We’re All Bad at Math; or, Should Skeptics Play the Lottery?

 

Bad Lottery Math

Bad lottery math, attributed to “Philipe Andolini.”

The image above has come across my Facebook feed at least a dozen times. It appears that most people are sharing it without a critical look. And yet I am the one that gets vilified when defending the ideas behind common core math!

Let’s talk briefly about how easy one could see how this doesn’t make sense: if every person had 1 million dollars, then 10 people would have $10 million. So 100 people would have $100 million, and 1,000 people would have $1 billion. It becomes a pretty far stretch to give the other 299,999,000 people in the US the leftover 0.3 billion dollars and expect everyone to end up with $4.33 million each.

This is my defense of common core: we are really bad at estimating. The process of common core is what those of us who use math regularly (like me teaching a physics class) would do in our heads to see if an answer is reasonable. This is is important in other fields, too. Imagine if a doctor says to give a medication at 0.1 mg per kg of body weight. If the pharmacy is directed to prepare 100 mg of medication, would that be a reasonable dose for an average adult? I’ll leave the answer as an exercise for the student.

As for the meme above: if the multi-state lottery association distributed the money to everyone in the US, you’d have just about enough for a decent cup of coffee or a happy hour beer. Please get your math right!

The Lottery is for Those Who Don’t Understand Math

Given that people seem to be bad at math, it is no wonder the lottery is so successful. It is interesting, however, to see the debate among skeptics as to whether or not skeptics should play the lottery, given that we should, presumably, know math and statistics a little better than the average person. According to the Powerball website, the odds of winning the jackpot is 1 in 292,201,338. In other words, it’s impossible to win. You have no chance. Really. At my age I have about a 1 in 1,000 chance of dying this year. If I really thought I could win the Powerball jackpot, I should also put my name in for president (1 in 10,000,000).

I saw one comment on Wil Wheaton’s social media, which suggested: “Just put the amount you would have gambled into a savings account and you’ll almost certainly end up with more money in that account than you ever would have won.” This is true. If the $2 per drawing was put into savings at 6% for 10 years, you would have $2,612. Not bad! Just sticking it in the mattress would total $1,920—also a nice chunk of money.

I could apply this to anything I spend money on. I could have skipped that second viewing of Star Wars, saving $20 (with snacks). I could cancel Netflix—I really don’t watch it that much—and save $8 a month. One of the wines I really like is about $16 per bottle. We all know wine tasting is mostly BS, but I just like the taste of this one wine. Should I skip it and go with the Two Buck Chuck? My point is that we all make decisions to spend on things we don’t need. It is really about the value they give back to us. I enjoy having Netflix at the ready. I enjoy that glass of wine on Friday night.

I admit it: I bought a ticket for the $1 billion+ jackpot this week. I know I won’t win. But that 30-minute conversation with my spouse about what we would do with that kind of money was really fun. It also feels a little like goal-setting, because some of our dreams are really ones we have and are working towards. The value in it wasn’t in planning on winning and making changes to our spending habits. The value was in how it felt to dream—just like seeing Star Wars as a kid made me dream of being an astronaut.

There are certainly economic and political arguments to be made against government-run lotteries. There are social arguments against them as well. I’m not arguing those points here. It isn’t a justification or criticism of the existence of lotteries. That is a much longer blog post—and probably not something handled on Skeptoid!

So for skeptics who refuse to buy a ticket: your reasons are valid and reasonable. I have no problem with that. For those skeptics who participate in the office pool or buy that ticket “just because,” that’s OK, too. I am pretty sure you understand you won’t win, but extract the joy out of dreaming. For me, it was $2 well spent.

About Eric Hall

My day job is teaching physics at the University of Minnesota, Rochester. I write about physics, other sciences, politics, education, and whatever else interests or concerns me. I am always working to be rational and reasonable, and I am always willing to improve my knowledge and change my mind when presented with new evidence.
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48 Responses to We’re All Bad at Math; or, Should Skeptics Play the Lottery?

  1. Craig Sachs says:

    Skeptics should play because if by some strange chance one of us does win we will donate to our favorite skeptical causes. I dont like to play but I was told to get the ticket and accidentally spent 6 dollars. I personally think no one will win for quite a while and the prize will keep getting larger. I am also very aware that these state games take their toll on the poor with hopes of a making it rich. That upsets mre as much as a family going to a faith healer with hopes of getting healed.

  2. Jeff Grigg says:

    Regarding the image and math:
    “1.3 Billion / 300 Million”

    Well, “billion” is 1,000 times a million.
    So this is 1.3 * 1000 / 300 = 1.3 * 10 / 3 = 13/3 = 4 1/3 ~= $4.33 each.

    That’s not much money. Practically no one would notice it.

    Do I have to be a “math genius” to compute this?!?!?

    • Eric Hall says:

      No. But my point is a quick order estimation would tell a person the meme is wrong. A billion divided by a million is a thousand. Thus the meme can’t be right.

    • David says:

      Does this mean that each punter spent an average of $4.33 on lottery tickets? Whatever the odds are, one cannot say there is no chance of winning,(small chance is not the same as no chance) unless you don’t purchase a ticket(no chance)

      People get all steamed up about the small number of rich people having as much money as the rest of the population. Spread out their money, and it probably amounts to $4.33 per poor person.

      • Jeff Grigg says:

        By design, lottery tickets are worth about half of what you pay for them. So it looks like “an average of all Americans” spent at least $8.66 on that particular lottery. It would actually be more than that, due to the non-jackpot payouts.

        I once did a calculation of “Expected Value” for the Publisher’s Clearinghouse thing, for my father, who was entering it. By my calculations, based on the odds they publish, they payouts were less than the cost of the stamps the participants used to enter the contest.

      • Nick Staker says:

        Mathematically, technically there is a chance. But like this old joke (http://tinyurl.com/zv3zf8o) it’s close enough to zero for all practical purposes.

        • Jeff Grigg says:

          The mathematician knows that the distance between them will never be zero.

          The engineer knows that the distance will fall rapidly, and that when it is smaller than the length of his member, then certain things are now possible.

          The process person knows that as long as you are sitting in a chair and she is laying on the bed, even a zero distance between the chair and bed would not allow you to touch her. It could, however, cut off your legs. (…unless you’re allowed to crawl from the chair to the bed.)

  3. starbucks says:

    this reminds me of chemistry class were every value has a unit

    • Geoff says:

      Relative density doesn’t. 😉

    • ausGeoff says:

      Every “value” doesn’t necessarily have a unit of measure. There are numerous examples of so-called “dimensionless quantities”; Mach number, urea dialysis, Planck’s constant, the gravitational coupling constant, and the ‘golden rectangle’ to name a few. Even gambling odds have no unit of measure.

      • engers says:

        You forgot to mention Avagadro’s number, that’s the number of Avocados you have to cut open before you find one that’s worth eating… 🙁

  4. Macky says:

    Combinations of arithmetic and probability seem to confound many, even otherwise competent adders for the everyday toting up of bills, groceries etc.

    One Indian chap I worked with late 90’s was adamant that in a game of Two-up (two coins tossed into the air with fair spin applied and hitting the ground) my pick of a head and a tail had the same chance as two heads or two tails. I told him anytime he wanted to play with real money he was welcome….

    A library book I took out on various investment choices had blatant erroneous estimations of chances of winning a prize in Bonus Bonds (NZ), dollar-per-number savings that you have a weekly and monthly prize draw, instead of interest.
    They are handy as savings and you have the added advantage of getting your money back when you want/need them cashed.
    The book’s calculations of chances erroneously compounded with each draw until by the end of the year one had over 100% certainty of winning a prize, an impossibility, and I sent them a note pointing this out.
    They sent me back fresh calculations which were still wrong. The book was written and issued from a govt department. I hope it wasn’t from the same people who construct the country’s Budget.

    I like my $6 NZ Lotto ticket each week. $6 buys 10 boards which give exactly one chance in 383,838 of winning first division (first 6 numbers out of the barrel, not necessarily in order).
    $6 also buys a little bit of fun, and a little bit of that prime mover of mankind, Hope.

  5. mudguts says:

    Yep.. you see dullards everywhere

  6. Iain mcnaught says:

    Nothing to do with being bad at estimating. They’re making the calculation but treating a billion as a million million as it used to be known but never is now.

    • Jeff Grigg says:

      No. If a billion was a million million, then it would be $4,333.33 per person: $4 thousand, not $4 million. Nice, but still not a “life changer” for most people.

  7. John Denys says:

    Another problem with this is that if, somehow, everyone had 4.3 million dollars, inflation would drive up the prices of everything. Germans in 1923 had trillions of marks but it was a terrible economic situation.

  8. mudguts says:

    ps.. My son broke up laughing at the terrible arithmetic.. Called me over.

    I suppose some people will call it math when the numbers don’t fit between 0 and 100.

    But should we lampoon this? Even Brian has had a foot stubbing moment with powers. I’d call it zeal to get something nice out before checking.

    Of course with a pop shared poster like the example; Its out and shared and probably reshared a million times before the originator notices. I have had the experience with a math students faux pas being reshared many times.

    I hope the skeptoid staff are enjoying the face plant PhD from the humanities department at Uni of Wollongong. Its going to get a zillion shares and whats more, A journal review panel let some of the content in for publication.

    That’s face plant under the egalitarian “free speech”.

    This is the sort of thing we have Quackwatch and Skeptoid for. Its not as if most do their own literature surveys .

    • Eric Hall says:

      I make math mistakes as well. But there should be a sense that something doesn’t make sense. If you notice, I wasn’t insulting – but rather encouraging more effort in mathematics.

  9. Macky says:

    Quackwatch ? What a laugh. Run by a person whose career was psychiatry, a largely unscientific regime of opinionated consensus, over-drugging and ECT.
    http://ahrp.org/two-nimh-directors-debunk-dsm-deplore-psychiatrys-unscientific-modus-operandi/

    Wiki “Barrett says he does not criticize conventional medicine because that would be “way outside [his] scope.”
    Of course it would be. He would then have to admit a huge chunk of quackery and fraud in said “conventional medicine”.

    Here’s only the top 20 in the last two decades : https://en.wikipedia.org/wiki/List_of_largest_pharmaceutical_settlements

    Stephen Barret is a quack in his own right. His main drive is against nutritional supplements etc which may or may not deserve some criticism, but he is not qualified in nutritional science or has carried out his own experiments in same, therefore he has not a full understanding of nutrients (I’m not personally advocating them) and how they work and possible side effects.
    His alleged campaign as a consumer advocate is blatantly lacking in the examination of conventional medicine, and he would probably have done a lot more for mankind by casting his critical eye on some of the dangerous drugs being prescribed for serious illnesses that have been criticized by even mainstream media for their lack of effectiveness and horrible side effects.

    • ausGeoff says:

      Ignoring the fact that this diatribe directed at Stephen Barrett is totally off-topic, you obviously have a skewed opinion of his ‘Quackwatch’ site and apparently take every opportunity to damn the man. You’re obviously unaware that a psychiatrist is also a medical doctor/general practitioner, and therefore as competent to talk about medication or preventive nutrition as anybody else… and most certainly any lay person.

      To call Barrett “a quack in his own right” requires evidence of same, and which you’ve failed to provide. Personal opinion does not equal evidence. Presumably your poor opinion of Barrett is based on your own clinical qualifications and/or knowledge of psychiatry?

      Your (again unevidenced) claim that Barret knows nothing about nutritional science—which is at odds with his membership of the Academy of Nutrition and Dietetics (AND)—the largest organization of food and nutrition professionals in the US, just doesn’t make sense.

      It’s also more than obvious that you’re a supporter of CAM; you list a mere 20 (conventional) drug regimes that’ve been brought into disrepute—but not necessarily because of any intrinsic clinical failure—rather many of those drugs were simply [sic] misrepresented, illegally prescribed for off-label use, or subject to coercive marketing practices. In fact only ONE of those 20 drugs has been withdrawn from the market (Rofecoxib in 2004) as of today. And many of the remaining 19 drugs are on the World Health Organization’s List of Essential Medicines and/or the European Medicines Agency listing (and which drugs are the most important medications needed in a basic health system). And you’ve chosen to ignore the other 6639 prescription + conventional OTC drugs [FDA: 16/10/2014] whose use is unquestionably efficacious.

      (I apologise in advance for continuing this off-topic thread direction commenced by Macky, but I reckoned his misinformation about prescription drugs/Stephen Barret needed a corrective response.)

      • Macky says:

        ausGeoff, I am perfectly happy to be corrected by better information than mine on any topic or assertion.

        If I seemed overly harsh on Stephen Barrett, then it was primarily for his overtly one-sided regime, and as a counter to a Sydney scientist (mudguts) whose specialty is throwing off-topic quips and diversions into otherwise straight arguments/comments.

        Re psychiatry, you have not appeared to address the criticism of its unscientific nature and the link I sent. Perhaps this one may help with that :
        https://en.wikipedia.org/wiki/DSM-5#Attention_deficit_hyperactivity_disorder

        I have no idea who CAM is, but I am certainly not against proper use of scientifically-proven drugs and their selective targeting.

        However, the “mere” 20 drug regimes that I posted the Wiki to were only the top by value of settlement, and were notable by the number of Off-label Promotions, a serious and deadly health risk of inappropriate drug dispensing that may have killed many people, plus the convictions for proven kickbacks to doctors who were encouraged by the extra money to debase their profession.
        The reason why I brought that up was not to criticize conventional medicine as such. I would be a hypocrite if I did, my life being saved by Ventolin on one unpleasant occasion.
        But people such as Stephen Barrett who wade into those who promote alternative medicine or nutritional supplements, whether justified or not, in my opinion deserve strong criticism for their refusal to examine the criminal actions of the conventional drug industry, and of doctors who by taking kickbacks as happens often here in NZ, prescribing dangerous psychotropic drugs for purely physical maladies even to children, is a biased regime that ignores the seriousness of conventional medicine misconduct.

      • mudguts says:

        Its been pointed out many times that Macky is the worst sort of Quack and he takes offence to it until he changes his anecdotes..

        Social hypochondria quackery is pretty poor form

        • Macky says:

          In what way am I the worst sort of Quack, Henk ?

          Or is that another straight question that you will refuse to answer ?

          • mudguts says:

            Macky, its one of those questions that never needs to be answered now skeptoid comments has gone.

            But if you will.. the long suffering “friend’ you invented was quackworthy and hyperchondriacal anectdotalism.

            The number of diseases you had her anecdotally suffer (from response to response) made any reader absolutely sure that you were making it up..|

            Especially as she started off being a boy you knew that was lifted from a local site.

            But skeptoid comments being gone.. Its only Brian and those of us who archived mackynations that can enjoy these for prosperity.

            PS, you have used up your questions whether they be straight, rhetorical, loaded or pre-emptive and especially, things you could have looked up yourself.

            Still social hypochondria is pretty poor form. Even if the victims and their diseases were invented for a lost argument.

            Has strandpulling rants and comedy died?

  10. Sean says:

    When I was a child I received antibiotics which had been formulated (mixed) at the pharmacy. I put the meds in my mouth and immediately my mouth just spit it out. It turned out to be 1000x too strong. Common math core, too true. I make simple math mistakes and I have a science degree. The facebook post didn’t even seem weird however I think it was because an answer was already presented so I glossed over it.

  11. Sean says:

    Oh, and the meds calculation at 100mg seems a bit high for an average adult. I myself weigh in around 80kg and I am a reasonably average male. The formulation is for a 100kg adult.

    • Macky says:

      It’s case for the pre-1965 education system (at least in NZ) where the primary schools engaged in quite a lot of rote learning, reciting arithmetic multiplication tables and alphabet every morning, then later using that basic grounding to solve examples of calculation.

      Many school children/teens can’t count well into their high school years, and the education system has certainly been dumbed down in many areas.

      Electronic calculators have done a lot of damage to the use of mental arithmetic, a trainable skill as any 301 dart game player knows.

      • Roland says:

        Mental arithmetic, and use of fractions. I can still remember the look of complete amazement I got from a genY guy as I did a calculation in my head and said “that will be about a third of a volt” while he was still punching buttons on his hand-held calculator. Of course, the look only came after he finished his calculation to verify my answer. “0.32567 volts … How did you do that ?!?!?!?!?!?”, he really did not know.

    • Sam forwst says:

      Sorry but it’s a 1000kg man.
      100mg divided by .1 = 1000.

  12. Charles says:

    Where can I open a savings account that pays 6%?

  13. Macky says:

    Macky says:

    Macky
    January 25, 2016 at 10:14 pm
    In what way am I the worst sort of Quack, Henk ?
    Or is that another straight question that you will refuse to answer ?

    Henk (mudguts)
    “Macky, its one of those questions that never needs to be answered now skeptoid comments has gone.”

    I rest my case.

  14. mudguts says:

    you forgot the rest of it..

    So I’ll add it for you Macky.

    “Macky, its one of those questions that never needs to be answered now skeptoid comments has gone.

    But if you will.. the long suffering “friend’ you invented was quackworthy and hyperchondriacal anectdotalism.

    The number of diseases you had her anecdotally suffer (from response to response) made any reader absolutely sure that you were making it up..|

    Especially as she started off being a boy you knew that was lifted from a local site.

    But skeptoid comments being gone.. Its only Brian and those of us who archived mackynations that can enjoy these for prosperity.

    PS, you have used up your questions whether they be straight, rhetorical, loaded or pre-emptive and especially, things you could have looked up yourself.

    Still social hypochondria is pretty poor form. Even if the victims and their diseases were invented for a lost argument.

    Has strandpulling rants and comedy died?”

    • Macky says:

      “Its only Brian and those of us who archived mackynations that can enjoy these for prosperity.”

      I believe the word you are searching for is “posterity”, Henk. I seriously doubt one could prosper on either of our archived comments, although one day when you are more receptive to open-mindedness you may realize on a quiet Sunday afternoon examination of my archived posts, that now and then I was right.
      I’m flattered actually….

  15. mudguts says:

    you are arguing the case.. good to see you have stopped whingeing tho.. it was getting unbearable over at skeptoid comments and you carried it a bit into here..

    Now we have to work on your research skills.

    Research requires analysis.. not copying what someone says in a blog or advertorial… or a non existent coffee table book..

    I suppose it will take a while..

    • Macky says:

      I didn’t have to research very far, the sources for my skepticism were easily accessed on mainstream, but seriously ignored by those whose belief system was being challenged.

      Other sources were US govt agency files, and you can’t get much more “official” than that, said files directly in conflict with whatever Official Story as endorsed by Skeptoid was dealing with.

      Other research was not research at all, nor did I ever promote it as such. It was simple things that those that slavishly adhere to what they are being told by “authority” can try for themselves, instead of having to look up the latest science journal to see if they are allowed.

  16. mudguts says:

    we know you didn’t do a skerrick of research.. copying, cutting and pasting is like that when you feel that you are Brian’s invited crank, woo, quack and conspiracist rep.. We understand that..

    No mea culpa necessary..

    I did check the archives and you did say you were commenting on pop culture and popular culture references and that was always only what you ever needed to do..

    No Mea culpa necessary..

    But I noticed that you were incredibly rude to Alex Cannara the bloke who is a guest at the commonwealth club a national nuclear design advisor and a promoter for nuclear energy.

    You could have looked him up before you popped your spout at him.. But.. research s research right.. gutter research (copying somebody else’s trash) lets you miss those opportunities.

    Mea culpa is required for that..

    Ok.. let me introduce you to google scholar.. its been around for so long you were working (ok.. functioning) when it was available.

    In the search bar type scholar. It will yield publications of all stripes, their authors dates, descriptions and abstracts, ISBN etc etc etc.. Have a field day..

    You will find that coffee table book you invented from the spiritual site was first published in 1983 and the methodology you described for :finger peeping” was a cut and paste job from the spiritualist site. Amasing how the two were identical!!!

    Can you imagine an energy of that type Macky??????

    • Macky says:

      “You will find that coffee table book you invented from the spiritual site was first published in 1983 and the methodology you described for :finger peeping” was a cut and paste job from the spiritualist site. Amasing how the two were identical!!!”

      Haha you are flat out lying through your dentures now Henk.

      I’ll tell you why. I don’t read spiritualist sites whatsoever, nor any of their recommended books. I pulled the technique out of a kung fu book from an earlier time, as you well know if indeed you are genuinely reading archives from then.

      The point is though (whatever the source is for the exercise) is that you asserted that you had seen what I was talking about immediately.
      You said it, right ?

      Describe what you saw ? That’s a straight question you’ve been avoiding for years.

      Care to change all that ?

  17. mudguts says:

    it was a Ki Chung book first.. then it was a Qi Gong book then it was a kung fu book.. Macky.. I loaded your text into a search and bingo..

    Imagine the coincidence .. Imagine the energy Macky!!!!

    I did describe it.. The problem was you didnt read it until you went off into one of your self protectionist rants. It was as said a property of the light (the small hole) and the way the light enters your eye at a forced unusual situation. Had you ever learned to use your cameras properly pretty much the same thing as when you stop right down. As I said.. on the post..

    No spooks.. no zip.. o spiritualist planes or religious dimensions with a hypochondriac at the centre.. Just the light.. But you can do the same thing with just looking at the edge of an object with a good light to dark transition edge. You will get phosphor like effects.. If you had a real coffee table book.. as I said at the time.. you could have tried it. D****t.. you could have tried just the coffee table.. But I said all this at the time.

    Really.. you dont even have to do the poncy hole thing.. as I said at the time.

    Problem was.. as here today.. you had to ignore it all for a rant op..with inclusive whingeing.. Nothing new then.. but you were playing the part of the invited loon, crank quack and conspiracist.

    Wonder if you learned anything from that.. A b******t book.. a b******t edition will leave you looking Chi’zy if you want to talk about anything else when you get an answer..and promptly ignore it.

    Etheric.. straight from the spiritualists and conspiracists. You sure you arent american? They have an awful lot of this woozy stuff going around. Thats why Brian started Skeptoid proper.

    • Macky says:

      If you actually knew what you were talking about you would know that Chi Kung ( not Ki Chung as you put it ) is one and the same as Qigong or Qi Gong. And it is a form of kung fu.

      So your statement “…:finger peeping” was a cut and paste job from the spiritualist site. Amasing how the two were identical!!!” is indeed muddyguts fabrication as I said.

      Your profound ignorance outside your chosen and “religious” scientific disciplines is frankly astounding, and your reluctance to convey to Skeptoid what it was that you alleged you had seen is not diminished by your paragraphs of diversionary “looking at the edge of an object” or small holes whatever.

      You made the statement that YOU HAD IMMEDIATELY seen what it was I was talking about.

      If you now allege at this very late date after well over a dozen (that’s 12 in English, Henk) requests that you had already described it, then why didn’t you simply repeat yourself for clarity and I would have acknowledged that I had missed it.

      You DIDN’T describe it before, in fact, and it remains yet another one of the many straight questions that you refuse to answer.

      I said several times that “etheric” was a convenient term to use, and acknowledged that it was certainly not scientifically valid. Your continued allegations “straight from the spiritualists and conspiracists.” is fraudulent and blatant lying.

      You’re a disgrace to your profession as a scientist. You would have made a better politician, with your fabricated and confabulatory remarks.

  18. mudguts says:

    PS I did warn you right at your entry with bluster, I will search blocks of texts.. as I hate copy artists.

    • Macky says:

      Go ahead. I’ve always said if I’m wrong I’ll admit it. The only thing I’ve copied and pasted from memory was my original LHC post from another more casual forum.
      I readily admitted that I did that for convenience, and asked you what was the problem.

      In the meantime “The point is though (whatever the source is for the exercise) is that you asserted that you had seen what I was talking about immediately.
      You said it, right ?

      Describe what you saw ? That’s a straight question you’ve been avoiding for years.

  19. ausGeoff says:

    Excuse me for interrupting here…

    Macky and mudguts; would you mind carrying on your puerile little vendetta somewhere else, rather than filling up this thread with your personal pet peeves against each other. You sound like a couple of little kids in the schoolyard with your “My dad’s truck is bigger than yours” type nonsense. And you need to understand that NOBODY else really cares what you think of each other. I’m surprised Brian hasn’t shut you down.

    • Marg says:

      I certainly agree ausGeoff.

      Henk van der Gaast and myself brawled for over 3 years on the old Skeptoid. We both had posts removed, quite deservedly.

      I am always prepared to be corrected by better information/evidence than mine, and I have altered my views to suit on several occasions.

      Most of the scientists who have posted to Skeptoid have been more than reasonable with mutual discussions, and I have corrected my stance accordingly when presented with their superior knowledge.

      Henk v unfortunately chose a rather more unsavoury method of delivery which normally I would have ignored, but for his outright untruths and snide insinuations.

  20. mudguts says:

    Look.. If you post quack garbage in a 1200 charachter forum, you get the equivalent response.

    I am not sure if skeptoid original was ever meant to be a forum for discussion so I left it alone.

    I am not sure what you “brawled” over Marg but had you done so, you think I would remember it..

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