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**Using Interactive Teaching of Probability to Explain Irrational Beliefs**

Ken Stange Nipissing University North Bay, Ontario

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**My Philosophy Re Teaching Intro Psychology**

Most students are not going to become psychologists or scientists, but science is going to be a major influence on the world they live in. So students will benefit more from learning critical thinking and understanding how science works and how to evaluate what tries to pass as science than from learning specific findings––which is not to deny the importance of knowing facts.

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**My Philosophy Re Teaching Psychology**

Because psychology is such a sloppy, soft science, an understanding of the scientific method is critical to attaining healthy skepticism. And that means understanding basic principles of statistics and probability theory. So I try to teach critical thinking and skepticism by the use of probability theory.

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**My Approach To Debunking Irrational Beliefs**

I eventually explain that irrational beliefs are often based on what seem like reasonable assumptions and the evolutionary benefit of our innate tendency to see relationships…

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**Causes of Irrational Beliefs**

Eight Reasons We Are Prone To Believe In Nonsense We are hardwired to see patterns and order. We only notice odd coincidences. We are prone to projection. We easily trust false memories. We are prone to wishful thinking. We are too willing to trust ‘authority’. We find it easier to believe than to question. We don’t understand probability and chance.

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I Become The Psychic But before I talk about this, I do a lecture unit where I pretend to be a psychic and get volunteers from the class to act as skeptics. I try to confound them with what appear to be inexplicable and counter-intuitive predictions, which in the following lecture unit I’ll explain in terms of probability theory.

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**Put Your Money Where Your Mouth Is!**

The best way to convince someone of the validity of one’s position is to make them put up or shut up–– and then take their money. So every game involves betting against me (the alleged psychic). Of course, in the end I (a soft touch) forgive all debts incurred, despite the fact that the university doesn’t pay me enough, and the lesson would probably be more effective if I didn’t let them off the hook.

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**So Here Is My Powerpoint For That Unit**

The lecture unit has five parts based on the following. Aces Game (Let’s Make A Deal) Spot The Human Game (Human Inability To Generate Random Events) Bonded By Birth Game (Negative Probability) Find Another Psychic Game (Exceptions Eventually Happen) Overdue To Win Game (Gambler’s Fallacy) I then follow the unit I’m about to present with explanations of the probability theory behind each con. But today, I’ll interweave slides with the actual counter-intuitive probabilities, so you see how safe my bets are.

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**Scientific Method I: What Isn’t Science**

Unit 2, Part 1 of 3 “Psychic Fun And Games” (‘Proof’ of Psychic ‘Powers’)

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Warmup/Wakeup A student from Nipissing spent study week in Las Vegas. He won $100,000! He didn't want anyone to know about it, so when he got home late at night he dug a hole behind his dorm and planted the money in it. The following morning he walked outside and found the hole empty. He noticed footsteps leading from the hole to a house down the street from the student residence, a house which he knew was owned by a deaf-mute. So he called up his psychology professor, Ken, who he knew understood sign language and asked him to meet with him at the deaf-mute’s house. The student then grabbed a gun that he kept in his room to impress his room-mate. The student and Ken intercepted the deaf-mute man leaving his house and confronted him. “You tell this guy that if he doesn't give me back my $100,000, I'm going to kill him!” the student screamed at Ken, pulling out his gun. Ken promptly conveyed the message to the frightened thief who promptly confessed in sign language, “I hid it in my backyard, underneath the cherry tree.” Ken then turned to the student and said… “He said he's not going to tell you. He said he'd rather die first.” Copyright Ken Stange 2007 2

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**Think About This Before We Begin**

“There’s a sucker born every minute.” – P.T. Barnum (attributed) Copyright Ken Stange 2007 3

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**Unit Outline Five Psychic Games Aces Game Spot The Human Game**

Bonded By Birth Game Find Another Psychic Game Overdue To Win Game Copyright Ken Stange 2007 4

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**Five Psychic Games Please be dogged in your quest for knowledge!**

Copyright Ken Stange 2007 5

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**Five Psychic Games! Let’s play five cool games!**

The “Aces” Game The “Spot The Human” Game The “Bonded by Birthday” Game The “Finding Another Psychic” Game The “Overdue To Win” Game All require two players: A Skeptic A Psychic – Me! Copyright Ken Stange 2007 6

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Five Psychic Games! As good students trained in critical thinking, I’ll let one of you volunteer to be the Skeptic for each of these games. I’ll be the Psychic! Copyright Ken Stange 2007 7

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**Five Psychic Games! Games are no fun without some risk.**

So these will be played for real money! I will accept IOUs from those who want to play and don’t have any cash on hand in the unlikely event they lose! (We can use pennies to represent loonies.) I, however, will pay up with hard cash immediately if I lose. Copyright Ken Stange 2007 8

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The Aces Game Copyright Ken Stange 2007 9

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1: The Aces Game There are two players in this game: A Skeptic and a Psychic. Each brings $10 to the game. There are three cards One of these is an ace, a winning card. Two of these are number cards and losing cards. The Skeptic shuffles these and holds up his hand. The Psychic guesses which card is the ace. Of course, he only has a one in three chance of picking the ace. Copyright Ken Stange 2007 10

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The Aces Game The Skeptic puts the selected card face down on the table and then reveals one of the other cards the Psychic did not choose and also is not the ace and puts it aside, face up. The Psychic can now choose to change his selection to the card the Skeptic is still holding or stick with his original choice which is face down on the table. Of course it shouldn’t matter, but he is still given the chance to fine tune and revise his original psychic intuition. Copyright Ken Stange 2007 11

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The Aces Game Once the Psychic has made his decision, the card he has chosen is exposed. If it is an ace, confirming his psychic powers, the Skeptic must give him a dollar. If is isn’t an ace, the Psychic has to give the Skeptic a dollar. The game continues until either the Psychic or the Skeptic loses the initial ten dollars invested in the game. Copyright Ken Stange 2007 12

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The Aces Game I am the Psychic! And you think I can’t possibly win in the long run? Okay, then… I need a volunteer Skeptic from the class with ten bucks to back up his skepticism, someone willing to put his money where his mouth is! Copyright Ken Stange 2007 13

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The Aces Game ON WITH THE GAME Copyright Ken Stange 2007 14

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**The Aces Game So you doubted I was psychic!**

That cost someone ten bucks. Copyright Ken Stange 2007 15

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**Overview Of Subsequent Explanation**

Aces Game The actual odds in favour of switching = 0.67! This is best explained to students by pointing out that if the game is played with a full deck of cards, it is an identical situation. Then surely anyone would switch if they were shown 50 non-winning cards.

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Spot The Human Game Copyright Ken Stange 2007 16

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2: Spot The Human Game I can feel the vibes from paper if what is written on it is the result of human consciousness or merely random. Copyright Ken Stange 2007 17

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Spot The Human Game For any Skeptic still doubting my psychic ability, I will now demonstrate the ability to feel residual human touch on paper. I need two student volunteers. One will flip a coin 200 times and record on a paper the sequence of head and tails with ‘H’s and ‘T’s. The other will write out a random sequence of 200 ‘H’s and ‘T’s. They will each write some code on the back to identify their paper. Another student will shuffle the papers and present them to me to ‘psychically bond’ with. Copyright Ken Stange 2007 18

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Spot The Human Game I then will take an equal odds bet of ten dollars (from any skeptical student) that I can select the paper which the student who generated the random numbers wrote, as opposed to the one who simply recorded what the coin flips generated. Takers? Copyright Ken Stange 2007 19

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**Spot The Human Game Sorry to take your money! Skepticism doesn’t pay!**

Copyright Ken Stange 2007 20

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**Overview Of Subsequent Explanation**

Spot The Human Game Humans trying to emulate random sequences believe ‘runs’ are rare, while in reality they are common...

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Humans trying to emulate random sequences will almost never place more than four heads (or tails) in a row.

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In a true random generation, the probability of at least one string of 5 or more identical outcomes is and for a sequence of 6 it is 0.96!

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**It is easy to spot which is human generated: it is the one that looks least random!**

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**The Bonded By Birthday Game**

Copyright Ken Stange 2007 21

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**3: Bonded By Birthday Game**

As a psychic I can feel vibes that tell me there is an astrological bond between two individuals in the first several rows of the class. Copyright Ken Stange 2007 22

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**Bonded By Birthday Game**

Ah yes, I feel it: it is identical birthdays indicating similar personalities and fates. I know that there are 365 days in the year and the likelihood of two people in a small group having the same birthday is extremely unlikely, but hey I’m psychic and I feel it has happened today! Copyright Ken Stange 2007 23

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**Bonded By Birthday Game**

For any Skeptic still willing to doubt my psychic intuition I propose the following. If I can’t find any two students with the same birthday among the 50 students sitting closest to me I’ll give the Skeptic $25! Actually I feel they are even closer than that, for the vibrations are strong, but certainly these kindred souls are in close range. So I’m willing to bet that this statistically improbable conjunction of souls has happened today in this classroom! Copyright Ken Stange 2007 24

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**Bonded By Birthday Game**

I will count out the fifty students closest to me. Then starting in the first row I will ask each student in turn to loudly say the month and day of their birth. If and when another student from the fifty selected hears the same month and day of birth as his or hers, that student must put up his or her hand signalling the finding of an astrological soul-mate—who of course I just knew was in this small group. Copyright Ken Stange 2007 25

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**Bonded By Birthday Game**

However, even skeptics have to put their money where their mouth is, so I need a volunteer who is willing to bet on winning that $25… and agrees to pay me… a mere $5 if I find two souls astrologically linked by the same birthday among the 50 students asked. $10 if I find two souls astrologically linked by the same birthday after only asking 40 students for their birthday. $15 if I find two souls astrologically linked by the same birthday after only asking 30 students for their birthday. $20 if I find two souls astrologically linked by the same birthday after only asking 20 students for their birthday. $25 if I find two souls astrologically linked by the same birthday after only asking 10 students for their birthday! Copyright Ken Stange 2007 26

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**Bonded By Birthday Game**

ON WITH THE GAME Copyright Ken Stange 2007 27

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**Bonded By Birthday Game**

So you still doubt my psychic powers! Copyright Ken Stange 2007 28

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**Overview Of Subsequent Explanation**

Bonded At Birth Game The actual probability of getting two people with the same birthday is better than 50% with only 23 people asked.

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**The Find Another Psychic Game**

Copyright Ken Stange 2007 29

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**4: Finding Another Psychic Game**

Don’t feel bad! Psychic powers aren’t as rare as usually assumed. As a Psychic, I can feel in my psychic soul that there is another psychic out there in my audience. I will now use my powers to find this person. Copyright Ken Stange 2007 30

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**Finding Another Psychic Game**

I am going to flip a coin, and each of you should dig deep into your souls and ‘see’ if it is heads or tails. I will then reveal whether it was heads or tails. If you are right, you should put up your hand. Unfortunately, if you are wrong you are removed from the game and aren’t allowed to make any more attempts to psychically ‘see’ the outcome of subsequent flips. (Keep your hands in your lap, please!) I will continue to do this until I have only a very few individuals who have always been correct in their psychic insight into the coin’s outcome. Copyright Ken Stange 2007 31

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**Finding Another Psychic Game**

ON WITH THE GAME! Copyright Ken Stange 2007 32

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**Finding Another Psychic Game**

Will the Psychics I have found please agree to the following game to confirm their powers? I’m going to toss a coin ten times. Given that you’ve already demonstrated an amazing ability at sensing the outcome of coin flips after many flips, you should win every time! So I’ll give you $1 every time you correctly sense the outcome of the coin flip. That’s an easy ten bucks for a psychic. However, it is only fair that if your psychic powers fail, you have to give me $5 every time your answer is wrong! Fair enough? Any takers among my psychics? Copyright Ken Stange 2007 33

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**Finding Another Psychic Game**

What!? No confidence in your own powers! I’m so disappointed! Copyright Ken Stange 2007 34

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**Overview Of Subsequent Explanation**

Find Another Psychic Game Each coin flip reduces the numbers of ‘psychics’ by 1/2. My lecture size is about 200 students. Obviously, I’m able to reduce the number of individuals consistently guessing correctly to 1, 2 or 3 by only 7 or 8 flips.

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The Overdue To Win Game Copyright Ken Stange 2007 35

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5: Overdue To Win Game Okay, is there still a Skeptic willing to agree to take on the Psychic with another little gambling game? It is a game that surely the Skeptic must win unless the Psychic (me) is really psychic! Copyright Ken Stange 2007 36

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Overdue To Win Game Knowing probability theory and having common sense, the Skeptic knows that if a fair coin is flipped and lands heads up three times in a row, tails are way overdue, for a fair coin has to come up (on average) heads fifty percent of the time and tails the other fifty percent. (The probability of four heads in a row is ½ raised to the fourth power or only 1 in 16!) Thus it is a pretty sure bet that the next flip will come up tails. Copyright Ken Stange 2007 37

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Overdue To Win Game “But this does not factor in psychic powers to control which way a coin lands!” says the Psychic. Those Skeptics who doubt this claim would certainly be willing to accept the following little gambling game and odds. Copyright Ken Stange 2007 38

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Overdue To Win Game An independent flipper flips a fair coin until it comes up heads three (!) times in a row. Remember the chance of four times in a row is only 1 in 16! But the psychic will accept 1 to 5 odds, being confident of his powers. The Skeptic (being probability-wise) knows the coin is highly unlikely to come up tails on the fourth flip so demands that… the Psychic (who claims to be able to control the flip by his powers) must pay the Skeptic $1 if the reasonable-to-expect tails comes up. Out of fairness, the Skeptic is sufficiently confident that tails are due that he agrees to pay $5 to the Psychic if the Psychic can use his powers to beat the odds and make heads come up a fourth time! To summarize: Tails means the Psychic pays the Skeptic $1, but heads means the Skeptic pays the Psychic $5. Copyright Ken Stange 2007 39

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Overdue To Win Game I need a volunteer who still doubts my psychic powers! Each player will start with $50 on the table, which will more than cover the bets. Psychic and Skeptic must agree to play at least six rounds of this game, after which either player can insist on another round. However, if any player runs out of money, the game is automatically over. We will start each round after a fresh coin has been flipped repeatedly until it comes up heads three times in a row. Copyright Ken Stange 2007 40

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Overdue To Win Game ON WITH THE GAME! Copyright Ken Stange 2007 41

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**Overdue To Win Game Hmm. Who has the greater winnings?**

Are there any Skeptics left?! Copyright Ken Stange 2007 42

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**Overview Of Subsequent Explanation**

Overdue To Win Game This is, of course, the famous Gambler’s Fallacy of which no more need be said.

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Conclusion 1 of 2 No animals were harmed in the making of this production. No psychic powers were used in the making of this production. No actors or confederates or shills were used in the making of this production. No marked cards or weighted coins were used in the making of this production. Not even any Skeptics were injured in the making of this production, for The Psychic will tear up those IOUs. Why? Cuz he’s a good witch! Copyright Ken Stange 2007 43

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**Conclusion – 2 of 2 No explanations will be given – for now.**

Stay tuned for the sequel: a lecture on “Why We Believe in Nonsense.” Copyright Ken Stange 2007 44

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That’s all folks! Copyright Ken Stange 2007 45

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**Cultural Enrichment “Bad Luck Soul”**

…by King Biscuit Boy & Sonny Del-Rio 5m Copyright Ken Stange 2007 46

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Acknowledgements Obviously all these counter-intuitive probabilistic results that I use are well known and not original with me. For example, I’ve seen Richard Dawkins use what I call “Find Another Psychic” in one of his lectures and Michael Starbird refers to most of these in his excellent Teaching Company lecture series on Probability. (Those charts of random versus human sequences of coin flips are borrowed from one of his lectures.)

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