Basic explanation of standard deviation

[BruceZ]

I don't normally cross-reference posts, but this may be of interest to many of you. I put a post on the general theory forum titled "Entry level explanation" in a thread which asks "What exactly is standard deviation?". My intention was to make it understandable to as many people as possible.

[Jimbo]

My intention was to make it understandable to as many people as possible.

That you did Bruce, probably the best and most lucid post I have ever read on this subject. Well done......

[BruceZ]

Thanks Jimbo, glad to hear someone appreciates it. Now see the post below in my ongoing war with Cyrus titled "WRONG! WRONG! WRONG! - IMPORTANT", for an equally lucid description of EV.

My gf never understands a word I write, but now even she says she understands what EV is. At least you can please SOME of the people. /forums/images/icons/wink.gif

[Cyrus]

Thanks, Bruce, for the time taken to explain EV to the board. I'm glad to hear your girlfriend also got to understand the concept. Also the concept of SD ("chance") is something we all should not tire of hearing about.

{Of course, me being eternally "pedantic", as you called me, I disagree with calling my arithmetic mean result in k number of samples ("sessions") my "EV". You see, when I want to compare my Average Win (or Loss, for that matter) against my theoretical Expected Value for the hours played, what will I do? Compare "EV" with "EV", I don't really appreciate.}

And btw, I'm not at "war" with you. I'm sorry you're upset (you warned us that you post in caps when upset and I see you have, twice in a row now) but I can't help you there. Not at a distance.

Take care.

[BruceZ]

You see, when I want to compare my Average Win (or Loss, for that matter) against my theoretical Expected Value for the hours played, what will I do? Compare "EV" with "EV"

What do you do when you compare your blackjack EV to your poker EV? Or your short term standard deviation to your expected theoretical standard deviation? Why don't you compare your short term EV to your long term EV the same way? Standard deviation is standard deviation whether it is short or long term; variance is variance whether it is short or long term; so why should EV be EV for short term but not long term? In fact, variance, from which we derive standard deviation, IS an EV. It's the EV of your squared excursion from the mean.

I made a post in the other forum that said if you don't want to call a short term EV an EV that is perfectly fine, and probably far less confusing for many people. On the other hand, I believe the best way to think about EV is that it is an average, and then we have short term and long term averages. This is only a semantic issue as long as we know what we are talking about. Knowing what you are doing is always a good thing. Being very precise about sematics but not being able to solve basic problems correctly due to muddled thinking is not a good thing in mathematics nor in life.

And btw, I'm not at "war" with you. I'm sorry you're upset (you warned us that you post in caps when upset and I see you have, twice in a row now)

That I post in caps when upset does not imply that I'm upset when I post in caps. That would be an imprecise deduction, and inaccurate as well. I also post in caps for emphasis. War doesn't make me upset. I relish war, remember? /forums/images/icons/wink.gif

[Cyrus]

"Being very precise about sematics but not being able to solve basic problems correctly due to muddled thinking is not a good thing in mathematics nor in life."

I fully agree. In fact, I am often guilty of "muddy thinking" myself. You see, and this may come as a major surprise to you, I'm not perfect.

But one aspect of "muddy" or at least one-track thinking is the persistence in minor points, when these points have been cleared enough. And while I am perfectly able to admit that "terroristic" exists as a word (albeit as a most ugly one!), you cannot even bring yourself to admit that "short-term EV" is NOT the same as the "artithmetic average short-term result".

"What do you do when you compare your blackjack EV to your poker EV?"

I compare two EVs. [shrugs shoulders] What else? Nothing spectacular there.
(And my EV(P) is still inferior to my EV(BJ). I could inteject here a fictitious example of my real results showing the opposite from what the above theoretical expectations show, but I won't.)

"Why don't you compare your short term EV to your long term EV the same way?"

I do, Bruce. I have Trip EVs, session EVs and lifetime EV (sigh). Only thing is, damn reality, i.e. actual results, don't abide exactly with my calculations. Ain't that the strangest thing! Must be my muddy play or something. /forums/images/icons/wink.gif

"Standard deviation is standard deviation whether it is short or long term; variance is variance whether it is short or long term; so why should EV be EV for short term but not long term?"

No one suggested as much. In one of your (and my) favorite books, Don Schlesinger's BJA, there are descriptions and calculations about "short-term" (e.g. trip) EV, RoR, SD, and "long-term" ones. When Don explains the SCORE (2nd ed.), he makes obvious and clear distinction between results and expectations.

"In fact, variance, from which we derive standard deviation, IS an EV. It's the EV of your squared excursion from the mean."

EV are the initials for Expected Value. The common use of EV refers to expected result, i.e. win or loss. (Emphasis, please, on expected). Of course, EV is or can be used for any expected value, like BR EV, etc. (The only semantic issue I see is when we denote the expectation in either percentage or monetary units, and denote them both as EV. But, given the context, this is rarely if ever confusing.)

"Knowing what you are doing is always a good thing."

Well, as the character in Pulp Fiction said, "I'm trying, Ringo, I'm trying real hard".

I knew a fellow in bj21.com who was posting there under the alias Man Bearing Angst, and other aliases as well. He used to have uncannily the same attitude of ---but let's not dwell on the past anymore.

Take care.

[BruceZ]

See the post I added to our thread in the theory forum before replying to this one since it expands on the points made here, but bring replies back here so we don’t have to have two threads going. Better yet, reply privately so we don’t have to clutter the board. You have a tendency to cause threads to fork off in many places, and you don’t want to be a fork off.


you cannot even bring yourself to admit that "short-term EV" is NOT the same as the "artithmetic average short-term result".

I do agree these are not the same. When I used “short-term EV” in the post above, I was emphasizing the fact that you can regard this as the EV you compute short term. I realize short-term EV has a different meaning, so in light of that let me reword my above answer to your question:

when I want to compare my Average Win (or Loss, for that matter) against my theoretical Expected Value for the hours played, what will I do? Compare "EV" with "EV"
Why don't you compare the EV you compute short term to your long term or theoretical EV the same way? Standard deviation is standard deviation whether it is computed short term, long term, or theoretical; variance is variance whether it is computed short, term, long term, or theoretical; so why should EV be EV only when it is theoretical, but not when it is computed from data? In fact, variance, from which we derive standard deviation, IS an EV. It's the EV of your squared excursion from the mean.


I compare two EVs. [shrugs shoulders] What else? Nothing spectacular there.

Exactly. So what are you saying is the problem comparing one type of EV to another then?


And while I am perfectly able to admit that "terroristic" exists as a word

Yeah, perfectly able after I beat you over the head for a week starting from the time I showed you the word in the dictionary!

It is clear that I could say the sky is blue, and you would expand it into massive debate, so what should we expect would happen if we ever have to discuss something complicated?


But one aspect of "muddy" or at least one-track thinking is the persistence in minor points, when these points have been cleared enough.

YOU ARE REALLY ONE TO TALK! I put a short post in the other forum just to direct people to the EV explanation, and you blew it into a whole new argument, WHEN I HAD ALREADY AGREED THAT IT WAS PERFECTLY FINE NOT TO USE MY TERMINOLOGY. You misread my post and thought it was something to disagree with. “Muddy” also involves not ignoring little but important words like “not”. Then I posted in this thread just to thank Jimbo and direct him to the EV explanation, and you started up a big debate again!


I fully agree. In fact, I am often guilty of "muddy thinking" myself.

Um…who do you think I had in mind? Cases in point:

1. Continued insistence on an exact answer to the AA vs. KK problem when an exact answer had already been provided numerous times.

2. Continued rejection of approximate answers which can be computed to arbitrary accuracy > 0 in favor of an exact answer, when the exact answer will always be rounded to less accuracy than the approximate answer anyway (total nonsense and waste of time).

3. Continued insistence on using the binomial distribution when other’s had told you that it does not apply due to lack of independent Bernoulli trials.

4. Failure to realize that the binomial distribution can be used to compute the probability of at least n occurrences in addition to exactly n occurrences, and failure to appreciate that 1 – the probability of not getting at least 1 occurrence of length at least m is the same as the probability of getting at least 1 occurrence of length m or greater (my solution, see your questions about what I have included).[/i]

5. Agreeing with another poster (Robk) without realizing that the reason he gave for my analysis being an approximation is precisely the same reason you cannot use the binomial distribution. If you could have used the binomial distribution, then my answer would have been exact too. This whole discussion was one confused mess on your part, made worse by the insertion of personal comments in the middle of a technical discussion.

BTW, I finally looked up “pique”, and I see it means resentment caused by wounded pride or vanity. Well I can assure you that none of my comments in the thread below stem from any wounded pride or vanity. If I say something is terrible or nonsense, you should not simply assume that I do so out of wounded pride, but rather because something is terrible or nonsense. I do not have wounded pride because you do not appreciate my mathematical discussions. It is a given that many people do not have the understanding and knowledge to appreciate them. You are the only one of these people who chooses to argue about things you do not understand. That is not cause for pique. It is cause for exasperation.

I knew a fellow in bj21.com who was posting there under the alias Man Bearing Angst, and other aliases as well. He used to have uncannily the same attitude of ---but let's not dwell on the past anymore.

That wasn’t me. I only used a single alias, and was a regular poster, respected by Don. I haven’t been there for a few years. Try again.

[Cyrus]

"You have a tendency to cause threads to fork off in many places, and you don't want to be a fork off."

A piece of advice: When you feel the need to swear, do so. Don't post words like "frick" or "fork". It doesn't help you vent. (Plus, you come off as somewhat of a dork, which I'm sure you aren't not.)

"I posted in this thread just to thank Jimbo and direct him to the EV explanation, and you started up a big debate again!"

Nope. I posted a short Thank-You-Too, of all things, with a very small remark about the need to amend your definition of EV. I even pointed out that this small thing shouldn't detract from the value of your post.

But you won't accept anything detrimental to your writings! Not even about simple and obvious things, like this one, which could've been a typo abt EV from your part. And you still insist! Watch :

"Why don't you compare the EV you compute short term to your long term or theoretical EV the same way?" [Umm, I do, Bruce. Emphasis on "compute", please.] "Why should EV be EV only when it is theoretical, but not when it is computed from data? In fact, variance, from which we derive standard deviation, IS an EV. It's the EV of your squared excursion from the mean."

Bruce, you're getting deeper and deeper into this, but you only have yourself to blame. For the last time, and I don't care what textbooks you wanna drag down next from your library and misquote: When you take measurements from k samples (say even from randomly changing variables) and you measure the arithmetic average of their actual values, the result is NOT expectation. It. Is. not. It is (duh!) the arithmetic mean/average of the samples. When you compute or estimate or calculate the theoretical mean of those samples (or of a population), then that value is an expected value. An expected one, Bruce. Ask John Cole for the definition of that adjective. Hence, <font color="red">E</font color>V. Period! End of story. (Wanna make a federal case out of this litle thingy, fire away, you're on your own. But thanks again for the thoughtful post about SD.)

"[Man Bearing Angst in bj21.com] wasn't me. I only used a single alias, and was a regular poster, respected by Don. I haven't been there for a few years. Try again."

Thanks for clarifying that... Well, I was merely pointing out the similarities betwen your "style" and MBA's. Since you claimed to be a "bj21.com regular", I assumed you'd recognize the posting "qualities" I had in mind.

..I realize you have a subconscious desire to be revealed for the "respected" poster you were, particularly "respected by Don". Do try again.

--Cyrus

PS : Your outlined "Cases in point" have little merit, I'm afraid. But let's not drag on : I undertake to be responding with 25% fewer words/sentences than any posts of yours that I will be responding to! If you do the same, the threads will have to end some time.

[BruceZ]

I do sincerely hope that people here trying to learn are ignoring this man and his outlandish statements, and understand why he is wrong.

But you won't accept anything detrimental to your writings!

I sure won't, not when they are dead wrong.

When you take measurements from k samples (say even from randomly changing variables) and you measure the arithmetic average of their actual values, the result is NOT expectation. It. Is. not. It is (duh!) the arithmetic mean/average of the samples.

I gave 3 examples of distributions in the other forum for which the arithmetic mean is an EV of those distributions, and you obviously did not read (likely) or understand (certainly) them. Go back to your definition of EV, and tell me what is the EV of a distribution that assigns a probality of 1/k to k observations Xn. It is sum[n=1 to k][(1/k)Xn]. That's an arithmetic mean, therefore the arithmetic mean is an expectation. QED.

When you compute or <font color="red">estimate</font color> or calculate the theoretical mean of those samples (or of a population), then that value is an expected value.

You just contradicted yourself. When I compute the arithmetic mean, I AM computing an estimate of the EV of those samples, it is the maximum likelihood estimate of the EV. It is the EV that is most likely given those results. So by your very statement, I have computed an EV. So thanks for agreeing with me, maybe now we can end.

For the last time, and I don't care what textbooks you wanna drag down next from your library and misquote:

I have not misquoted anything. You need to learn that in mathematics, one does not evaluate definitions from their "context" in the same way one does in law or literature or whatever other subject you may be familiar with, and you don't go to a damn English teacher for mathematical definitions. Mathematical definitions are much more precise than this. For many games, you certainly don't "expect" to obtain the results indicated by your mathematical expectation. Those results could be extremely unlikely and you would never expect them. They may even have probability 0!

PS : Your outlined "Cases in point" have little merit, I'm afraid.

I can assure you that they have every merit in the world. If you do not understand why, then I'm sorry you don't know enough to be worthy of any more of my time, and you have absolutely no business taking up the time of this forum. As usual, you haven't told me why you think these points have no merit, so that I might educate you. Your response simply amounts to "you are wrong".

A piece of advice: When you feel the need to swear, do so. Don't post words like "frick" or "fork". It doesn't help you vent.

I respect the terms of usage of this site. Besides, fork refers to your creation of threads off of other threads. You seem to be reading some other meaning into it.

I undertake to be responding with 25% fewer words/sentences than any posts of yours that I will be responding to!

Good, start by typing these phrases into your word processor:

I agree
You are right
I was wrong
Good point

and again...

I agree
You are right
I was wrong
Good point

Practice typing these phrases 50 times or so each day. Pretty soon you will be able to use one of these phrases in an actual post.

[Cyrus]

"I do sincerely hope that people here ... are ignoring this man and his outlandish statements, and understand why he is wrong".

You did that whine for help (calling "any patriots") in the other forum, as well, and it was equally pathetic. Come on.

Bruce, you seem like a decent fellow, really, so I will accept your definition of EV! /forums/images/icons/smile.gif

To recap, you stated that we play three 4-hour sessions. In the first session we win $200, in the second session we win $400 and in the third session we lose $300. You also wrote that our EV for those sessions is the arithmetic mean of those results, i.e. $25/hour.

Terrific. No problem! That's EV. Don't bust a vein, that's an EV, if I ever saw one. Let's all live happily ever after. (OK I'll have a problem comparing the mean of those results with the, well, EV I had calculated but I'll find my way around this, no worries.)

"I have not misquoted anything. You need to learn that in mathematics, one does not evaluate definitions from their "context" in the same way one does in law or literature or other subjects, and you don't go to a damn English teacher for mathematical definitions."

Well, sorry, Bruce, but you misquoted Feller. Plain an' simple. No "context" or anything complicated like that. You claimed that Feller considers EV to be synonymous with the arithmetic mean of observed results, while Feller, of course, had written nothing of the sort, bless 'im.

Wanna try DeGroot next? /forums/images/icons/tongue.gif

[BruceZ]

You did that whine for help (calling "any patriots") in the other forum, as well, and it was equally pathetic. Come on.

You misunderstand both statements. The one on the other forum (which we should never discuss here anyway) invited others to join in the discussion so we wouldn't monopolize the board. The one here expresses my sincere wish for others on this forum that they not be misled by your posts. Kind of like "don't let BruceZ's pique keep you from seeing this". I certainly don't need anyone's "help" to make these points since I am as qualified to make them as anyone here, although agreement by other knowledgeable people would probably appear to vindicate me in the eyes of some whose understanding may not be perfect.

To recap, you stated that we play three 4-hour sessions. In the first session we win $200, in the second session we win $400 and in the third session we lose $300. You also wrote that our EV for those sessions is the arithmetic mean of those results, i.e. $25/hour.

Terrific. No problem! That's EV. Don't bust a vein, that's an EV, if I ever saw one.

It's an estimate of the EV of your hourly rate for those sessions, and of your long term EV as well. It is not in general equal to the EV of your hourly rate for those sessions, or the long term EV of your hourly rate. It is, however, an EV in its own right, being the EV of the probability distributions used to estimate your EV as I have described. I am glad though that you seem to have decided that I was right all along.

Bruce, you seem like a decent fellow, really, so I will accept your definition of EV!

Thanks, and thank GOD, but it isn't *my* definition.

Well, sorry, Bruce, but you misquoted Feller. Plain an' simple. No "context" or anything complicated like that. You claimed that Feller considers <font color="red">EV to be synonymous with the arithmetic mean</font color> <font color="blue"> of observed results</font color>, while Feller, of course, had written nothing of the sort, bless 'im.

Not only didn't I misquote it, I copied the text exactly, which stated what you just stated in red, which implies the part you added in blue, making it unnecessary to state the part in blue explicitly, but it does in fact imply the part in blue. The statement in blue is taken up further in DeGroot.

If you are arguing that the statement in red does not include the statement in blue, then you are indeed arguing that the statement in red applies only in a limited context, and I claim that you are misquoting, and that the distinction you are making is an artificial one. You have also made up your own terms to interpret Feller (mean expectation, average expectation) which are never used by Feller or anyone else.

I can assure you that I am as qualified to be the supreme court judge in this interpretation of Feller as anyone, and no superior court exists to which you can appeal this interpretation. I also said I will not hear any arguments about semantics which this is, so case dismissed &lt;gavel down&gt;. Balif, remove this man. /forums/images/icons/grin.gif

Wanna try DeGroot next?

Please, bring it on, it's one of my favorite texts, and one which I am highly familiar with, having used it for 20 years. I think it will be beyond you though, since you have trouble with Feller. If you wish, you can note the following about the sample mean (or arithmetic average of results) from DeGroot:

1. Top of page 343. The statement made about the sample variance and variance also applies to the sample mean and mean (or EV) which we are discussing.

2. P. 341, it is shown that the sample mean is the mean (or EV) of the likelihood distribution which maximizes the likelihood estimate of the mean or EV.

3. Example 4 on p. 334, it is shown that the sample mean is the mean (or EV) of the posterior distribution or Bayes estimate of the mean of a normal distribution (which we are assuming) when the absolute value loss function is used (not the mean square error loss function as I wrote in the other thread, that gives a different estimate).

These are in addition to the quote at the bottom of page 180 that I gave earlier, and which states that the terms mean and expectation can be used interchangeably. The context of this section is random variables, and as such it is equivalent to the discussion in Feller; however, the fact that this strong statement appears in a stats book which deals with the analysis of observations provides very strong support for my interpretation.

[Cyrus]

"You misunderstand both statements."

Don't think so. I'm a whine expert. Can tell a whine from miles away.
And yours was a grand cru.

"I can assure you that I am as qualified to be the supreme court judge in this interpretation of Feller as anyone, and no superior court exists that to which you can appeal this interpretation."

What can I say? I'm just not worthy.

"Bring it on, [DeGroot's] is one of my favorite texts, and one which I am highly familiar with, having used it for 20 years."

I'm tempted to enquire what have you been using that "for 20 years" but nah.

Take care. /forums/images/icons/cool.gif

[BruceZ]

I added something to the bottom of that post after you read it.

Don't think so. I'm a whine expert. Can tell a whine from miles away.

I have no reason to whine, except for the poor souls who must now be disabused of confusion caused by the reading of your posts. You see, it is my purpose in life to reduce confusion in the world, kind of like reducing entropy. I don't know why, it is one of the few immutable values I have. It is the reason I help you, even though I should be finished with you. It's kind of like a doctor who feels an obligation to treat the enemy, or vicious criminals. I don't like it when my attempts to reduce confusion result in the creation of more confusion.

I'm tempted to enquire what have you been using that "for 20 years"

Well, for an example of one of many applications, I have used it to estimate the EV AND VARIANCE of pseudorandomly generated waveforms used in discreet multitone broadband data transmission. I also use it in the development of ways to improve estimation of the EV for gambling given prior information. Most recently, I have used it to beat you over the head.

[Cyrus]

"I have no reason to whine, except for the poor souls who must now be disabused of confusion."

Well, even for poor souls, a good whine is a good whine. Kudos! The aroma is unmistakable.

"It is my purpose to reduce confusion in the world."

Didn't I just say we are not worthy? Bears repeating.

"Well, for an example one of many applications ... I have used [DeGroot's] to beat you over the head."

That's the best use you have put it for 20 years, I'm sure.

/forums/images/icons/cool.gif

[BruceZ]

Now I've added something important to the last post after you responded. We need a chat feature in here.

Didn't I just say we are not worthy?

I completely agree that you are not worthy. Finally we agree on something.

That's the best use you have put it for 20 years, I'm sure.

It was far from the best use, but it was by far the most entertaining.

[Cyrus]

C &gt; "Didn't I just say we are not worthy?"

Bruce &gt; "I completely agree that you are not worthy."

Brucie, thanks for addressing me with the royal plural. Made my day.

Arise.

[BruceZ]

Just have to have the last word don't you? Even if it is something silly. This is not chess, where you must make the last move. Go on, I dare you to not respond to this post.

[BruceZ]

I can assure you that I am as qualified to be the supreme court judge in this interpretation of Feller as anyone, and no superior court exists to which you can appeal this interpretation.

I am not saying, BTW, that nobody knows more about probability and statistics than I do. I am just saying that given this particular text, and this particular issue, that I don't believe there is any additional information which could allow anyone else to form a more correct interpretation.

[Cyrus]

"This is not chess, where you must make the last move."

This is not correct, neither grammatically nor chessically.

Feel like a 50-post thread about Chess?.. /forums/images/icons/grin.gif

[Cyrus]

It was perfectly clear.

/forums/images/icons/laugh.gif

[BruceZ]

I knew you had to respond.

This is not correct, neither grammatically nor chessically.

So you are agreeing then that it IS correct chessically, since you used the double negative neither and nor which cancel out. My word processor flags this as a gramatical error, and says the correct word is "or". What was wrong with my grammar?

Of course you must usually make last move in chess to win, except in cases where your opponent resigns on your move.

[BruceZ]

[BruceZ]

When I compute the arithmetic mean, I AM computing an estimate of the EV of those samples, it is the maximum likelihood estimate of the EV. <font color="red">It is the EV that is most likely given those results.</font color>

The statement in red is not correct. It's easy to state this wrong, and I have accidentally done so on several occasions. I have even seen a textbook state this incorrectly . The arithmetic mean of observed results is indeed the maximimum likelihood estimate of the EV; however, this does not mean that it is the most likely value of the EV. It means that it gives the EV which is most likely to result in the observed values. The likelihood that is being maximized is the likelihood of the observations, not the likelihood of the EV. This is a subtle point, and one which gives rise to some controversy among different schools of statisticians which I've alluded to earlier. If you want to maximize the probability of the EV, you must use a Bayesian estimator which multiplies the likelihood function by a prior distribution of the EV. This prior distribution is an a priori distribution which takes into account your predisposition as to where the EV should lie, based on your experience or prior knowledge. The maximum likelihood estimator would give the most likely value for the EV if the prior distribution assigns an equal probability of 1/n to each of the n observed samples. This is not important to the rest of the post, but it is a very important point in itself.

For example, it is not correct to make the statement that "there is a 97.7% chance that I am at least a 1 bb/hr winner" just given the fact that your average win is 2 standard deviations above 1 bb/hr. What would be true is that "a 1 bb/hr winner would only achieve my observed results or better 2.3% of the time".

[Cyrus]

I fully and unreservedly agree with everything you have written in your above post. It is what I have been trying (clumsily? ungramatically? unclearly?) to say all along about Expected Value. I do not care whether this is what you have been saying all along or whether it's something a little different : I agree with the contents of your above post and that's it. End of post/thread/story.

--Cyrus

PS: Thanks for the effort to be clear. I, for one, appreciate it, even if you take my posts to be a pain.

[Cyrus]

"You used the double negative "neither" and "nor" which cancel out. My word processor flags this as a gramatical error, and says the correct word is "or"."

Nice catch! Yes, my grammar was off. I should have written it the way you suggest.

"What was wrong with my grammar?

Perhaps nothing. I termed as "grammatical" the error I perceive of using "last" instead of "next". I was trying to force the joke too much.

In Chessical terms, it is even more obvious that one should write "next move" instead of "last move". Yes, Chess is a game in which no player can ever lose his turn to play/move (and this must be a phrase full of grammatical errors!). So, I thought you were trying to say that, in every thread, I feel like I have to respond, i.e. have the last word, make another move, have the last move.

You explained it yourself when you wrote "Of course you must usually make [the] last move in chess to win, except in cases where your opponent resigns on your move *."

The qualifier is these words which you correctly inserted, "to win". Because, the way you had stated it before, it could seem that in any case, you have to make some "last" move, even in stalemates! So, yes, to win, in Chess, you have to make some move as your last --- except when your opponent's flag falls as soon as he has moved (although technically his move has not been completed); or when he is disqualified if in a tournament; or when he doesn't show up to play; or when his last move is throwing his King at your head; etc.

Take care.

________________________

* : Psst! You have still made the last move when the opponent resigns on your move! /forums/images/icons/smile.gif

[Mason Malmuth]

That I post in caps when upset does not imply that I'm upset when I post in caps.

Any good statistician would immediately know that this is a good example of sampling error.

MM

[Mason Malmuth]

But one aspect of "muddy" or at least one-track thinking is the persistence in minor points, when these points have been cleared enough.

YOU ARE REALLY ONE TO TALK! I put a short post in the other forum just to direct people to the EV explanation, and you blew it into a whole new argument, WHEN I HAD ALREADY AGREED THAT IT WAS PERFECTLY FINE NOT TO USE MY TERMINOLOGY. You misread my post and thought it was something to disagree with. “Muddy” also involves not ignoring little but important words like “not”. Then I posted in this thread just to thank Jimbo and direct him to the EV explanation, and you started up a big debate again!

This is a good example of what I call "self weighting" details. By seizing on minor points and debating them to obscurity almost any argument can be defeated because the really important points get lost. This is my main complaint against many of the Cyrus posts on the Other Topics forums. It's unexpected that it took Bruce's mathematical skill to point it out here.

MM

[Mason Malmuth]

Hi Cyrus:

You wrote:

A piece of advice: When you feel the need to swear, do so. Don't post words like "frick" or "fork". It doesn't help you vent. (Plus, you come off as somewhat of a dork, which I'm sure you aren't not.)

Another example of a self-weighting argument. By the way, I haven't used a swear word in well over twenty years, yet I can irritate people whenever I want. It's not necessarily how you say it, but it's the meaning behind what you say.

Best wishes,
Mason

[Mason Malmuth]

Hi Bruce and Cyrus:

Yes this thread is a mess. But in my opinion, Bruce is correct on virtually every point. That's because math is far more precise than living in the real world, and I suspect that Cyrus is looking at it as if he's in the real world. That might be alright when debating world affairs, but it doesn't work when debating mathematical or statistical concepts.

Part of the reason for this is that when doing statistical type arguments, like we do in some of our books, the situation of the objective must be what mathmeticians refer to as well defined. Thus when Bruce says that an EV is ... he either has it right or he doesn't. He can't have it partially right or sometimes right. Furthermore, he can't stray from strict definitions of the statistical concept. If he does he violates the underlying mathematics and what he has will make no sense.

Now from what I have read of this thread and the other arguments, it appears to me that Cyrus wants to add some flexibility into the definitions. Now when dealing with real world events having flexibility can be very important. But when dealing with precise statistical concepts that can't be the case even if the concepts are themselves defining flexibility. I hope everyone understands this and sees the difference.

Best wishes,
Mason

[lorinda]

But you won't accept anything detrimental to your writings! Not even about simple and obvious things

Whilst I have never seen BruceZ make an outright blunder (although I would bet he has), I have seen him make tiny mistakes many times. (This is actual number of cases, not percentage, he is incredibly accurate on a per post basis)

About half of the time he corrects this before anyone notices, because it is so tiny that only he has spotted it.

A poster with the kind of pride you are talking about would not correct it because he would know full well that noone else will notice and that pointing it out himself, would, in the eyes of the proud man, make him look stupid.

The other half of the time, he will go immediately back and work out the problem again with the error properly addressed and come back and post the results, with not only a more accurate answer, but more often than not an apology for his (usually miniscule) oversight.

He is one of the best, most accurate, most honest and hardest working posters on these forums and accepts he makes errors when he makes them because he understands that this enhances his knowledge and accuracy as well as ours.

Lori

[Mason Malmuth]

Hi Lorinda:

This is actually the way it should be. If you're trying to improve your gambling, whether it be poker or something else, coming to these forums and treating them as a learning experience and challenging yourself to improve is probably one of the best ways to do just that. And of course part of that challenge is to find and correct any errors that you might make.

Best wishes,
mason

[lorinda]

Hi Mason,

I agree entirely... It is for this reason I watch at least one hour's tourney play a day, despite considering myself to be pretty strong in that format.

To be better than everyone else, first you have to get as good as the best there is.

Lori

[Cyrus]

Greetings, Mason.

It is a little puzzling to see so many of your posts in this unfortunate thread, so late in the day too, but I guess you have only now chanced upon it. I don't feel like re-hashing anything, since I've already posted a detailed apology ("Other Topics" forum) about my over-posting and possible over-reacting -- more a cardinal gambling mistake than a breach of netiquette.

I don't even want to comment on your disapproval of my "persistence in details", a persistence that tends to "obscure the main points" -- or words to that effect. I covered that too in that same post (viz. the Feyerabend aside, which was not altogether in jest).

Now, ALL this started when I made a two-sentences comment in a post about a single word (ie EV) among a thousand words in Bruce's post abt Standard Deviation. Bruce gave the results from 4 observed trials, averaged those results and named EV their arithmetic mean. After expressing my personal appreciation for Bruce's effort in explaining to one and all the concept of SD, I observed that it is incorrect, IMHO, to name 'expected' an observed result. The few Stat books I've read, when referring to results (not theoretical computations, but results), do not use the term 'expected' when referring to the results' mean, variance or SD.

The soap opera that ensued is, unfortunately, still up for all to see, so I will only say this : I happen to fully agree with you (and Bruce) about the need for precision in Mathematics. So, there's one and only one correct response to my above objection on mathematical nomenclature: it's either a legitimate objection or it isn't.

And that's all I wrote.

--Cyrus

[Inthacup]

I also use it in the development of ways to improve estimation of the EV for gambling given prior information. Most recently, I have used it to beat you over the head.


Funny stuff Bruce. The wit and irony involved here is one of the few things I can read that makes me laugh out loud. Thanks!

[Gitz]

The microscope is extremely hard to live under no matter what the weather /forums/images/icons/smile.gif /forums/images/icons/blush.gif /forums/images/icons/tongue.gif /forums/images/icons/grin.gif
Paul