Solution To The Kind-Hearted Magician — REVEALED!

Solution To The Kind-Hearted Magician — REVEALED!

Kip Hansen last week gave us the following scenario (which I’ve pared to bare essentials here, but check the original if you fret):


Sam shows us three cards, two Jokers and one Ace, then lays them on the table, face down and swirls them around a lot, mixing them up.

Sam then tells his Dupes that he will pay them $10 if they can “find the Ace”, and if they fail, they pay him $10. (Sounds a lot like street-side Three Card Monte doesn’t it?) The Dupes pick the middle card and the Magician puts a little Yellow Star sticker on it, but the Magician doesn’t turn it over yet.

The Magician takes pity on them and says, “Look, this card is a Joker”, and turns over the card on the left, leaving two cards – the one the Dupes picked and one other. Sam asks “Now, do you want to stick to your choice – card B? Or switch to the other one, card C?

Now, our Kind-hearted Magician, says “I can’t bring myself to cheat such a nice young couple. When you first picked, you had only a one-in-three chance of being right and winning $10. I’d like to improve your odds to make it fair. Here’s what I’ll do, using my Magic Wand as an Event Eraser, I’ll wave it over the cards like this . . . (waving wand slowly over the three cards now on the table) . . . and erase the last few minutes of time, when you were picking from three cards.”

Sam waves the Magic Wand and lo-and-behold the Joker on the left, in position A, begins to fade from sight leaving just a little shadow. “That’s better,” Sam says, “now, would you like to move your Yellow Star sticker to card C or leave it on card B?” If your star is on the Ace, then you win $10, and if on the Joker, you pay me $10.”


First, the three-card Monte. It’s always a trick. The odds are based on information hidden to you. You cannot win. Anybody that wins is a plant. But, on the rare chance you do win, because the “performer” slips up (it happens), you will be met as you walk away with your winnings and asked, with gusto, to donate them back to the performer.

I repeat: the probability you win, given the nature of the scam, well known to magicians and con artists, is 0. It will not happen.

Second, the re-envisioning of the Monty Hall problem in the kind-hearted magician. The answer is exactly, precisely, with no changes, the same as in the original Monty Hall problem, which I wrote about long ago.

Hansen’s clever re-telling of it resulted in a huge number (for us) comments, with a lot of misunderstandings and fuzziness.

Let’s walk through the answer. Recalling our unbreakable true motto: all probability is conditional on the evidence assumed. Nothing has a probability: probability is a direct deduction of the premises accepted. That’s it, and nothing more.

First set of premises: the card positions are unknown to you, the Dupe. This, in notation, which can be helpful, is this:

     Pr(You pick right | Unknown positions ) = 1/3.

Nobody is confused about that. But it’s not an interesting probability, because nowhere does the Magician (or Monty) allow you to pick the card at the outset. The trick only commences after you point to one.

Which, we see, you did. Now either you picked the true Ace or you picked a joker. The first has probability 1/3, the second has probability 2/3, as we just agreed.

If you picked the true Ace, the Magician can turn over any of the other two cards. Again, this has a 1/3 chance of happening. If you switched here (and the Magician allowed you to), then you will lose. With probability 1/3.

But if you picked a Joker, the Magician is limited to turning over only the remaining Joker, and not the Ace. This has 2/3 probability of happening. If you switched in these two situations, you win. With probability 2/3.

So switching is the best move.

That, so far, is a retelling of Monty Hall problem. We now move to the Magician’s final maneuver, which is to make the card he overturned disappear.

Well, making it is disappear is no different than putting a cloth over it. Or coloring it purple. Or lighting it on fire. Or doing whatever to it. It still remains the card he could turn over, which brings us right back to Monty Hall.

Switching is still the best move. Nothing has changed. The probability is:

     Pr(You pick right | Unknown positions & M can turn over only Joker ) = 1/3.

And that does not change if we add “He made cider squirt out of the Joker he turned over and into your ear” to the right hand side.

The confusion is this:

     Pr(You pick right | Unknown positions of 3 cards ) ≠ Pr(You pick right | Unknown positions of 2 cards ).

The first equals 1/3, the second is 1/2, as you’d expect. But that second probability has nothing to do with nothing. It certainly does not represent the situation you’re in. Why are you purposely throwing away information about what the Magician’s limitations are (he can’t overturn the Ace)?

There we go.

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  1. Dean Ericson

    Oh. I knew that.

  2. Dean Ericson

    I actually did get it right the first time — he called a tail a leg. But then the more I got to thinking about it the more my mind turned into a mobius pretzel, and the monster Uncertainty began to devour me. Thank goodness Briggs just cut its head off in no uncertain way.

  3. Dean Ericson

    How does the three-card-monte man make it impossible to win?

    I’m from Minnesota.

  4. Dean Ericson

    Nobody wants to admit they got snookered by Three-Card Hansen.

  5. john b(s)

    I feel like I was three-card-monte’d

  6. Your assumption is that the magician will ALWAYS turn over one of the two cards that you didn’t pick, and give you a chance to change your choice. But he hasn’t promised to do so, has he?

    If we assume that he knows what the three cards are, then when you pick one of the jokers, he can just stop, and take his winnings.

  7. Addendum:

    “he can just stop” (or he can just turn over the ace — same thing, but it enables him to pretend that he doesn’t know what the cards are)

  8. John

    Here is the confusion that your initial post generated.

    The magician “erase[d] the last few minutes of time, when you were picking from three cards.”

    If he only erased the presence of the 3rd card, then it is the Monty Hall problem. My assumption was that by “erasing the last few minutes of time” he also erased the chooser’s memory of there ever having been 3 cards, or that he overturned one. In that case, it seems as though there is some conditional – the actual real-world probability changes if the chooser switches, but the chooser, deprived of the information, can do no better than 50/50.

  9. john b(s)

    Ditto with John

    And Kip’s comments added to the confusion

    From an outside observer who doesn’t experience the loss of memory, it’s Monte Hall all over

    And Question 2 seems to make us out as advisors
    Q2. Regardless of your answer to Q1, what would you advise our young couple to do? Stick with their first choice, switch their choice, or flip a coin to pick between the two remaining cards?

    I can only ASSUME that advisory role remains and we DO know the odds even if the Dupes do not

    (Of course now we have a 1/3 chance of being the “goat”

  10. Kip Hansen

    Dean Ericson (re: June 21, 2021 at 9:08 am)

    It is hard to get people to think — really really think. That’s what Magicians do — they force you to think about the impossible (the Magic).

    All Stage Magic involves tricking the audience (whether 1 person or 1000 people). ALWAYS.

    My Kind-hearted Magician magically talked some of the knowledgeable readers here into doubting what they already knew about probability and the Monty Hall Problem.

    That’s all PATTER — the things a Magician says that distracts and leads the audience astray so that they see what he wants them to see and believes what he wants them to believe.

    My hope was that I could walk at least some of the smart people here down a garden path to a point where they had to really think hard about what principles their understanding of probability rests on.

    The road to true understanding is to force students to discover the basic rock-solid true principles for themselves.

    It is, in fact, as The Master says: “Recalling our unbreakable true motto: all probability is conditional on the evidence assumed. Nothing has a probability: probability is a direct deduction of the premises accepted. That’s it, and nothing more.”

  11. Kip Hansen

    Dave Burton (re: June 21, 2021 at 9:48 am and one more)

    Both MH and the Magician are forced to obey the rules as laid out my vos Savant in the original problem. Once the Dupe picks a card, MH or the magician MUST turn over one card. And it is that rule (evidence assumed) that forces the odds to 2/3 on switching.

    I may write a bit more about forcing later on.

  12. Brad Tittle

    Anytime the magician is telling me he is not cheating, I just assume he is cheating a different way. The more the magicians asserts his kindly heart, the more I choose not to play.

    But there is a guy on YouTube that wanders around his local area and films himself cleaning up yards. He cleans for free. He is getting some repeat business from it. But he is also racking up 1.5M views.

    If the Kindly Magician is truly kindly, chances are the backend is picking up the $10.

    The cynic does not go very far away.

    Because I read this initial article as a discussion of the Covid Vaccination game. I am a bastard right now. I don’t wear my mask even though I haven’t been vaccinated. No one is giving me crap..

    I jus lied. My son’s are both giving me crap. Wisely they only do it as we are leaving the house and not when we are wandering through stores. They are wearing their masks. I have explained to them why I am not wearing my mask. They are both Boy Scouts. Trustworthy is the first point of th law. I am violating trust doing what I am doing. But the magicians is always violating our trust. The vaccines are little more than a shell game.

    I am part of the control group. I hav volunteered myself into that position. Someone has to be in the control group.

  13. Kip Hansen

    Dean Ericson ==> (re: June 21, 2021 at 9:07 am)

    I was once a professional personal behavior counselor — and was working with a professional gambler. He made $200k a year playing poker in the casinos of Nevada. (His personal problem wasn’t gambling, but something else.) After many sessions, exasperated, I told him I was going to have to give up on helping him, but had one final question: Since poker is a game of chance, how is it that you are so successful, making a profitable career out of it? “Oh, simple,” he replied, “I cheat.”

    “How does the three-card-monte man make it impossible to win?” That’s simple — he CHEATS.

    There are many great YouTubes explaining how three-card-monty, as performed as a street-scam, works. Watch a few and never ever let yoursef get sucked into playing three-card-monty against a street artist.

  14. Kip Hansen

    john b(s) ==> (re: June 21, 2021 at 9:24 am)

    “I feel like I was three-card-monte’d” — I’m afraid you are correct. That’s the wonder and joy of magic.

    But I hope that it has been a powerful lesson to you and that you will have had that lesson firmly established in your mind:

    “…. all probability is conditional on the evidence assumed. Nothing has a probability: probability is a direct deduction of the premises accepted. That’s it, and nothing more.””

  15. Kip Hansen

    John ==> (re: June 21, 2021 at 10:03 am)

    You say confusion, the Magician says “distraction” or “misdirection” which is an essential part of his Art.

    Of course, you are right — you all were right, not matter which view you took on the points raised in The Kind-hearted Magician.

    You chose what conditionals you were willing to consider, and with that, were justified — RIGHT – in deciding the probabilities.

    Why were the answers different? DIFFERENT CONDITIONALS.

    The Master has spoken: “…. all probability is conditional on the evidence assumed. Nothing has a probability: probability is a direct deduction of the premises accepted. That’s it, and nothing more.”

  16. Kip Hansen

    john b(s) ==> (re: June 21, 2021 at 10:53 am)

    And you have my humble apologies — it is the Magician’s job to trick you into seeing what he wants you to see.

    Every participant in the MH Game has a different viewpoint, different levels of knowledge, and thus a differing set of conditionals when he sets out to determine the probabilities.

    Every answer can be found to be correct for the conditionals assumed. If some evidence is dropped then the probabilities shift — because . . . . “…. all probability is conditional on the evidence assumed.”

  17. Kip Hansen

    Brad Tittle ==> (re: June 21, 2021 at 11:30 am)

    To bring your issue back to the realm of probability — you and your kids are using different sets of conditionals regarding the risks (read probabilities for “risks”) surrounding Covid-19, mask wearing, vaccination, viral transmission, etc etc etc.

    And because “…. all probability is conditional on the evidence assumed” you arrive at different conclusions about those risks.

    This is what we all do in everyday life about almost everything, unconsciously.

    There is one tiny little other truth — for many things, we are playing only once. In a “playing only once” sense, probability doesn’t apply — you get the result you get. This is known also as the “Don’t Play Russian Roulette” rule.

  18. Dean Ericson

    Kip explains: “That’s all PATTER — the things a Magician says that distracts and leads the audience astray so that they see what he wants them to see and believes what he wants them to believe.”

    All the world’s a stage. We just saw the Globalist Magicians conjure up a frightful pandemic out of a minor bug. They made Global Warming look real by tricks of distraction, misdirection, and lies. They made an epidemic of racist cops shooting innocent blacks appear out of thin air. And so on. There is great power in magic, lies, and deception. The Overlords who mean to master us have mastered all the wicked arts of their master, the Father of Lies.

    A fine lesson, Kip.

  19. Brad Tittle

    @Kip Hansen — And “they” have managed to make not pointing a gun at your head with a bullet in it the roulette. Pointing the gun at your head and pulling the trigger is NOT Russian Roulette.

    My youngest just got in the driver’s seat of the car. I had to push him a little to press on the gas a little harder to get up to the speed limit. We managed to inject just a little of the conditional probability into the instruction. You can die driving too fast. You can die being too timid. The chance of dying in the passenger seat with a new driver is much greater than the chance of dying of COVID.

  20. john b()


    The police will stop you for driving too slow – in some states over 5 MPH below, they can stop you

  21. Kip Hansen

    john b(s) ==> (re: June 21, 2021 at 12:57 pm)

    And you are just as right today as you were then.

  22. Kip Hansen

    Dean Ericson –==> (re: June 21, 2021 at 1:04 pm)

    “All the world’s a stage. ” And the Magicians are hard at work — the ultra-Woke media leading the way with twisted presentations of what is going on — distracting and misdirecting the public’s attention from the Truth to the Magician’s Altered reality, using words that have had their meanings slightly altered to fit the 1984-ish “New Improved History”.

  23. Kip Hansen

    Brad Tittle ==> (re: June 21, 2021 at 1:16 pm)

    My father was a doctor, but had studied the required physics and hard sciences on the way. He rightly taught me, on then then already crowed and very dangerous Los Angeles, California Freeways that the safest speed to travel on the road is the speed of the other cars — matching the other’s speed results in fewer and safer accidents.

    The force in a two car collision is a factor of their relative speeds. Two cars head on at 60 mph – running into a brick wall at 120 mph.

  24. Joy

    Kip Hansen ==> (re: June 21, 2001 at 1:58 pm)

    The safest speed depends which vehicle you’e upon while ‘travelling.’
    On a bike, it’s faster than the rest, where the traffic is far behind and no faster than that, is safest. If it’s snowing? different premise!

    There’s safest speed to travel on the road statistically speaking
    then there’s the safest speed depending on what information you have about the situation as hand.
    so it’s the same illustrated point.
    and It’s not speed that kills, it’s coming to a sudden standstill without the niceties of breaks.

    According to Jo kenda
    “If it’s 1:00 in the morning on a Tuesday evening, hide in the wardrobe”
    That’s statistics for you.

  25. john b(s)


    … It’s not speed that kills, it’s coming to a sudden standstill without the niceties of “breaks”.

    pun unintended?

    Ray Bradbury said 3:00 AM was the most dangerous hour and there was no hiding in the closet

  26. Brad Tittle

    @Kip Hansen — Exactly. @John B — Exactly.

    When merging onto the freeway, a whole bunch of factors come into play. When I went to driver’s ed, my teacher taught me that I had responsibilities both in getting onto the freeway AND for letting people get onto the freeway. She suggested that I watch cars coming onto the freeway and put my car either ahead of where they would be when they merge OR behind where they will be when they merge. When I get on, I need to get up to the speed of the freeway and be actively assessing if I can get into traffic. Those rules have worked well for me.

    Others have suggested that when I am on the freeway, I should just maintain a constant speed so the people getting on can make their assessment without having to assess whether you are going to let them on or not.

    I am not here to give the right answer. I can only say that I do everything I can to not be in an accident while at the same time still leaving my house without curling up into a ball. Upping my EDC game though is causing me fits…

  27. john b()

    I remember the old PSA from the 60’s. A man walking down the highway kicks a headlight to the side of the road
    . . . . . . This guy was right … dead right … Watch Out For The Other Guy

    It used to physically drain me when I was learning to drive …

    I was 30 before I got my license (I would bicycle just about everywhere … bus in the winter)

  28. Joy

    Ask the biker, who came off his bike at 80mph, then found a new skill in the ability to run like the bionic man in slow motion giant steps until coming to another breaking method: rode on his bottom along the road for a bit moving from ‘cheek to cheek’ as they heated up in turn.

    He used his bottom, equipped with the correct leathers, kevlar, together with his new found skill, to slow himself down.
    Cars, incidentally were driving around him! nobody stopped…typical car drivers *dam bikes!
    He still ‘broke’ things

    Or the one who rode at 180mph or higher, on his fancy bike to Wales along the M4 but had to slow down for the tolls. flew off a bridge, through a deep pit of brambles which cushioned his fall. Landed on his shoulder, which he was asking someone to fix.

    It takes all sorts
    “It’s not bikes that kill it’s Volvo drivers. They kill more people than guns”
    I’ve heard it all now

    Statistics is rubbish!

  29. Nate

    So… the original comment was the correct one: “No, because it’s a con from the start. They don’t have *any* chance of winning.”

  30. Dean Ericson

    Kip Hansen: “There are many great YouTubes explaining how three-card-monty, as performed as a street-scam, works. Watch a few and never ever let yourself get sucked into playing three-card-monty against a street artist.”

    Thanks, I’ll do that. Always interesting learning how tricks are done. Finding out how you’re being fooled is salutary.

    “Everything You Know is Wrong” — someone oughta write a book.

  31. Russell Haley

    Kip Hansen said:
    “Oh, simple,” he replied, “I cheat.”

    I now assume that anyone presenting a game of chance or skill as a way to make money is “cheating” and anyone that participates and is successful is also “cheating”. Sports, Gambling, Insurance, Elections; You name it. If either the house or a specific player is successful it is because there is un-even odds created by external forces (e.g. cheating). It doesn’t always need to be overt (steroids) and can often be hidden in technical, legal or other complexity (e.g. Election machine software) so that only those well vetted in ALL the components of the system can see the true slant of the system.

    Institutions and governments cheat: “No counting cards” or “Equalization/Equity” initiatives
    Players cheat as well: counting cards anyway, steriods, eternal victim status

    The rules are only valid for those of us stupid enough to believe institutions are playing fair.

  32. Kip Hansen

    Nate ==> (re: June 21, 2021 at 3:36 pm)

    ” They don’t have *any* chance of winning.” – in the street-con known as 3-Card-Monty, that is correct.

    In he Monty Hall Game/Problem (or the real TV show, “Let’s Make a Deal!” contestants could and did win both big and small and some one very expensive new automobiles.

  33. Kip Hansen

    Joy ==> (re: June 21, 2021 at 3:12 pm)

    I have had the pleasure of coming off a (motor) bike at 60+ mph on a newly paved asphalt road — bare foot, swim suit and t-shirt for protective equipment.

    You can hardly tell by looking a me, all these 50 years later.

  34. Kip Hansen

    Russell Haley ==> (re: June 21, 2021 at 4:16 pm)

    Well, as one other reader put it, there are a lot of Magicians out there distracting and misdirecting us.

    My poker cheater used a team method — consisting of a team of ten or so participants who were well-know regulars at all the casinos. Well know players but not well know to be a team. They had a series of signals that informed each other of the values of their hands and thus could shift the pot to one of the team members. All it took was for any given table to serendipitously end up with at least two, three better, players from the team. Needing only two or three out of ten members made the combinations impossible to spot. They would meet up later for breakfast far out of town to split up the combined winnings. Sometimes, if they found a high-roller intent on losing his shirt, they would call in a team member to join them at a table. Each player on the team had to be an excellent poker player, so that they could stay and play all night and come out more or less even if they didn’t find someone to fleece.

  35. Xens

    The Monty Hall problem relies on the fact that the presenter will always reveal a wrong choice. If that can be changed, as with this strategy, it’s no longer Monty Hall. Two ways that a magician could change this.

    1) Reveal a card at random. This could be an Ace, it could be a Joker.

    2) (Much more sneakily) Reveal the Ace if the Dupes did not choose it, call them losers and send them home. If it was the Ace that they chose, convince them that this is the Monty Hall problem with the star trick, get them to change their choice to “improve their odds”, and once they do, show them that they’ve lost and send the home.

    I love Briggs, but were I a magician, I would definitely use trick 2 on him, and remind him about his own statements about probability while I counted my money afterwards.

  36. “Pr(You pick right | Unknown positions & M can turn over only Joker ) = 1/3”

    Let A = You pick right | Unknown positions & M can turn over only Joker

    then Pr(A) = 1/3

    (and definitely not let A = You pick right | Unknown positions & M can turn over only Joker & today is Monday & the cards are red & cards are turned over by my dog’s tongue. We have to have method to only list things we know are casual, I’m sure.)

    Great example of frequentism though if cannot derive probability by other means. Easy to pseudorandomly simulate games and see probability converge to 1/3.


  37. brad tittle

    @Kip == Let’s Make a deal was about the eyeballs of the viewers. Monty wanted the people to win. Winning brought more eyeballs. My grandmother laughed at the contestants. All she saw was the taxes on the winnings and the poor folks who thought they had won a car accepting below market payment for the car to pay the not so insignificant taxes. But she was born in 1918 and had experienced “Real” taxes. So she avoided paying them the same way Buffet did. Never realize more gains than you need to.

  38. Briggs


    For those who have any doubts, try it. Find a friend and just do it. Play a few dozen games staying, then play a few more switching. See which ones you win more.


    No, frequentism is always wrong: in frequentism no probability can ever be known until an infinite sample arrives. People always forget this and become logical probabilists when asserting/deducing probabilities, like in this example.

    We’re not adding wholly causal information, only some. If you say “Here is a bad with 1 red marble and 2 blue” the chance of drawing a red is 1/3. No efficient cause in that information. But there probative information. You can add sock color, but there is no probative, nor causal, information in it, thus it doesn’t change the probability.

  39. Joy

    Kip Hansen ==> (re: June 21, 2021 at 3:12pm)
    Then you became a statistician!
    Time is a great healer but statisticians never recover.

    Your bike experiment inspired the terms ‘asphalt ballet’ and ‘ gravel rash’

  40. Kip Hansen

    Joy ==> (re: June 21, 2021 at 6:08 pm)

    That is a scurrilous accusation! I never ever became a statistician….the very thought of it curls my hair.

    I became a lot of things . . . . a magician, a mariner, a spook (intelligence officer), a roadie, a hamster rancher, and a few things less-mentionable . . . . but never would I stoop to being a statistician!

    Take it back . . . or I’ll . . . I’ll. . . . I’ll . . . . I don’t know, but you take that back!

  41. Joy

    It’s retracted! (sorry, my projection entirely)

    …but now you’ve told me you were a spook! A spook! That’s done it now..
    so it was you all along…

    Did you ever train dolphins?

  42. John B(S)

    Why does Fa speak?

  43. DAV


    The Monty Hall problem relies on the fact that the presenter will always reveal a wrong choice. … a magician could change this.

    1) Reveal a card at random. This could be an Ace, it could be a Joker.

    No it doesn’t depend on the presenter revealing a wrong choice. As long as the revealed card is not an ace, it’s identical to the MH problem. If it is an ace, the game is over. The presenter knowing which of the two is not an ace allows extending the game and heightening the tension.

    The probabilities are deduced by realizing the chance of selecting the ace from three cards is 1/3 while the chance is 2/3 the ace is one of the unpicked cards. These probabilities remain regardless of what the presenter does although when a joker is revealed there is a seeming paradox where probability of picking an ace seems to change from 1/3 to 1/2. This paradox is caused by faulty reasoning.

    If the presenter has the option of not offering the switch based on the presenter’s knowledge what has changed is the probability of winning and not the probability of the location of the ace.

  44. John B(S)

    I’m remembering the trailer for the movie

    I’m guessing Fa or Pha was short for Alpha

    (Day of the Dolphin – George C Scott)

    Hmmm … the next year George was in Firestarter …

  45. “No, frequentism is always wrong: in frequentism no probability can ever be known until an infinite sample arrives. People always forget this and become logical probabilists when asserting/deducing probabilities, like in this example.”

    “Wrong” and “known” are interesting choices of words to me. Of course, something doesn’t have to be known to work (and if it was literally known already there would be no need for experiments and surveys in the first place). Ever heard of approximations? Much like one doesn’t need literal infinite number of infinitely skinny rectangles under curve to get an area, or engineers don’t need all the digits of pi to do a calculation, just enough until convergence. Another example, the long-term relative frequency within a reference class “settles down” in [p-e, p+e] by the Strong Law of Large Numbers (SLLN) for any small e>0.

    Are you really going to argue that seeing the relative frequency of heads for a googolplex to the power of a googolplex to the power of a googolplex, 84 times number of flips isn’t enough?


  46. Robin

    @Kip Hansen:

    “the safest speed to travel on the road is the speed of the other cars — matching the other’s speed results in fewer and safer accidents”

    One of my subjects of study was Transportation Engineering – the design of traffic signalling, highway and bridge elevations, gradients and banked curves (we call these things ‘Super-Elevation’ in geek-speak).

    Your father was a smart man. We were taught clearly and with supporting data that “speed doesn’t kill, differential speed kills”. Our instructor even went as far as to say “If you are driving the speed limit, and everyone is passing you, speed up, you will be safer”.

    I studied Classical Statistics (ANOVA, p-values etc), but have migrated over the years to self taught probability theory (Cantor, Kolmogorov, Axiomatic Set Theory, Measure Theory, Bayes, etc). I’ve discovered I can break down almost any engineering problem using these tools (requires a great deal of prior experience and knowledge, however). Unfortunately few engineers are ever taught these things.

    Because my work is all about predictability, I cannot remember ever using p-values for decision-making.

    I also never understood why the experiments should be blindly randomised. In my investigative work I have always sorted the data into buckets of similar initial properties, geometries, design characteristics, etc, then select samples from these groups for comparison purposes. Measure theory can help greatly in this process.

    In the end, the most basic concepts and assumptions are the hardest to grasp. To do so requires a very deep understanding of the given subject, but they also make the problem at hand all the more interesting.

    Thank you Kip Hansen and Prof Briggs for this excellent set of articles. This website is truly a treasure.

  47. Kip Hansen

    Robin ==> (re: June 24, 2021 at 6:04 am)

    There are more ways to look at something than . . . . . (fill in he blank). . . .

    This is one of the Secrets of the Universe( a little grandiose but something like that…). Quite true.

    I have used what I learned as a junior performing Magician in my work as an essayist/science journalist many times.

    Briggs is certainty a treasure for the Pragmatist in us all . . . . (though he might deny even that).

  48. brad tittle

    I can take the discussion of the playing of the cards and Monte Hall at face value. I have a compartment in my brain where I play such games. Given all of the information and a kind hearted magician, our beloved host is correct.

    As much as I would like to wander the world where that is true. It is never true. We are constantly in the midst of misdirection. But since I have no money on the table, the misdirection is of little import, which takes us back to that little part of my brain where I can play the game.

    The Monte Hall problem is NOT the 3 card monte problem, but the reason it is not has more to do with who the stooge is. In Monte Hall, the stooge is the audience on the other end of the TV. But the Monte Hall answer is still that probability thing where the audience is the one who is winning or losing NOT the person on the stage. The person who loses on stage may actually be the winner overall. Being told you have won a car and then realizing 20 minutes later you really only won maybe 1/2 a car is a kick in the sensitive parts. Getting the consolation prize may be better emotionally. Monte Hall was still a magician. He got people to watch. He got people to wait in line to watch live and participate in the show. The show is still on … I think.

    How do you measure the value of that?

    Did Brave New World predict the show? How close is it to “feely”?

    Understanding the answer the Monte Hall problem is not about how to win at Monte Hall. It is about how to make everyone else think they are winning at Monte Hall and walking away with the cash.

    My next door neighbor works for an online entertainment company. People send the company money so they can play casino games and win fake money. What do they do with the fake money? Play more games. No cash. No Prizes. Except to the entertainment company. I have to go talk to him some more. He does their math for them on winning ratios. Their business has expanded over the last year.

    Interesting conversation in line with our hosts predictions from a pathologist.

  49. john b()


    Heck of a video

    He wants the conversation opened up by Dr McCullough opened up


  50. Ryan

    I’m sorry but this is simply incorrect. The magician removed the card from the universe. He performed the most difficult of the three categories of miracles, the creation or destruction of material reality. Satan or a demon could move the card to another place in the universe, and that of course would not change any underlying information the probability is contingent on. That is simply an illusion. But the miracle magician has actually deleted the card from the whole history, present and future of the universe. By work of his miracle, *the card was never there to begin with*, thus changing the information the initial probability was contingent on. Prior to the miracle the probability was 1/3, but post miracle both the original and current probability are 1/2. Thus there is no advantage to be gained by switching choices.

    Of course, if our magician wants to achieve sainthood he should really stop evacipating jokers and get to brain tumors and the like.

  51. Doug M

    When I was in high-school, some friends of mine went into New York City. They saw the 3 card monte dealer, and spent several minutes watching him work the crowd. After watching several dupes lose their money, they picked up on a few of the tricks the dealer was employing. With their confidence up one of them placed their $20 bill on the table.

    The dealer shows the cards, mixes them around and invites them to choose.

    My friend chooses.

    The dealer says, “you’re obligated to take the other card.”

    My friends look at each other, and back at the dealer.

    Someone behind them says, “That’s right, you’re obligated.”

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