy's analytics but it might be interesting to see what the others come up with.

I've kicked the idea around a couple of times about trying to collect results from LLSNL players. I'd love to look at statistics beyond just WR and SD, like breaking things by day of the week, session length, etc. Comparing different players the population.

It'd be a bit of a pain to deal with different formats, but workable I think. Or at least, it's something I could do at work that would look exactly like work

The biggest sticking point was figuring out a way to actually collect stuff in an easy and relatively anonymous way.

Many people in this thread HAVE claimed that LAGs have greater confidence in their win-rate, including cannabusto and Avaritia. I was asking about you.

I'm curious about this part, as it is very close to an arguable claim. Are you saying someone on a short-roll with the choice to buy-in full or buy-in short are better off buying in full, in terms of RoR? Are you saying they are better off attempting to play Lag if they have the choice to play Tag vs. Lag (Tag and Lag still need to be defined).

In this thread I have proven that a higher pre-flop vpip leads to greater swings, all else equal, and for my definition of "swings." If you have a problem with part of the proof, I will explain or fix it if necessary. If you want it all in one post, I can do that.

If I wanted to I can't attempt to argue against your claim because it isn't well-defined. What is Lag? What is Tag? What are "swings?"

Again, if I had the data that your own opinion is founded on then I could otherwise just use that to form a counter-argument, or maybe just agree with you. Of course you have no obligation to participate beyond your own whims, but I would greatly appreciate seeing mpethy's data.

I said you have not posted "empirical" evidence. You said there was data. I asked for data and you gave me something else. If I misunderstand the meaning of empirical evidence I apologize.

There is no straw-man, I re-posted others' arguments very carefully and still made a mistake. I know that you are claiming Tags are swingier, I simply mis-spoke. I legitimately didn't even realize I posted the opposite of what I meant to until after re-reading it three times.

This cannot be proven mathematically. I’m not going to sort through your posts to identify something that I know to be incorrect but it is not something that can be proven, as you only have one piece of the data. VPIP actually has nothing to do with stdev. The different outcomes of each VPIP are all that matter. And they are more condensed with lag play. This is what you fail to understand and by judgement of your tone will never understand.

You continue to have the false assumption that win rate per hand is some kind of static equity. This is not true, mainly because of non showdown winnings. A lags wr per hand is lower and has less spread from the mean overall.

Browni as someone that portends to be a consummate pro your attitude/EQ is pretty -EV. I can’t imagine people willingly dumping you money for the next 5, 10 or 20 years.

Actually, you said "I have asked several times for you to support your argument with evidence, yet you have not come up with any." I can see that maybe you meant specifically empirical evidence, as that's what you'd been talking about earlier in the para, and if that's what you meant, I take back some of my annoyance.

I have not posted empirical evidence, I have simply posted evidence of empirical evidence existing. I'm sorry but 1) I don't have access to mpethy's data, 2) mpethy doesn't post anymore, and 3) I doubt he'd share it anyway, since it was confidential data from his clients.

I suspect that you could find some of these old discussions if you search, but since they were before the great archiving, I don't know how easy that would be. I *think* they were in the micro full-ring forum, but I'm not sure.

As for a short-rolled newb, obviously all other things are not equal. I suspect that given the other limitations they would likely have, I'd prob recommend a 2/3-stack ABC style as least likely to lead to bustoville. I would definitely recommend against a classic short-stack style (20bbs, very tight, very aggro when VPIPing, AI pre of OTF in most hands played), as I have seen first hand the graphs that those created, even for profitable players, and the ROR would be very high.

You're not the first to say something like this, and I honestly wish I knew what you were talking about. Alas, my EQ is too low to have that self-awareness.

Somehow I get along just fine. Believe it or not the majority of people like me as far as I can tell, so I must be doing something right. I even get invited to home games and have somehow managed to get a wife.

You snipped important parts of my post when you quoted me. I have proven it under certain conditions. If you don't want to look through my posts, Jay S summed up my thoughts exactly.

This means that holding the rest of our strategy and villain's strategy fixed, choosing not to fold a breakeven hand pre-flop necessarily increases the variance of our strategy, which in turn leads to a higher probability of loss over any given period of time if we hold win-rate constant.

The relevant differences must be how Lags vs. Tags play post-flop, not pre-flop.

I meant it when I said I don't have much self-awareness, so I'm not sure what is wrong with my tone, other than maybe being a bit egotistical. You could take your ego down a notch, too. Neither one of us knows everything on this subject, and I'm sure we could both learn something from one another.

I'm not sure what you mean by "static equity" in this context.

Yes, I did specifically mean empirical evidence. As much as I try to be precise in my wording, I apparently make many more mistakes than I'm aware of.

Thanks for pointing me in a direction. I'll look at some point.

If that's the case, I think we're mostly on the same page. Playing with a 20BB stack should have a lower standard deviation than a full-stack, but the edge will be much smaller as well, and I imagine rake is a huge issue at that stack size. I wouldn't challenge the claim that a 20BB stacker will have a higher RoR than a full-stacker.