I have to say that that is the first of these selected quotes that would really stop me in my tracks and spoil the flow of my reading. Maybe in the context of a paragraph in the book it's just sloppy writing. But out of context and highlighted here, it's just nonsense.

I agree the statements aren't correct, but I am not surprised to see the term used in this context in poker.

I'm shocked that someone who calls himself a mathematician would write this. These statements are clearly incorrect.

Yes, we all have an idea what he means, but anyone who has done mathematics at an advanced level is used to writing rigorous proofs, which includes using terminology very precisely.

This is my experience, also. I have always attributed it to late position openers being suspected of stealing, and early openers being given too much respect. I don't know if this phenomenon exists at nose-bleed stakes, but it is (and always has) been common in 1-2 through 10-20.

This is a meaningless statement if winrate is not factored in.

For a 1BB winner? Yes, millions of hands.
For a 20BB winner? A few thousand.

Also lot of people in poker tend to misuse statistical terms, but it's something that is generally accepted on the whole by the population. Everyone understands that "variance" used in the context of poker means something different than "variance" use in the context of statistics.

Also as humans we have a built in intuitive measure of winrate that converges much faster than just relying on pure statistical analysis. If you're at a 6max table where everyone is playing 24/20/9 you don't need to wait around for millions of hands to know that your winrate will be very small, if there at all.

Here’s another one from “Playing First In” in the tournament section:

It could be the case that your hand can call an all-in against the range from one position but not from another, or that you can call a 15bb all-in but not a 20bb all-in.

Mason

I don't think that's quite right? Or maybe I just don't understand what you're saying.

If you're talking about the number of hands that you need to be sure that you are a winner, then, yes, a huge winner can be fairly sure that he is playing a winning game with fewer hands. Just because a 5BB error on an estimate of 20 still leaves someone in positive territory, while even a small error on an estimate of 1 could leave someone negative.

But I don't think that your data for a winrate of 20 will converge that much faster? I don't really know what game conditions in a no limit game would make someone that huge of a winner, but certainly in a limit game the opposite tends to be true. The really big winrates generally are the result of huge multiway pots (work people putting a lot of bets in taking much the worst of it) which result in much higher variance on each individual hand, which means that your estimate takes longer to converge to reality.

Is that not right? Game theory suggests that you should play tighter against larger bets / raises (I'm assuming that you have the opponent covered, so these are effective stack sizes). And if an opponent's position suggests a tighter range, you also need to call tighter.

What am I missing here?

I’m sorry, but i’m focusing on the 15bb to 20bb part of the sentence.

Mason

Are you suggesting that if you're calling 1715bb, you're calling 2220bb?

If you have barely the correct odds to call an all-in with 15bb, then you probably don't have quite the correct odds to call with 20bb effective.

In reality, what is more about psychology or math on poker?

My friend and I argued for a long time on this issue and did not come to a consensus, I still think that this is psychology. If it is enough to develop intuition, and everyone can be careful, it is possible to predict cards and moves with more than 90% probability.

This is what I'm thinking. Surely there are borderline hands which are a fold for 20 and a call for 15? Is this controversial?

I'm sure that there's a point here that I'm not getting...

It seems to me that it would almost never occur that it would be correct to call for 15bb but fold for 20bb. Not only are the odds you're getting only very slightly worse when you call 20bb, but most players actually will have a slightly weaker range when they move in for 20bb because they're not apt to want to drive players out with their best hands.

Best wishes,
Mason

It's perfectly possible that a hand could call a shove for 15bb and not for 20bb. I tought this was common knowledge.

All math aside I have always found statements like this to be difficult to apply to my own game improvement and study because of live play. When playing live its harder to keep track of hands and how many you have played/folded. So leaving all mathematical aside, how does one even begin to to truly know if their win rate is correct based on this statement? I have been playing poker for years and when I started I did not make any attempt to keep track of my hands at all. It wasn't until I saw that I had a natural knack for playing that I became interested in learning more about the game and improving (maybe my natural sense of competitiveness has something to do with it as well). Even then I did not keep track of all my play. It took me years to start to even try to keep track of my losses and wins. Now that I play poker more seriously I can give you more statistics about my play in terms of profitability but in terms of hands... Lets just say I do have some of my own data but I know there is a lot of data missing from over the years of random online play.

WTF?!?!? Seriously? Has the author just had a very good run that has lasted the entirety of his poker career? I mean just look at youtube... Most of the vloggers are talking about how they are stuck (admittedly they do have a lot of small cashes that add up and the occasional big cashes over the long run for profit). Playing a mixture of exploitative/GTO in live I have had some huge swings. Overall I still have what could be considered a winning win rate but that brings me back around to the original quote... How do we know that this data is accurate? If I start to think about the years I spent playing without even keeping track of how I was doing in games, then maybe my win rate would be higher? Even then that data is taken and broken down by dollar amounts and time spent playing. It does not consider the up and down swings of playing hand to hand and I can see extreme check mark like ups and downs in my wins/losses back when I started to keep track of my play.

I think we have to take these comments with a grain of salt when it comes to win rates and variances. Most of the time it seems to be more based on anecdotal information/experiences. There is just way to much "what ifs" and "possibilities" to consider.

P.S. - Is there an easy way that I am not aware of to get the comment ID# so I can use markdown html to quote? Or just an easier way to make multiple quotes in one post?

It depends on where you play and what limits you are playing. Personally I don't find the lower limits ($1/$2, $1/$3, $2/$5) to much different from other cities that I have played in, especially in some of the more "local" casinos. On the strip is a different story but with the added "drunkenness" and "tourist" factors it tends to balance out the games.

You would use statistics to analyse the data you have and then determine how confident you are in a certain range of values for your win rate. You can't really say anything about your winrate without math and statistics.

Also there is no way to guarantee your winrate is "correct" or to know what your "true" winrate is. It's all based on sampling data from your poker hands and there will always be a range and an impact from chance. The more hands you have though the more likely it is that the random chance flucuations get "smoothed out" and you can be more and more certain your winrate lies within a particular range of values.

The way the author used variance in the quote is the issue. In statistics variance is a precisely defined term that isn't related to how most poker players use it, which is usually short hand for "random chance" or "short term bad luck".

In statistics variance is metric of your data that helps to describe how spread out your data is from the mean. In that sense you can have any size data set with large or small variance. Just because a sample is larger doesn't necessarily mean it has lower variance.

The author was likely using variance as poker players do, to mean that the larger the sample size the less your data is inluenced by short term random chance and the closer you are to the range of values that your winrate is contained within.

There are ways in statistics to analyze the data you have to make statments and inferences about your dataset and how confident you are those statements and inferences about your data.

If a variable has statistical variance V in some population distribution, then in a sample of n trials, V/n is the variance of the sample mean. That means that the more volume played the lower the variance of the sample mean.

But, as you and Arty implied, context is important.

For example, if one tracks his profit over a number of tournaments, noting the smallest profit (largest loss) and largest profit over all tournaments played, then the range (max – min) over all tournaments will either stay constant or increase over time. So, if the range or something equivalent is considered to be the variance measure, "variance" can increase with more samples.

Hi just_grindin:

I'm just going to address this one idea because it's often not correct. When in a poker game you can often quickly see how your opponents are playing. If they're playing well, expect your win rate to be small at best. If a couple of them are playing poorly, your win rate can be quite good.

On the other hand, if you're multi-tabling a bunch of games are using a GTO type strategy, then your comment becomes correct.

Best wishes,
Mason

I think that this just confuses the issue.

Yes, context is important, but most people reading the statement that Mason quoted would infer that, as they play more, the variance of their overall results drops. That is the exact opposite of what is true. The variance grows linearly with hands played (assuming that hands are uncorrelated, which is probably close enough to be true for these purposes -- even if individual hands within a session are correlated, hands in different sessions are probably close enough to uncorrelated to make this statement true).

That is, if you play 10 sessions (of about the same length) the variance of your overall win/loss is 10x your variance of playing 1 session.

Now, this is somewhat mitigated by the fact that many people reading that statement won't know what variance is, and, those who do know what it is won't believe the statement.

I think that the concern is that this raises questions about whether the author himself knows what variance is. If I'm buying a book, I'm paying for an expert opinion. If he's confused about the definition of variance, what else is he confused about?

Basically, if I buy a book that makes 100 statements, and the 99 statements are things that I don't know much about (so I expect to learn something) and there is one statement about something that I'm absolutely sure of, and I know that that one statement is completely wrong... how much faith should I put in the other 99 statements?

Hi Everyone:

Let's do another one from this book. There's a short chapter on "The Mental Game" which has a list of "several mindset traits that winning players have in common." One of these traits is:

Takes care of their health by eating healthy foods, working out, meditating, and drinking a lot of water.

There's also similar list for losing players -- "while losing players tend to be on the opposite side of the spectrum" and one of the losing player's traits is:

Doesn't take care of their health, eats junk food and never works out.

By the way, at first this may look to some of you that this belongs on the psychology forum, but it actually belongs here in theory, and understanding why is quite important.

All comments are welcome and I'll come back later to enter the discussion.

Best wishes,
Mason

I agree that taking care of your health is correlated with positive results at the poker table.

Physical health is correlated with mental health.
And just generally need to be feeling your best at the table in order to play your best poker.

Poker involves sitting at a table for long periods of time, and being too sedentary can cause tons of health problems. The human body needs a certain amount of physical activity in order to function optimally.
All it takes is a few hours a week of some kind of exercise.

A healthy diet is important as well. Keeping meat and dairy to a minimum is best.

To me, there is the theory and there is the practice.

If one is helped by sleep, food, meditation, physical energy and stamina, drinking a lot of water, emotional balance, therapy, I don't see too much purpose in denying it.

The latest I read was about drinking a lot of water, that it is now possibly considered wrong for the balance of the body.

Physical stamina, one can get the mental jobs done without it but it is possible one plays worse when the physical/body energy and stamina are less (the drunken drivers overestimate their ability). I didn't like it as much when I wasn't in as good a shape physically. At least it helps physically.

I have played worse than I play now but most of the improvement in practice comes from the study of the game but I also have more energy and stamina that helps my mind, balance, emotions. My performance has been better than I hoped for. It can be worse and deteriorate during the winter especially if overworking, so enough rest is also important.

If the physical helps, it is important. There are a lot of top players in mental gaming who think it is important and they train the body well before the long matches.

Eating meat, Kasparov was or became a world chess champion by eating a large meat meal before the game(s) as it lasts longer.

Coffee plus D-vitamin is an energy drink and I take that combo when the energy level drops at some time of the day. The head is more awake then. Some programmers use stimulating drugs to be able to work for long hours.

Haha that sounds like a statistics problem :-)

Taking the words in my post literally I agree your counter example to my post is correct, you can say some things with some level of certainty about your winrate with small samples of information that is likely correlated with your winrate (i.e. quality of players and the amount of money each player has on the table).

But in the context of the argumemt I was making it should be clear that what I meant was that you can't make meaningful inferences about your winrate as a quantity without math, statistics, and data which I assume is what the poster I quoted was talking about when the poster kept saying things like "...how do we know for sure..." when talking about winrates.

I agree my wording was poor when I used "...you can't say anything meaningful...".

Thanks!