Taleb: “I am going to flip this fair coin 100 times, and after the 99th toss, I want each of you to tell me the probability of the 100th being heads. You should know that each toss is independent and the that the coin is fair.”
Taleb flips the coin 99 times and each of the 99 tosses results in a heads.
Taleb: “Now before, I toss the coin for the 100th time, I want each of you to tell me the probability of heads on this next toss.”
Dr. John replies in a calm, studied, and restrained tone, “The probability of the next toss being heads is 1/2 (0.5). This is because you originally told me that the coin is fair and each toss is independent of the rest. So, despite the previous 99 heads, the probability of the next toss being heads is unchanged from the beginning (i.e. 0.5).”
Fat Tony replies in a visible excited and somewhat agitated demeanor, “This is one big set up! The next toss HAS to be heads! I don’t trust you. You lied when you told us the initial rules.”
What is more likely? That a fair coin lands heads 99 times in a row, or that Taleb lied? Fat Tony doesn’t need to be very intelligent to know the answer: his experiences in life have given him the wisdom to distrust claims like this. Dr. John may have more knowledge about probability, but not about deception.
Fat Tony can smell bullshit and never lets his guard down.
Using a contrived example to warn us against trusting contrived examples. Either outcome is a gotcha. Only fair move is to not play. and the outrage fat tony has should apply to the OP as well.
Using a contrived example to warn us against trusting contrived examples.
It's only a "contrived example" after you have seen the result, which was intended for you to see. Con artists rely on contrived schemes that are not easy for you see before; their objective is the opposite. This is what happened with Bernie Madoff, Elizabeth Holmes, and Sam Bankman-Fried. You think you are able to see the "contrived examples" before the fact, well, everybody does, and that's precisely what the next con artist relies on.
What I'm saying is that the entire thought experiment is contrived in bad faith against Dr. John. The sin of the Dr. John here is credulity in believing Taleb's assertion that coin will be fair but Fat Tony's priors have equally been captured. For all Fat Tony knows Taleb switched the coin out so that his statement was true and the story could just as easily have ended with the next toss coming out tails as a parable to not fall for the gambler's fallacy. Fat tony in taking the other side of the bet has also been taken in by the con. The real lesson if any can be taken from this story is don't play sketchy probability games with other people's coins/dice. And the Fat Tonys of the world seem much more likely to buy things like lottery tickets on this same vague intuition I'm supposed to be so impressed by.
I have done the experiment with academics without mentioning that the coin is fair, the result is the same: they assume the probability is 0.5.
You've had an academic sit there and watch you flip a coin 99 times landing it on heads each time?
Yes, because everyone knows thought experiments don't translate to the real world.
But narratives where the conclusion depends entirely on what the author wants aren't even thought experiments. For it to be a thought experiment you'd need to have actually caught some flawed logic and worked out why it was flawed. If the author is trying to differentiate Fat Tony and Dr. John then the author needs the victory of Fat Tony over Dr. John to rely on something other than that the author would prefer Fat Tony to be right instead of Dr. John as the narrative could just as easily have been written the other way.
Here is an alternate ending to illustrate the points:
Taleb: “I am going to flip this fair coin 100 times, and after the 99th toss, I want each of you to tell me the probability of the 100th being heads. You should know that each toss is independent and the that the coin is fair.”
Taleb flips the coin 99 times and each of the 99 tosses results in a heads.
Taleb: “Now before, I toss the coin for the 100th time, I want each of you to tell me the probability of heads on this next toss.”
Dr. John replies in a calm, studied, and restrained tone, “The probability of the next toss being heads is 1/2 (0.5). This is because you originally told me that the coin is fair and each toss is independent of the rest. So, despite the previous 99 heads, the probability of the next toss being heads is unchanged from the beginning (i.e. 0.5).”
Fat Tony replies in a visible excited and somewhat agitated demeanor, “This is one big set up! The next toss HAS to be heads! I don’t trust you. You lied when you told us the initial rules.”
Taleb: "Fine I'll give you 4:1 odds, put up $300 and you can walk away with a cool hundred for catching me in a lie!"
Fat Tony can smell bullshit and never lets his guard down, he takes the bet and already knows where he's going to spend that sweet cash.
Taleb flips the coin and it lands.... Tails!?!
Fat Tony has now fully lost his temper, "You cheated me!"
Taleb: "I told you it had a 50/50 chance of landing on tails, this is a normal result."
No. I ask them what is the probability that the next coin flip will land heads.
So at the end you told them the probability was 50/50 and then asked them what the probability was? Presumably you'd be the one determining if their answer was right or wrong. If they can't trust your premises why should they trust you evaluation?
Which I did.
You did not. Their logic was "I'm going to accept the premise given". You got to decide whether the premise was true or not. The outcome depended entirely whether you decide that the 99 coin flips in a row are the lie(in the form of a coin switch) or the statement about the probability was the lie.
So? You haven't illustrated anything. According to you, you need to show the flawed logic.
It not illustrating anything was the point, I agree I did not show the flawed logic of Tony. I was demonstrating the flawed logic of thinking these stories can be used to show anything at all.
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Notes -
Using a contrived example to warn us against trusting contrived examples. Either outcome is a gotcha. Only fair move is to not play. and the outrage fat tony has should apply to the OP as well.
It's only a "contrived example" after you have seen the result, which was intended for you to see. Con artists rely on contrived schemes that are not easy for you see before; their objective is the opposite. This is what happened with Bernie Madoff, Elizabeth Holmes, and Sam Bankman-Fried. You think you are able to see the "contrived examples" before the fact, well, everybody does, and that's precisely what the next con artist relies on.
What I'm saying is that the entire thought experiment is contrived in bad faith against Dr. John. The sin of the Dr. John here is credulity in believing Taleb's assertion that coin will be fair but Fat Tony's priors have equally been captured. For all Fat Tony knows Taleb switched the coin out so that his statement was true and the story could just as easily have ended with the next toss coming out tails as a parable to not fall for the gambler's fallacy. Fat tony in taking the other side of the bet has also been taken in by the con. The real lesson if any can be taken from this story is don't play sketchy probability games with other people's coins/dice. And the Fat Tonys of the world seem much more likely to buy things like lottery tickets on this same vague intuition I'm supposed to be so impressed by.
I have done the experiment with academics without mentioning that the coin is fair, the result is the same: they assume the probability is 0.5.
Yes, because everyone knows thought experiments don't translate to the real world.
You've had an academic sit there and watch you flip a coin 99 times landing it on heads each time?
But narratives where the conclusion depends entirely on what the author wants aren't even thought experiments. For it to be a thought experiment you'd need to have actually caught some flawed logic and worked out why it was flawed. If the author is trying to differentiate Fat Tony and Dr. John then the author needs the victory of Fat Tony over Dr. John to rely on something other than that the author would prefer Fat Tony to be right instead of Dr. John as the narrative could just as easily have been written the other way.
Here is an alternate ending to illustrate the points:
No. I ask them what is the probability that the next coin flip will land heads.
Which I did.
That's
1:3odds.So? You haven't illustrated anything. According to you, you need to show the flawed logic.
So at the end you told them the probability was 50/50 and then asked them what the probability was? Presumably you'd be the one determining if their answer was right or wrong. If they can't trust your premises why should they trust you evaluation?
You did not. Their logic was "I'm going to accept the premise given". You got to decide whether the premise was true or not. The outcome depended entirely whether you decide that the 99 coin flips in a row are the lie(in the form of a coin switch) or the statement about the probability was the lie.
It not illustrating anything was the point, I agree I did not show the flawed logic of Tony. I was demonstrating the flawed logic of thinking these stories can be used to show anything at all.
No, I already said what I specifically did not ask them.
I very clearly explained it in the article.
So it had absolutely nothing to do with my thought experiment.
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