Heads or tails

Jeremy · Post by **Jeremy** » 04 Feb 2009 04:46

Here's an innocuous little question. I have a coin. I show it you and tell you that it's completely fair and balanced. I allow you to inspect it to check for yourself. I then toss the coin 99 times in a row and all 99 times it comes up heads. I then ask you to tell me what you think the odds are (as an approximation) of the 100th toss. How do you answer? Please feel free to explain why you answered this way, rather than just voting in the poll.

mc · Post by mc » 04 Feb 2009 07:07

I chose 50/50. I've heard it called the Gambler's Fallacy; when you think that the results of past trials affect the results of future trials.

King Monkey · Post by **King Monkey** » 04 Feb 2009 07:27

Yeh, theres no way the previous results could affect the odds of your next coin toss. So, 50/50 it has to be. You should probably buy a lottery ticket if that happened though.

Jeremy · Post by **Jeremy** » 04 Feb 2009 13:25

Ok so nobody's got this right at all yet. The answer is a little debatable but the explanation is not. I'll explain a little later, but let me share this anecdote that might help things first;

This question comes from a book I'm reading on risk taking. The author of the book recounts a story where he attends a risk management think tank in Las Vegas. The think tank meets at one of the casinos and the head of risk management at that place goes through all the millions of dollars that casino spends on trying to catch and prevent cheaters. The Author then lists the top 4 biggest risks that casino has faced.

Number 1 was when in one of the entertainment shows put on at the casino a tiger mauled its owner - which cost the casino in excess of $100,000,000.

Number 2 didn't cost much money, but could have, when an employee was injured at work and so disgruntled with the pay out he was offered that he wrapped dynamite around the supports of the building and attempted to blow it up.

Number 3. Casinos have to report all earnings to the tax man (I forget what the exact office was called - something about social security I think). For completely inexplicable reasons, the person who was meant to be sending the forms off to the tax person hid them in his desk instead, and did so for a large number of years. When this came to light the Casino nearly lost its licence and was forced to pay a massive undisclosed fine.

Number 4. The owner's daughter was kidnapped and in order to pay the ransom for her the owner was forced to (illegally) dip into the casino funds.

Now consider the cost of these 4 individual events, compared with the cost of people cheating at casinos - especially when you consider the large number of people attending casinos and a comparison between how much a high roller would be spending vs the majority of people. Of course the 4 events I mentioned are a lot harder to predict than people trying to cheat, but perhaps if you're in risk management you should be worrying about the events that you can't predict that are going to cost the most, rather than the small change...

mc · Post by mc » 04 Feb 2009 13:41

Jeremy wrote:I have a coin. I show it you and tell you that it's completely fair and balanced. I allow you to inspect it to check for yourself.

I guess I read this wrong. I didn't read it as "I tell you it's completely fair and balanced." I read it as "it's completely fair and balanced".

Taking that into account, I would say that I would have to vote heads, because the previous 99 trials really bring into question your assertion that it's completely fair and balanced.

looking forward to your wonderfully enlightening explanation of the situation

Jeremy · Post by **Jeremy** » 04 Feb 2009 14:07

Matt is spot on. It doesn't even matter how you read that sentence, or if I didn't say anything about the coin being balanced at all.

The odds of throwing 99 heads in a row are 1 to 633825300114114700748351602688. What are the odds that I'm somehow cheating?

The book is "The Black Swan" by Nassim Nicholas Taleb. He calls the fallacy of applying sterile laboratory results (or logic) to real world situations as the "ludic fallacy." He suggests the reason for our current financial crisis is people making that error, and so far he's made a rather large amount of money from this financial crisis (as in, many millions of dollars).

FlexThis · Post by **FlexThis** » 04 Feb 2009 16:11

I said heads before I read the thread.

Do I win a casino?

Jeremy · Post by **Jeremy** » 04 Feb 2009 16:17

Yes. You just need to go into which ever one you like the most and mention my name and it's yours. Good job.

BainbridgeShred · Post by **BainbridgeShred** » 04 Feb 2009 16:55

I said heads before I read the thread.

Do I win a casino?

I don't like making a habit of laughing at Flex but here goes. Lawl

This thread is super dumb

sidekick · Post by **sidekick** » 05 Feb 2009 13:07

BainbridgeShred wrote:
This thread is super dumb

I at least learned something from this. I didn't think that if you flipped 99 heads in a row that, of course, something must be wrong. I just thought, "Hey, the next one has to be tails"

Interesting topic, that book sounds good

mc · Post by mc » 05 Feb 2009 14:53

also, the question is "how do you answer?"

so, I nailed it the first time.

Blue_turnip · Post by **Blue_turnip** » 06 Feb 2009 21:47

sidekick wrote: I at least learned something from this. I didn't think that if you flipped 99 heads in a row that, of course, something must be wrong. I just thought, "Hey, the next one has to be tails"

Interesting topic, that book sounds good

Hey I'm like hosting a poker game next week... do you want to come along?

SlashC · Post by **SlashC** » 07 Feb 2009 09:43

When I used to work at a hobby shop I had a manager that could flip a coin and hit heads or tails however he wanted. It had nothing to do with the coin and everything to do with how he tossed it. In this particular case it would have less to do with the probabilities of the coin and more about him messing with my head. In other words, the probability outcomes of the entire coin tossing system would not just be a function of the random uniform distribution of the coin itself, but would be some complex function of the small chance he flubs the toss and our perception of what each other's predicted outcomes would be.

If I had to hazard a guess, I would call heads in the air because I think he would expect me to call tails.

EDIT: I just read through the rest of the thread. I attended an interesting talk last semester on black swan innovations. Basically, they are innovations that completely change the way our society works and that are very difficult to predict (i.e. development of cars, computers, internet). The organization giving the talk funds research in areas where black swan innovation might occur. As part of the presentation, they also warned against using linear functions to predict changes in non-linear systems and attributed this practise to some of our present day financial issues.

Jeremy · Post by **Jeremy** » 07 Feb 2009 14:51

Yeah, Nassim Taleb makes an interesting (if rather irrelevant to this discussion) point about the argument from design from creationists. Creationists claim that if you look at a car or a computer or something like that you see very clear order and the strong evidence of a designer. However most of the objects of technology in our life (not cars, but the components in cars for example - and computers etc.) were originally invented inadvertently - essentially the creation was entirely random and coincidental and then the design was improved on afterwards. It's a fairly good (if shallow) analogy for abiogenesis and evolution.

The book really is fantastic - it will change the way you view risk and the world. The other thing that impressed me was this;

Who can tell me what 22 degrees C means in real terms as a description of the properties of an environment? We all vaguely know what temperature is in real terms (energy transferred into making particles vibrate) but how many people know specifically what specific temperatures mean? There is a massive void of knowledge when using the term.

Not really related to anything - just something worth thinking about.

Heads or tails

What result of the coin toss is most likely?

Heads or tails

Re: Heads or tails