Predicting Random Events Accurately 60% of the Time?

[Chris Connelly]

Today, my psychology professor asserted that people can accurately predict random events roughly 60% of the time (he qualified this statement by saying that the actual figure lay around 57% and he was rounding). I asked him for an explanation of this claim, and in the following class discussion, he proceeded to assert that a random person predicting coin tosses would be right, on average, 60% of the time. I countered that that was impossible and the figure should be 50%, but he insisted on 60%. He said I was confusing the actual event with the prediction and that, while ratio of heads to tails should average 50/50, any person or machine making predictions should expect to average around 60% accuracy.

I discussed this claim further with a friend in the class, who said he had seen the study the professor referenced and insisted that a person predicting coin tosses would, in fact, average 60% accuracy. I insisted this was not possible, but he said that it was statistically proven, even though it seemed counterintuitive.

Later, I got a chance to engage the professor further, and he reaffirmed his assertion. He also added that a person predicting what card would be chosen at random from a deck of Zenner Cards would observe the same 60% success rate. He again countered my arguments by saying I was confusing the probability of the event itself with the probability of the prediction. I realize these figures are different (the ratio of heads to tails in a sequence of coin tosses may be 50/50 while the percentage of current predictions may differ substantially), but as far as I can see, the rate of accuracy for predictions should be 50% for a coin toss or 20% for the Zenner Cards no matter how you slice it.

I'm getting the feeling my friend and professor are misquoting whatever study they're trying to reference, but both were adamant about a 60% rate of prediction accuracy on coin tosses and Zenner Cards. Can anyone shed some light on what they might have been getting at?

[Ladewig]

The most efficient counter argument would be that if large swaths of the population could do that 60% of the time, the casinos with roulette wheels and craps tables would be out of business. They are not, therefore the claim fails.

The second most efficient argument would be to have him predict the outcome of three groups of 30 flips.

[lionking]

If this were true, casinos would go broke tomorrow. I don't believe it and would love to see a reference to the so-called study.

ETA, bugger, Ladewig beat me by a millisecond.

[wardenclyffe]

I have no idea what they are talking about, but why not test it with them? It only costs a penny and 15 minutes.

Ward

[fls]

What study did the professor refer to?

It sounds like he is arguing for anomalous cognition (i.e. psi), but there are some normal biases in coin tosses (the coin is more likely to land with the same side facing up, and in a toss it is more likely to land heads and in a spin it is more likely to land tails (or is it the other way around?)), which changes your knowledge about the results.

Linda

[GreyICE]

There's a couple of times you can utterly bug out statistics, but it all works mathematically.

If you flip two coins, and one comes up heads, there's a 67% chance the other one was tails.

It really sounds like he was getting something like that screwed up with predicting which coin flip does what.

[sailingsoul]

Not to be off topic, what does ETA mean? Lionking or anyone. SS

[GreyICE]

Edited to add

It means someone hit the edit button because they saw something and didn't feel like double posting. Or triple posting. Or one time, 8 posts in a row.

It's much more polite ;)

ETA: See? There's now an 'edited by GreyICE at the bottom of my post'

... well, if I wait the two minutes.

[GreenLines]

Sounds possible, but one study isn't enough for me, need to have a few more to be certain.

[Brian-M]

He's wrong... ask him for a demonstration.

The coin-toss suggestion is a good one, but 50% is not too far away from 57% -- you'd have to add-up the results, and even then he could claim the lower result was a chance anomaly, or that he wasn't at his best that day.

A Zenner-card test would be better because wrong answers would be much more frequent, and by placing cards from the correct guesses in one pile, and cards from the incorrect guesses in another you'd have a nice visual demonstration of how badly he's failing that he can't ignore.

[Chris Connelly]

Ladewig,

It's funny that you bring up casinos - I made the same point during my conversation with the professor, specifically regarding roulette. He said a roulette wheel was "different" and he'd have to think about why. He also said that a roulette wheel would need an enormous amount of trials to produce the 60% results, and most people don't gamble long enough to see it work out (inconsistent, I know - never mind the thousands of "trials" happening nonstop in Vegas).

At one point, I thought the professor might have been thinking that the person could see the coin in the air and project its outcome, but he said the results could be obtained blindfolded. He also insisted no paranormal ability was involved, and it was sheer probability.

During the same conversation, I tried to explain that a 60% rate of accuracy would be unimpressive over, say, 10 trials, while the same 60% rate would be far more impressive over a greater number of trials. The point was lost, unfortunately - the professor said it only sounded more impressive and that there was no statistical difference, while my friend said that the probability of hitting 6 out of 10 is the same as that of hitting 60,000 out of 100,000.

Unfortunately, neither my friend nor the professor has much interest in experimenting (though I do have an outstanding bet with my friend). I'll post the study here if the professor tracks it down - he said he'd look for it. My friend thought it had been conducted by the American Psychological Association.

Incidentally, would this qualify for the MDC? I brought up the Challenge, and my professor said he had heard of it, but it required a rate of accuracy of 95%. I may be mistaken, but I'd imagine if someone could predict the identity of a Zenner Card 60% of the time under properly controlled conditions, that should earn them the million.

Chris

[fls]

It's also important to realize that the probability of each event is not necessarily one divided by the number of possible events. And when you are dealing with an ordered set, like a deck of Zener cards, then the probability is described by permutations instead of combinations, which increases the probability of getting it right compared to one in five.

Linda

[Chris Connelly]

fls,

Regarding the Zenner Cards, I did bring up that issue, but the professor had in mind an experiment with 5 shuffled cards where a prediction was made and one was selected. The card would then be replaced and the deck shuffled before another prediction was made, making each trial independent.

If I do decide to experiment, are there any online calculators or tools that would help me calculate the odds of, say, getting 60 coin tosses right out of 100? I'm also thinking about doing something with a coin toss simulator or random generator - if there was a way to generate two lists of coin toss results (prediction and trial) and cross reference them, that would be a fairly quick way of showing the professor's claim wrong.

Chris

[back2basics]

Read this book, its covered in there. I am not even going to try and explain it and don't have the book with me. The thing that stood out was his comment "probability of the event itself with the probability of the prediction" i remember that's what was covered. He does a good job of explaining it.

http://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0375424040

[roger]

Where on earth are you going to university? This professor doesn't understand the simplest aspects of statistics.

[roger]

I wonder if they are referring to something like this:

http://www.telegraph.co.uk/science/science-news/6911463/Coin-toss-is-all-in-the-wrist-say-scientists.html

(for people unwilling to click - it points out you can learn a coin flipping technique that is biased somewhere between 54-68%, which is entirely different from predicting a fair coin toss)

[wardenclyffe]

I would think that a 60% Zener card test would easily qualify for the MDC. As a professor, it should be easy for him to get whatever academic affidavits he'd need and if he does that, the media should not be far behind. And depending on where you are, there are other challenges (for less than a million) available:

There's the Australian Skeptics' AU$100,000 Prize
http://www.skeptics.com.au/features/prize/

There's the IIG's US$50,000 Challenge
http://www.iigwest.org/challenge.html

There's the North Texas Skeptic's US$12,000 Challenge
http://www.ntskeptics.org/challenge/challenge.htm

There's Prabir Ghosh's 2,000,000 Rupee Challenge in India
http://rationalistprabir.bravehost.com/

There's the Swedish 100,000SeK prize offered by Humanisterna
http://www.humanisterna.se/index.php...d=27&Itemid=49

The Tampa Bay Skeptics offers a US$1000 prize in Florida, USA
http://www.tampabayskeptics.org/challenges.html

In Canada there's the CAN$10,000 from the Quebec Skeptics
http://www.sceptiques.qc.ca/activites/defi

In the UK, the ASKE organization offers £14,000
http://www.aske-skeptics.org.uk/challenge_rules.htm

Tony Youens in the UK offers £5,000
http://www.tonyyouens.com/challenge.htm

In Finland, Skepsis offers 10,000 Euros
http://www.skepsis.fi/haaste/

The Fayetteville Freethinkers offer a US$1000 prize
http://fayfreethinkers.com/

There's a 1,000,000 Yuan prize in China offered by Sima Nan
I've found a lot written about it, but no official web address for it. If anyone's got one, let me know.

The Belgian SKEPP organization offers a 10,500 Euro prize
http://www.skepp.be/prijzen/de-sisyphus-prijs/

Good Luck,
Ward

[Jeff Corey]

If I do decide to experiment, are there any online calculators or tools that would help me calculate the odds of, say, getting 60 coin tosses right out of 100? I'm also thinking about doing something with a coin toss simulator or random generator - if there was a way to generate two lists of coin toss results (prediction and trial) and cross reference them, that would be a fairly quick way of showing the professor's claim wrong.

Chris

Here you go http://www.graphpad.com/quickcalcs/binomial1.cfm
Here is the probability for 60 out of 100.

"Number of "successes": 60
Number of trials (or subjects) per experiment: 100

Sign test. If the probability of "success" in each trial or subject is 0.500, then:

* The one-tail P value is 0.0284
This is the chance of observing 60 or more successes in 100 trials."

[Chris Connelly]

back2basics,

That's exactly the book my professor was using (The Drunkard's Walk by Leonard Mlodinow) - he had it in hand as he lectured and read an excerpt to the class! Unfortunately, he couldn't track down the part specifically addressing the issue I posted about.

I understand the distinction between the probability of the event and the probability of the prediction - if you predict heads-tails-heads-tails... and the coin toss comes out exactly that way, the results are 50% heads and 50% tails with a 100% rate of accuracy for the prediction (that part is from my professor). The probability of predicting accurately, however, is still 50% on a coin toss!

Roger,

I'm actually taking a college-level (AP) course as part of my senior year in high school. I hear you though - I mentioned this to a statistics professor in the same school and he just shook his head.

ETA: On your second post, the same thought occurred to me (manipulation of the coin toss), but the professor said I'd still get the same results if I threw the coin from a cup while a blindfolded participant made predictions.

Maybe someone who has read The Drunkard's Walk can shed some light - I'm stumped at the moment as to what they were getting at.

Chris

[back2basics]

back2basics,

That's exactly the book my professor was using (The Drunkard's Walk by Leonard Mlodinow) - he had it in hand as he lectured and read an excerpt to the class! Unfortunately, he couldn't track down the part specifically addressing the issue I posted about.

I understand the distinction between the probability of the event and the probability of the prediction - if you predict heads-tails-heads-tails... and the coin toss comes out exactly that way, the results are 50% heads and 50% tails with a 100% rate of accuracy for the prediction (that part is from my professor). The probability of predicting accurately, however, is still 50% on a coin toss!


Chris


Listen to fls, she explained it simpler than they did in the book. The book covers it in more detail.

[Brian-M]

It's also important to realize that the probability of each event is not necessarily one divided by the number of possible events. And when you are dealing with an ordered set, like a deck of Zener cards, then the probability is described by permutations instead of combinations, which increases the probability of getting it right compared to one in five.


That's ignoring the effect of human fallibility. Chances are, the professor isn't going to be much good at keeping track of which cards have been used (unless he's a professional card-counter -- or the Rain Man).

If he's still be making his guesses on the assumption that each card is equally likely to show up, the results will still be close to 20% correct.

An extreme example would when there's only two cards left. If there's only two possible outcomes, in theory he has a 50% chance of getting it right, but in practice he'll have no idea which two cards are left, and only have get it right 20% of the time.

And as for the last card, there's only one possible outcome, so in theory he has a 100% chance of getting it right... but if he still has no idea which card it is, that doesn't help him at all.

[fls]

fls,

Regarding the Zenner Cards, I did bring up that issue, but the professor had in mind an experiment with 5 shuffled cards where a prediction was made and one was selected. The card would then be replaced and the deck shuffled before another prediction was made, making each trial independent.

That brings up the issue of adequate mixing (http://en.wikipedia.org/wiki/Markov_chain_mixing_time) if it was an actual experiment.

It does sound interesting. I hope the professor is able to give you more information about what he is talking about.

If I do decide to experiment, are there any online calculators or tools that would help me calculate the odds of, say, getting 60 coin tosses right out of 100?

There are lots of free online binomial calculators (or apps if you have a smart phone).

I'm also thinking about doing something with a coin toss simulator or random generator - if there was a way to generate two lists of coin toss results (prediction and trial) and cross reference them, that would be a fairly quick way of showing the professor's claim wrong.

Chris

You could do a Monte Carlo simulation with Excel, although it sounds like the experiments are taking advantage of a bias which might not show up in a model. Does this have something to do with early stopping (i.e. stopping when you're ahead) or a Random Walk where one side tends to be ahead more than the other?

ETA: I see you've answered the question as to the source. I'll look through Drunkard's Walk to see if I can figure out which part he's referring to.

Linda

[Chris Connelly]

I'm really inclined to set up an experiment now - using coin tosses, I'd need at least 59 / 100 accurate predictions to confirm my professor's hypothesis at the .05 level of statistical significance. That still leaves wiggle room (since the actual figure may be around 57%), but Zenner Cards would do the trick pretty quickly and easily. 5/10 accurate predictions would be statistically significant while remaining below the 57-60% figure my professor is claiming.

[Ladewig]

He also added that a person predicting what card would be chosen at random from a deck of Zenner Cards would observe the same 60% success rate.

He is talking about a case where there are only two symbols in the deck, or is he talking about a standard Zenner deck where there are five different symbols in the deck. If the latter, that is an amazingly simple thing to disprove with only a few minutes time. If I were you , I would bet him money on the outcome.

[Chris Connelly]

Ladewig,

He's talking about a packet of 5 cards, one of each symbol. The cards would be mixed, then a prediction would be made and a card would be chosen. The card would be replaced (after being recorded of course), the packet would be shuffled, and the procedure would be repeated. I couldn't believe he was making that claim, but he was adamant that that was the probability, and insisted I was confusing the probability of the event with the probability of the prediction being accurate.

It would be very easy to disprove - the chances of his predictions being accurate even 50% of the time over 10 trials is just over 3% - but I'll have to see if I can interest him in trying it.

Chris

ETA: I do have money riding on this, but not with the professor - I bet my friend $50 that he and the professor were wrong.

[blutoski]

Today, my psychology professor asserted that people can accurately predict random events roughly 60% of the time (he qualified this statement by saying that the actual figure lay around 57% and he was rounding). I asked him for an explanation of this claim, and in the following class discussion, he proceeded to assert that a random person predicting coin tosses would be right, on average, 60% of the time. I countered that that was impossible and the figure should be 50%, but he insisted on 60%. He said I was confusing the actual event with the prediction and that, while ratio of heads to tails should average 50/50, any person or machine making predictions should expect to average around 60% accuracy.

I discussed this claim further with a friend in the class, who said he had seen the study the professor referenced and insisted that a person predicting coin tosses would, in fact, average 60% accuracy. I insisted this was not possible, but he said that it was statistically proven, even though it seemed counterintuitive.

Later, I got a chance to engage the professor further, and he reaffirmed his assertion. He also added that a person predicting what card would be chosen at random from a deck of Zenner Cards would observe the same 60% success rate. He again countered my arguments by saying I was confusing the probability of the event itself with the probability of the prediction. I realize these figures are different (the ratio of heads to tails in a sequence of coin tosses may be 50/50 while the percentage of current predictions may differ substantially), but as far as I can see, the rate of accuracy for predictions should be 50% for a coin toss or 20% for the Zenner Cards no matter how you slice it.

I'm getting the feeling my friend and professor are misquoting whatever study they're trying to reference, but both were adamant about a 60% rate of prediction accuracy on coin tosses and Zenner Cards. Can anyone shed some light on what they might have been getting at?

I'd start by asking for this alleged citation.

Over and above that: it sounds like your psychology professor does not understand statistics. Like... at all.

[ctamblyn]

Did the professor say that the number of trials would be fixed in advance? This is crucial. If not, then don't bet against him. Flip coins for long enough, and he could well indeed end up with a 60% hit rate, eventually. At that point he stops the experiment and collects his winnings. It's called "cheating".

[gnome]

I'd ask if he understands the result to be a consequence of the probabilities involved, or if he believes the study demonstrated an unknown factor at play, for example "humans have some unknown ability to predict at better than chance". If it's the former, he ought to be able to find a proof. If it's the latter, the circumstances of the trial need to be examined carefully. Will it work if it is a perfectly balanced coin, and if the human is isolated from clues about how the flip is being performed? Will it work if it is a random number generator rather than a physical coin?

[Chris Connelly]

One other thing that comes to mind - the professor said that 60% of people choose 60% of their lottery numbers correctly. In other words, if you could gather up all the lotto tickets that have ever been played, 60% of them will have 3 out of 5 numbers correct.

ETA:

Ctamblyn, we didn't get into an experimental design - it was discussed as a function of the laws of probability. I agree that setting the number of trials would be crucial.

Gnome, he seems to think it's a matter of probability - he did say a machine could perform just as well as a human.

[Vic Vega]

Over and above that: it sounds like your psychology professor does not understand statistics. Like... at all.


Other people have said or intimated that in this thread, but you don't say WHY he's wrong. That leads me to believe that you don't understand statistics any more than he does.

Unless of course you want to expand on your post and prove me wrong.

:duck:

[Marduk]

just cut to the chase, bet your professor $100 that he can't predict the outcome of a coin toss 60% of the time in front of the rest of the class

thats that solved eh

[Ladewig]

Can you get a math professor to talk to this professor?

[Michael Redman]

One other thing that comes to mind - the professor said that 60% of people choose 60% of their lottery numbers correctly. In other words, if you could gather up all the lotto tickets that have ever been played, 60% of them will have 3 out of 5 numbers correct.

As with the casinos, such results would put the lottery out of business. The MegaMillions and PowerBall lotteries, for example, pay out $7 for getting 3 correct standard numbers.

[ctamblyn]

One other thing that comes to mind - the professor said that 60% of people choose 60% of their lottery numbers correctly. In other words, if you could gather up all the lotto tickets that have ever been played, 60% of them will have 3 out of 5 numbers correct.

ETA:

Ctamblyn, we didn't get into an experimental design - it was discussed as a function of the laws of probability. I agree that setting the number of trials would be crucial.

Gnome, he seems to think it's a matter of probability - he did say a machine could perform just as well as a human.

Well, it was the reference to drunken walks that made me wonder about the number of trials. The ratio hits/trials would fluctuate up and down as the experiment progressed. If you're extremely patient, it seems to me that you would be very likely to see that ratio fluctuate as high as 0.6, at which point you halt the process. I've been trying to find some good references, but I expect some bright statistician will beat me to it :)

[DavidS]

There's a couple of times you can utterly bug out statistics, but it all works mathematically.

If you flip two coins, and one comes up heads, there's a 67% chance the other one was tails.

It really sounds like he was getting something like that screwed up with predicting which coin flip does what.
Somebody help me out with how that's not slippery language on the slope toward the Gambler's fallacy.

There are four possible outcomes to a set of two coin flips: HH, HT, TH, TT

If you flip two coins, and you know at least one has come up heads (TT didn't happen) there's a 2/3 chance that at least one has come up tails (one of HH, HT, or TH).

Fixing which one has come up heads (say, the first), however, eliminates *two* of the possible outcomes for the set (TH and TT now out of play), leaving only a 50% chance that the specified other will be tails (either HH or HT)

[Ladewig]

As with the casinos, such results would put the lottery out of business. The MegaMillions and PowerBall lotteries, for example, pay out $7 for getting 3 correct standard numbers.

Furthermore, sites like this one Texas lotto (http://www.txlottery.org/export/sites/default/Games/Lotto_Texas/index.html) show that in the last drawing, only 35,207 people got three out of six. No one could seriously believe that 35,207 represents 60% of all the people who bought lotto tickets in Texas.

[blutoski]

Other people have said or intimated that in this thread, but you don't say WHY he's wrong. That leads me to believe that you don't understand statistics any more than he does.

Unless of course you want to expand on your post and prove me wrong.

:duck:

I hear what you're saying, but this is an informal discussion forum.

The prof's statements are a sort of 'this one goes to eleven' type of thing that is so not right it's not even wrong. It's hard to know where to start with a refutation. "Dogs are not animals", "the sky is made of fish", "three is a colour, not a number" - how do you refute these claims that are just so obviously wrong?

After 20+ years of dealing with cranks as a skeptic, I want to start a proper debate carefully, lest it go all Neal Adams.

[fls]

I can't help but think that if he truly understood what he was talking about, he would have been able to explain or indicate what he was talking about much better. It sounds like he misunderstood something or it's a trick.

Linda

[GreyICE]

Somebody help me out with how that's not slippery language on the slope toward the Gambler's fallacy.

There are four possible outcomes to a set of two coin flips: HH, HT, TH, TT

If you flip two coins, and you know at least one has come up heads (TT didn't happen) there's a 2/3 chance that at least one has come up tails (one of HH, HT, or TH).

Fixing which one has come up heads (say, the first), however, eliminates *two* of the possible outcomes for the set (TH and TT now out of play), leaving only a 50% chance that the specified other will be tails (either HH or HT)
You gave me different information than I asked for.

All I asked is if one came up Tails. If it did, the chance the other one was Heads is 67%. Period.

You can do this in all sorts of ways. If a family has two kids, and one of them is a boy, the chances that the other one is a girl is 67%.

You worked this out yourself, and then tried to deny what you found out ;)

P.S. Fixing which one was tails totally doesn't help you at all. If I ask 'did one come up tails' and you respond 'the first one came up tails' the second one still has a 67% possibility to be heads. You only decouple the system if I ask 'what did the first coin do' at which point it goes back to 50/50 that you want to see.

P.P.S. This doesn't let you predict the outcomes of any one coin flip 67% of the time, just the outcome of a pair of coin flips given information about the pair.

[carlitos]

It sounds to me like your psych prof needs help with rudimentary statistics, if such an obviously-bright student thinks he is saying what it sounds like he's saying. Coinflip = 50/50. Next question.

[athon]

I can't help but think that if he truly understood what he was talking about, he would have been able to explain or indicate what he was talking about much better. It sounds like he misunderstood something or it's a trick.

Linda

Bingo. My thoughts too.

I was intrigued enough to have a hunt around the web to see what might offer some hints on what the book said. There were a lot of interviews with the author that were quite interesting, focussing on our brain's clumsy handling of statistics. Lots of Monty Hall problem stuff, etc.

The closest I could find were some explanations on how it was our ignorance on a coin flip that produced the 50% accuracy, and the huge variation in contributing factors that produced the 50% probability. In other words, if we knew prior to a coin flip all of the factors that went into determining its spin, we'd guess better than 50%. And if we could control all of those factors, we'd be able to vary the probability by more than 50%. At least, that's how I interpreted it.

But I could find no figures of 60%, or any hint on how we might consistently get that figure of guessing. It makes no sense.

Athon

[ctamblyn]

If you're extremely patient, it seems to me that you would be very likely to see that ratio fluctuate as high as 0.6, at which point you halt the process.

On closer inspection, this is nonsense :(

I think I had in mind the fact that in a random walk, the distance from the origin will cross any given threshold an infinite number of times. Sadly this does not apply to the hits/trials ratio, as far as I can see.

I was tired. Honest :)

[Brian-M]

P.S. Fixing which one was tails totally doesn't help you at all. If I ask 'did one come up tails' and you respond 'the first one came up tails' the second one still has a 67% possibility to be heads. You only decouple the system if I ask 'what did the first coin do' at which point it goes back to 50/50 that you want to see.


I think you made a mistake typing up you post. Surely that should be...

P.S. Fixing which one was tails totally doesn't help you at all. If I ask 'did one come up tails' and you respond 'the first at least one came up tails' the second one each coin still has a 67% possibility to be heads tails. You only decouple the system if I ask 'what did the first coin do' at which point it goes back to 50/50 that you want to see.

[roger]

In other words, if we knew prior to a coin flip all of the factors that went into determining its spin, we'd guess better than 50%. And if we could control all of those factors, we'd be able to vary the probability by more than 50%. At least, that's how I interpreted it. I posted a link on that here (http://forums.randi.org/showpost.php?p=5577976&postcount=16).


Nobody read me. Nobody. :mad:



:D

[gnome]

Gnome, he seems to think it's a matter of probability - he did say a machine could perform just as well as a human.

Some monte hall experiments should shut that one down right quick, then.

But still I would rather make him squirm to find a proof :P

[athon]

I posted a link on that here (http://forums.randi.org/showpost.php?p=5577976&postcount=16).


Nobody read me. Nobody. :mad:



:D

Hey, weird - an empty post with nothing in it, written by nobody. Huh, odd.

;)

Athon

[dasmiller]

On closer inspection, this is nonsense :(

I think I had in mind the fact that in a random walk, the distance from the origin will cross any given threshold an infinite number of times. Sadly this does not apply to the hits/trials ratio, as far as I can see.

My experiences in Vegas had already lead me to suspect that the "keep betting until you come out ahead" strategy might not be reliable ;)

[ctamblyn]

My experiences in Vegas had already lead me to suspect that the "keep betting until you come out ahead" strategy might not be reliable ;)

:)

Of course, you can eventually beat a coin-toss game, as long as you have unlimited resources: http://en.wikipedia.org/wiki/Martingale_(betting_system)

Then again, if I had unlimited resources, I could probably think of better things to do.

[Skeptic]

Perhaps what we have here is a garbled version of the fact that sometimes the event is not as random as people assume it is. For example: when people guess if a coin lands "heads" or "tails", they tend to alternate between "heads" and "tails" pretty regularly, rarely guessing the same result more than twice. If the coin-tosser whose tosses someone guesses is human, they, too, are likely (if they get, say, four "heads" in a row) to ignore the last flip and try again, thinking that the row of "heads" shows those last few tosses were somehow not "really" random. This has the joint effect of making correct guesses more likely. But we need to know the context.

[Dancing David]

Welcome CC, I did a ten minute Google search. Your prof has access to paper no one else is talking about.

I think a citation is in order, Author, and date would be nice.

The only issue I found on Google is the well know fact that coins tosses are not random, unless they are controlled for.

[fls]

I've searched through Drunkard's Walk and can't figure out what he is referring to. His point about separating the probability of an event and the probability of a prediction is valid, but it doesn't alter your accuracy in the absence of knowledge, except through chance.

Linda

[GreyICE]

I think you made a mistake typing up you post. Surely that should be...

Nope. I made no mistake. Volunteering extra information doesn't actually change the probabilities.

For instance, if one was a red coin, and one was a blue coin, and I asked if one came up tails, if you told me 'the blue one came up tails' then the probabilities still stand. Order of flipping is about as relevant as the color of the coin - not at all. You might think that I've learned extra information about the red coin (that it has a 67% probability of being heads), and that that violates the fact that the coin flip is 50/50, but in fact I have not. The reason is that when I ask the question, the coin flip is no longer 50/50 (it is not half way between heads or tails. It is merely one or the other). To put it in populist terms, we've 'looked in the box.'

Unless in you're hypothetical you wouldn't tell me if the second one came up tails, but that just makes the entire thing worthless (if we assume you're lying to me, anything goes).

[paiute]

Today, my psychology professor asserted that people can accurately predict random events roughly 60% of the time

Very true. It is due to the wisdom of coinage:

http://www.scribd.com/doc/13366448/The-Wisdom-of-Coinage-A-Play-in-One-Act

[Robin]

In order to test this for a coin flip I tried entering 100 guesses of one and zero down a spreadsheet and then used the rand function in the next column to put in 1's and 0's at random, then in the next column I put a one or a zero depending on whether my guess is right.

Then I recalculated it twenty times - I get an average of 49.5 right guesses

Tried again with 100 new guesses - after recalculating twenty times an average of 50.1

Tried again with 100 new guesses - and after recalculating twenty times I get an average of 49.2

So it seems to me that the prof is a little off

Even if your guesses are not at random, there is still just a 50% chance of each being correct.

[Dave Rogers]

For instance, if one was a red coin, and one was a blue coin, and I asked if one came up tails, if you told me 'the blue one came up tails' then the probabilities still stand. Order of flipping is about as relevant as the color of the coin - not at all. You might think that I've learned extra information about the red coin (that it has a 67% probability of being heads), and that that violates the fact that the coin flip is 50/50, but in fact I have not. The reason is that when I ask the question, the coin flip is no longer 50/50 (it is not half way between heads or tails. It is merely one or the other). To put it in populist terms, we've 'looked in the box.'

No.

Let's look at the possibilities. The blue coin can be heads or tails (B+ or B-) and the red one can be heads or tails (R+ or R-). Possible outcomes are B+R+, B+R-, B-R+, B-R-.

You ask, in effect, "Can we eliminate B+R+?". You receive the reply, "We can eliminate B+R+ and B+R-". It doesn't matter that this is not a reply to the question you asked; you have been given information to the effect that two possibilities are excluded. Therefore, the only possible results are B-R+ and B-R-; the probability of red being heads is 50%.

The same is true, of course, if you don't even ask the question. In fact, your asking is completely irrelevant to the probability of a particular outcome, as it gives you no information. It's only the information you receive that matters.

For the same reason, if I flip two coins, then tell you 'At least one of these coins came up heads. What's the probability of one being tails?' the answer is 2/3, whereas if I tell you 'The first one came up heads [...]' or even 'The one that landed nearer my feet came up heads [...]', then the answer is 1/2. Counter-intuitive but true.

Dave

[Ladewig]

Very true. It is due to the wisdom of coinage:

http://www.scribd.com/doc/13366448/The-Wisdom-of-Coinage-A-Play-in-One-Act

Thanks, but I am not going to to read a 27-page play. Would you sum up the point for us?

[GreyICE]

No.

Let's look at the possibilities. The blue coin can be heads or tails (B+ or B-) and the red one can be heads or tails (R+ or R-). Possible outcomes are B+R+, B+R-, B-R+, B-R-.

You ask, in effect, "Can we eliminate B+R+?". You receive the reply, "We can eliminate B+R+ and B+R-". It doesn't matter that this is not a reply to the question you asked; you have been given information to the effect that two possibilities are excluded. Therefore, the only possible results are B-R+ and B-R-; the probability of red being heads is 50%.

The same is true, of course, if you don't even ask the question. In fact, your asking is completely irrelevant to the probability of a particular outcome, as it gives you no information. It's only the information you receive that matters.

For the same reason, if I flip two coins, then tell you 'One of these coins came up heads. What's the probability of the other being tails?' the answer is 2/3, whereas if I tell you 'The first one came up heads [...]' or even 'The one that landed nearer my feet came up heads [...]', then the answer is 1/2. Counter-intuitive but true.

Dave Interesting. I graphed it out and it worked. That's odd.

[paiute]

Thanks, but I am not going to to read a 27-page play. Would you sum up the point for us?

Okay. A simple play about flipping coins and about how you have a 1 in 16 chance of calling heads, say, four times in a row but that does not mean that the next throw has only a 1 in 32 chance of being heads again.

PEABODY
You know what is the most beautiful thing about a coin? It
has two sides and only two sides. You got your head side
and your tail side, and every time it lands, it lands
either heads or tails. It is a piece of the finest
craftsmanship. Pleasing to the eye. Durable. Manufactured
by the United States Government to exact specifications. It
is the gold standard. Not just in commerce, but in a game
of chance. You see?

and

GILLY
You damn fool! A coin has got two sides. Only two sides. It
don’t remember. It doesn’t know how it landed in the past.
Every time it goes up it can only come down heads or tails.
Fifty-fifty, Vernon. You bet one hundred and seventy-three
dollars against sixty on an even chance.

[fls]

Thanks, but I am not going to to read a 27-page play. Would you sum up the point for us?

It's an example of the gambler's fallacy, which does not explain the OP.

Linda

[Waterman]

One other thing that comes to mind - the professor said that 60% of people choose 60% of their lottery numbers correctly. In other words, if you could gather up all the lotto tickets that have ever been played, 60% of them will have 3 out of 5 numbers correct.

ETA:

Ctamblyn, we didn't get into an experimental design - it was discussed as a function of the laws of probability. I agree that setting the number of trials would be crucial.

Gnome, he seems to think it's a matter of probability - he did say a machine could perform just as well as a human.

That is an interesting challenge and introducing the machine or computer into it allows you to play with the idea. All spreadsheets have a random number generator function. Set up two columns One as the event and One as the prediction. Then compatre the two with an IF statement and them total the results.

I collected data on 20 trials of 100 events each (total of 2000 events).
For teh 20 sets of 100 event the accuracy ranged from 41% to 55% correct. With the total average over the 2000 events of 49.3% correct predictions. It would be possible to get a run of 100 that could be 60% but that goes away as you increase the number of trials.

Done - 10 minutes - could it be that simple or am I missing something that allows it to be the quoted 57% value. Is that assuming bias (intentional or not) on the part of the participants or equipment (unbalance coin, consistent flipping method).

[Waterman]

Bringing in 'if one is head guess tails' skews the results if both are tails.
H-H - wrong
H-T - Guess right
T-H - Guess Right
T-T - No guess gimmie

So 75% accuracy can be achieved if you require that head be declared if one exists
Likewise 66% accuracy can be achieved if you toss out all TT results and require declaration of at least on head

[jakesteele]

There's a couple of times you can utterly bug out statistics, but it all works mathematically.

If you flip two coins, and one comes up heads, there's a 67% chance the other one was tails.

It really sounds like he was getting something like that screwed up with predicting which coin flip does what.

I'm not sure I follow that, could you please explain? The reason I ask is that I worked in the casino biz for 10 yrs. and if you get 10 red spins of a roulette wheel everybody is going to bet on black and more often than not, within the next couple, three spins, it will come up black most of the time.

I know in theory if you flip a coin to infinity you can get a million heads in a row but in all my dealing days I never saw 30+ wins either way. There always seemed to me to be what I would call the "odds within the odds", if that makes sense.

[GreyICE]

I'm not sure I follow that, could you please explain? The reason I ask is that I worked in the casino biz for 10 yrs. and if you get 10 red spins of a roulette wheel everybody is going to bet on black and more often than not, within the next couple, three spins, it will come up black most of the time.

I know in theory if you flip a coin to infinity you can get a million heads in a row but in all my dealing days I never saw 30+ wins either way. There always seemed to me to be what I would call the "odds within the odds", if that makes sense.
The thing is, by the time you're on 10 spins of red, in the next three spins your chances of getting all red are... 1 in 8.

1 in 8 isn't very high. I mean it's not unnoticeable, but it's not very high. So sure, most of the time if you have 10 spins of red, 7/8 of the time at least one of the next three spins will be black (this is ignoring the 0, yes).

A run of 30 spins of red will only happen one in one billion run of 30 spins. The probability goes up when the run is longer (as any group of 30 red spins in a row works) but your chances of seeing it in any given night are probably only one in tens of millions.

But when you've spun 29 red spins in a row, the chances that the wheel will come up red on the 30th spin are 1/2 (approximate, I do know about 0).


Infinity is a tad different. The point is not that you will get 'a million spins of red in a row if you spin infinite times.' The point is you will get a run of one million reds in a row. Exactly. And you will get a run of 1 million, five hundred thousand reds in a row. Exactly. And you will get a run twenty billion spins long where every spin goes red, black, red, black, red, black. Exactly. Every single combination of spins you can possibly imagine, and every one you can't occurs in an infinite string of spins.

[Everett Spair]

if you want further data I just slapped together a quick program to test this.
It randomly predicts a number of tosses, then it actually make the tosses and then compares the predictions and the results. I set it to make 100000 tosses 10 times and this is the result I got:

1. 50379 correct predictions.
2. 50135 correct predictions.
3. 49679 correct predictions.
4. 49935 correct predictions.
5. 50026 correct predictions.
6. 49911 correct predictions.
7. 50152 correct predictions.
8. 50063 correct predictions.
9. 49934 correct predictions.
10. 49887 correct predictions.

As anyone can see all the outcomes are very close to 50% correct predictions.
Your professor should rethink his claim. :)

[Robin]

if you want further data I just slapped together a quick program to test this.
It randomly predicts a number of tosses, then it actually make the tosses and then compares the predictions and the results. I set it to make 100000 tosses 10 times and this is the result I got:

1. 50379 correct predictions.
2. 50135 correct predictions.
3. 49679 correct predictions.
4. 49935 correct predictions.
5. 50026 correct predictions.
6. 49911 correct predictions.
7. 50152 correct predictions.
8. 50063 correct predictions.
9. 49934 correct predictions.
10. 49887 correct predictions.

As anyone can see all the outcomes are very close to 50% correct predictions.
Your professor should rethink his claim. :)
However your program is randomly generating the guesses and human guesses do not come at random, so it is not really testing the professor's claim.

The one I did about (http://forums.randi.org/showthread.php?postid=5580170#post5580170) was based on actual guesses I made, but it still came up with around 50% correct guesses even with a human guesser.

[Brian-M]

I've just been thinking it through, and we're using the wrong percentages. It should be 75%, not 67%.

We've been assuming the possible outcomes are: HH HT TH

Which is true, but HH is twice as likely than either HT or TH alone, so we should be basing our assumptions on the possible outcomes of: HH HH HT TH

The reason for this is:

We have a 50% chance of getting a coin with a 100% chance of being heads (because that's the coin that the coin-flipper was talking about when he told us that at least one coin came up heads). This gives us a 50% chance of getting heads to start with.

We also have a 50% chance of getting a coin with a 50% chance of being heads, which adds another 25% chance of getting heads to the outcome, bringing it up to 75%.

If you draw a probability tree, you've gotta keep track of the probability of each branch.

Does anyone know if there is any kind of two-coin-flip situation that actually gives you a 67% (or 66.66667%) chance of being right?

[Brian-M]

No wait... I'm wrong. :( It is 66.6667% not 75%. Should have thought it through a bit more. :o

[Towlie]

I can predict 57% of the time whether or not a pair of dice will show a total greater than seven.

[dasmiller]

I can predict 57% of the time whether or not a pair of dice will show a total greater than seven.

I can correctly predict coin tosses nearly 100% of the time, unless I'm limited to one prediction per toss.

[Mr.D]

Was the professor in the OP lecturing on statistics in the context of interpreting psychological experiments? Or was he lecturing on the psychology of predictions?

If it's the former then either he wasn't communicating some missing bit of info, or he's just dead wrong - claiming the same probability for coins and cards is enough to destroy the pure statistics bit.

I _might_ buy the hypothetical claim that if Person A predicted a coin toss, then tossed a coin without showing the outcome to Person B, then Person B has a roughly 60% chance of "predicting" that Person A's prediction was correct - just by observing Person A's reaction. But that would be a psychological experiment, not a statement on probability.

I'm curious if your professor can come up with the original cite.

[Andrew Wiggin]

Should this be merged with the thread discussing this in Science, mathematics, etc?

http://forums.randi.org/showthread.php?t=166405

A

[Dancing David]

Should this be merged with the thread discussing this in Science, mathematics, etc?

http://forums.randi.org/showthread.php?t=166405

A


Not really, I started that one after this one.

:)

[Chris Connelly]

Update - I spoke to the professor again, and he said the coin tosses didn't really work in the context of the theorem he had in mind, but his assertion about Zenner Cards was still valid. He said an average person would accept someone as being psychic if that person could correctly predict the identity of a Zenner Card 4 out of 10 times, but you can do better than that by chance alone (again, up to 57-60%).

I would be surprised if an average person would be "impressed" by 4/10, but I suppose a competent performer could make it seem paranormal. Statistically, the probability of hitting 4 or more out of 10 is about 12% - improbable, but not very impressive. 5 / 10 would be more impressive at 3%, while 6 / 10 would occur roughly .6% of the time. I can't see any validity in the claim that a person could consistently perform better than 40% of the time predicting Zenner Cards. It would be even more difficult to get 40 / 100 (4E-4%) or 400/1000 (which the binomial probability calculator I'm using bugs out on). At those numbers, even 40% would be very impressive, let alone 57-60%. My professor is going to look up the study and get back to me - I've got to imagine the claim it actually makes is different, or else it's woo.

[GreyICE]

4/10, assuming traditional decks, and with a sufficient level of repeatability and oversight to assure no trickery, would be sufficient to prove paranormal powers.

Granted, it would probably take 200 or more repetitions, but if you're consistently hitting 40% when you should be hitting 20%, that's insanely good.

60% on zenner cards would just be ridiculous. No joke, if you could improve the odds that much, you'd be psychic (once again, with no trickery. Obviously you can do most anything if you're tricking people, or reading them, or whatever).

[fls]

Update - I spoke to the professor again, and he said the coin tosses didn't really work in the context of the theorem he had in mind, but his assertion about Zenner Cards was still valid. He said an average person would accept someone as being psychic if that person could correctly predict the identity of a Zenner Card 4 out of 10 times, but you can do better than that by chance alone (again, up to 57-60%).

I would be surprised if an average person would be "impressed" by 4/10, but I suppose a competent performer could make it seem paranormal. Statistically, the probability of hitting 4 or more out of 10 is about 12% - improbable, but not very impressive. 5 / 10 would be more impressive at 3%, while 6 / 10 would occur roughly .6% of the time. I can't see any validity in the claim that a person could consistently perform better than 40% of the time predicting Zenner Cards. It would be even more difficult to get 40 / 100 (4E-4%) or 400/1000 (which the binomial probability calculator I'm using bugs out on). At those numbers, even 40% would be very impressive, let alone 57-60%. My professor is going to look up the study and get back to me - I've got to imagine the claim it actually makes is different, or else it's woo.

Then I wonder if he's talking about Zener cards which aren't drawn randomly. Uri Geller would ask his audience to pick one of the five cards and then he would guess which one they had picked. Since most people (maybe 60 percent?) would pick the star, all he had to do was guess the star and he would be right for the majority of the audience members.

Otherwise, he may be talking about Zener cards experiments where reasons were found to exclude wrong results (the subject was tired or not concentrating, the examiner was a goat, etc.), which then biased the total results to an overall hit rate that was greater than chance (although I don't think it was as high as 57 percent.

We should probably just shut-up and wait for him to look up the study. :)

Linda

[Ririon]

Then I wonder if he's talking about Zener cards which aren't drawn randomly. Uri Geller would ask his audience to pick one of the five cards and then he would guess which one they had picked. Since most people (maybe 60 percent?) would pick the star, all he had to do was guess the star and he would be right for the majority of the audience members.

(...)
If an audience was asked to pick heads/tails instead of a coin toss, how many would pick heads? 57-ish %? :p

[Dave Rogers]

Let me just think out loud for a moment about the cards.

You have a set of five cards. One is drawn, and you make a guess. Your chance of getting it right is 0.2. A second is drawn; if you know what the first one was, your chance of predicting the second is 0.25. Your chance of getting the third is 0.3º, the fourth is 0.5 and the fifth 1 (because you can eliminate the other four). I haven't done the arithmetic, and I'm not sure I can be bothered, but it seems to me that the expectation value is that you'll get about three right purely by guess and elimination. Is that what he meant?

Dave

[Zax63]

I suck at statistics but I'm a decent programmer. I like to write simulations of things like this. Yes, computers are only pseudo-random but I think it's close enough.

10 trials of 100,000 flips each - random head/tail generated as prediction, then random head/tail for the flip

Trial # 01 100,000 flips 50.14% correct - 50.21% heads 49.79% tails
Trial # 02 100,000 flips 49.90% correct - 49.94% heads 50.06% tails
Trial # 03 100,000 flips 50.17% correct - 49.96% heads 50.04% tails
Trial # 04 100,000 flips 50.00% correct - 50.02% heads 49.98% tails
Trial # 05 100,000 flips 49.77% correct - 49.94% heads 50.06% tails
Trial # 06 100,000 flips 50.14% correct - 49.93% heads 50.07% tails
Trial # 07 100,000 flips 50.40% correct - 50.01% heads 49.99% tails
Trial # 08 100,000 flips 50.11% correct - 50.09% heads 49.91% tails
Trial # 09 100,000 flips 49.78% correct - 49.89% heads 50.12% tails
Trial # 10 100,000 flips 49.97% correct - 50.04% heads 49.96% tails

Just to show how sample size matters, here is the same program with trials of only 100 flips.

Trial # 01 100 flips 55.00% correct - 57.00% heads 43.00% tails
Trial # 02 100 flips 49.00% correct - 48.00% heads 52.00% tails
Trial # 03 100 flips 58.00% correct - 50.00% heads 50.00% tails
Trial # 04 100 flips 46.00% correct - 47.00% heads 53.00% tails
Trial # 05 100 flips 50.00% correct - 53.00% heads 47.00% tails
Trial # 06 100 flips 48.00% correct - 51.00% heads 49.00% tails
Trial # 07 100 flips 52.00% correct - 51.00% heads 49.00% tails
Trial # 08 100 flips 43.00% correct - 55.00% heads 45.00% tails
Trial # 09 100 flips 44.00% correct - 48.00% heads 52.00% tails
Trial # 10 100 flips 48.00% correct - 47.00% heads 53.00% tails

[athon]

If an audience was asked to pick heads/tails instead of a coin toss, how many would pick heads? 57-ish %? :p

That's a damn interesting question. I know I tend to pick heads, and even have a serious case of confirmation bias towards 'always' having coins land on this side.

I try hard to shake it by paying attention to those occasions when it does come up tails, but it's a fairly stubborn feeling. It's possible that I am a statistical anomaly, and I do experience an abnormally large sample of flips coming up head-side. But I tend to keep it in mind as an example of the power of confirmation bias in my own mind.

Athon

[Chris Connelly]

Well, the study seems elusive - now several classmates are insisting to have seen it, but no one can give me a link, name, or citation. I'll keep trying to track it down and let you know if I have success.

One of my friends is making the argument that all coin tosses are biased (he says there is no such thing as a "fair coin toss"), and humans can recognize the inherent patterns and use this information to increase their accuracy. I can only buy this to a very limited extent - in a decently controlled experiment, I'd expect any bias to be a fraction of a percent if present at all. At such a level, I would expect most people to be unable to catch on and use this to their advantage. I suppose, however, that it would be possible for someone to use this bias to increase their performance over a long run of trials, but only to a very limited extent (a fraction of 1%, maybe?). I don't see any way to get the 7% improvement forecasted by the alleged study.

Perhaps someone more knowledgeable can shed some light on the bias of coin tosses. I'm taking it for granted we're talking a "fair coin," with no special flipping techniques or other funny business. I don't doubt that it's possible to flip a coin in such a way as to make one side significantly more likely to appear, but my prof and classmates have explicitly denied this possibility. When you get into that sort of manipulation, you can make the statistics say anything, but unless I'm seriously mistaken, sufficiently large runs of "fair coin tosses" will always average around 50%.

Quite honestly, I'm at a loss to deal with the claims my prof and classmates are making. The only thing that came even close to making sense was the point about bias, but that was grossly exaggerated. Am I crazy, or am I just surrounded by people who have no clue about statistics?

ETA:

Just looked up statistics on the bias associated with tossing coins:

...coin tossing is fair to two decimals but not to three. That is, typical flips show biases such as .495 or .503.

From Persi Diaconis, Professor of Mathematics and Statistics and Stanford University:
http://www-stat.stanford.edu/~cgates/PERSI/papers/thinking.pdf

Absolute best case scenario (and I'm talking biased flips and a participant with the ability to keep track of trials as a professional card counter would), you can increase your accuracy by half a percent.

[Paul W]

Let me just think out loud for a moment about the cards.

You have a set of five cards. One is drawn, and you make a guess. Your chance of getting it right is 0.2. A second is drawn; if you know what the first one was, your chance of predicting the second is 0.25. Your chance of getting the third is 0.3º, the fourth is 0.5 and the fifth 1 (because you can eliminate the other four). I haven't done the arithmetic, and I'm not sure I can be bothered, but it seems to me that the expectation value is that you'll get about three right purely by guess and elimination. Is that what he meant?

Dave

The arithmetic has been done.

See Epstein, R A: The Theory of Gambling and Statistical Logic.

My memory is that the expected score is about 8.3 out of 25 (eg Zenner cards): the maths is beyond me, but simulation shows that it works.

If anyone wants the reference, I'll get it.

[carlitos]

Just ask your classmates to prove it. Seems simple enough.

- Work out the math for 57% likelihood (of predicting Heads / Tails) based on standard distribution
- Make a few bets.
- Flip a coin and count.
- Profit!!

[Robin]

Just ask your classmates to prove it. Seems simple enough.

- Work out the math for 57% likelihood (of predicting Heads / Tails) based on standard distribution
- Make a few bets.
- Flip a coin and count.
- Profit!!
Yes, I think that is the way to go. Obviously the professor and the classmates have gotten the wrong end of the stick about something or other.

But my guess is that they would not agree to it. It is often embarrassing to admit you have been wrong about something like this.

I actually started flipping coins and guessing the result. By the time I got to 25 coins I had guessed 60% correctly and was half thinking maybe there was something in it after all.

But by the time I got to 50 coins I was back to 50% accuracy. I haven't done the maths, but I am guessing that even at 100 flips you might get as many as 57% correct guesses.

[Robin]

I once claimed to my brother that there was a certain plant that was estimated to have lived since prehistoric times. When he challenged me I went to look for the research and found that I had simply misremembered and that the root system was estimated to have lived only since Roman times.

The great temptation was to simply say that I couldn't find the research and let the matter drop, especially since my brother has a habit of rubbing in silly mistakes like that.

In the end I 'fessed up about my mistake but it was a close decision.

I suspect the professor is in a similar position to this.

[GreyICE]

I once claimed to my brother that there was a certain plant that was estimated to have lived since prehistoric times. When he challenged me I went to look for the research and found that I had simply misremembered and that the root system was estimated to have lived only since Roman times.

The great temptation was to simply say that I couldn't find the research and let the matter drop, especially since my brother has a habit of rubbing in silly mistakes like that.

In the end I 'fessed up about my mistake but it was a close decision.

I suspect the professor is in a similar position to this.
Amusingly, you may have been right.

http://news.nationalgeographic.com/news/2008/04/080414-oldest-tree.html

9,500 years is, if not prehistoric, close.

But it's a good story.