Book 'em, Dano

My goal of posting at least one entry per week is proving tough this week, so here's one that doesn't take much effort on my part, spurred by an email from Geoff, posted here with his permission...

Hi Scott,

I'm fairly new to the industry and am loving it so far. I've become fond of the business side (producer/project management) of things as well as the design. (I am a level designer). Your Game Matters site has peaked my interest a lot more recently.

I was wondering if you had any books you could recommend on game matters or in here that deal with that part of the business. Any other industry related books that you think are worth reading as well would be great. I plan on building a good library.

Thanks a lot,

Geoff Gordon
Threewave Software

Perhaps, counter-intuitively, learning is a double-edged sword. Learning about a subject often closes a person's mind to newer ideas that don't confirm what was already learned. We naturally build up a "confirmation bias," as it's known, as we grow in knowledge over a topic, leading us to reject new information that disagrees with what we already know to be true. Often, then, we establish a rock solid belief that can lead to a closed mind.

Three different studies that I cannot point to right now due laziness, have confirmed this about our species. Fresh minds are open minds. This is perhaps why most science breakthroughs come from young thinkers, such as Einstein. An open mind is freer to accept unconventional or new ideas.

A person can overcome this hardening of the mind by thoughtfully practicing objectivity, by reevaluating beliefs in the face of compelling evidence, and by maintaining an open mind throughout life. And so with this speck of feeble psychobabble out of the way, I submit my first of many book recommendation lists, this one with a business and marketing focus:

Positioning, by Jack Trout and Al Ries (1982)
This is the bedrock, the place to start. Ground zero. Game designers who are interested in successful game concepts and design must read this book. The authors take the simple concept of the unique selling point (USP) and expand it into positioning, the most important facet of marketing, above advertising, PR, and research. "Positioning" is a phrase they coined for a series of articles first appearing in Ad Age magazine in the early 70's. Their concept is based on how the consumer mind naturally thinks and perceives the world, rather than trying to force our minds' to change with new beliefs. I like to think of positioning as applied psychology or the science of consumer behavior. The basic premise is that in today's advertisement deluged society (a recent study by the 3M company showed that we are slammed by 3000 advertisements per day) it's feeble to sell products to consumers. Instead, we must create products that people want to buy -- a subtle, but pivotal difference. Positioning shows us how to do this.

The same authors team up for several other highly recommended books, such as Bottom-up Marketing, Marketing Warfare, and The 22 Immutable Laws of Marketing.

Focus, by Al Ries (1997)
The first book written by Ries after splitting from Trout, and another foundational book for any developer starting or running a game studio. Use this as a business bible. How is it that companies that didn't exist when the mighty worldwide powerhouse IBM introduced their PC, such as Dell, now completely dominate the PC market, while IBM is no where to be seen? Did IBM just concede this multi-billion dollar market without a fight? Or is there another force at work? And, similarly, how do new developers stand a chance making it in this hyper-competitive industry? Read this book, apply its teachings, and your chances of success skyrocket.

Soon after GT Interactive Software (GTIS) became 3D Realm's publisher in 1997, they began an expansion spree that I knew was leading them over the cliff. Crazily, GTIS even bought an established Internet entertainment portal. I couldn't resist sending Ron Chaimowitz, CEO of GTIS, a new copy of this book along with a fresh highlighter. I bet, looking back, he wished he would have followed this book's guidance.

Buzz, by Marian Salzman, Ira Matathia, & Ann O'Reilly (2003) and
The Anatomy of Buzz, Emanuel Rosen (2000)
Two books, both great, and each covers the topic from a different angle. Buzz is the next new wave in marketing, and the purposeful harnessing of buzz can lift a product from obscurity to sensational success. For game designers, it's a mistake not to understand how to make your game buzz-worthy, which can be done from within the game's design to the game's advertising. Most game designers have little to do with their project's marketing and advertising, but building something buzz-worthy into the design itself is still within their grasp, and can make a giant impact on sales. Buzz is the fancy term for word-of-mouth advertising, and for entertainment focused businesses, like restaurants, movies, and video games, buzz means everything. Especially with how gamers talk to each online. It's up to developers to make sure gamers are saying something positive, otherwise, your game is sunk, regardless of the quality and quantity of traditional advertising.

Big Brands Big Trouble, by Jack Trout (2002)
Here's one of Jack Trout's better solo efforts, after splitting from his partner, Al Ries. This book is jammed with great advice that's useful to game developers, and especially publishers who are managing multiple brands, like Take-Two and EA, both of which could definitely learn from this book -- especially EA, whose brands have been horribly mishandled. This book is also available on tape, which I listened to recently as a refresher. The tape covers all the material in the book, and for those who like to listen to books-on-tape in their cars or wherever, I recommend it.

Patton on Leadership, Alan Axelrod & George, III Steinbrenner (2001)
Patton is one of my heroes. He's easily one of the great field commanders in the history of warfare, and his innate leadership skills are unmatched. This book has 183 leadership lessons, each with its own one- to three-page easily chewed chapter. One of the book's best parts is the author's dissection of the Patton's famous speech, given to new troops under his command (portrayed fairly accurately in the opening of the movie with him standing in front of the American flag). Every line of that speech shows a level of brilliance that cannot be appreciated until you've read this author's explanation. I've read a dozen plus books on leadership, and this is the Tiger Woods of the group.

The Power of Logical Thinking, by Marilyn Vos Savant (1996)
Nothing to do with the game industry, but useful nonetheless for exposing flaws in our thinking and reasoning skills. Easily one of my most recommended books, especially to those trying to be more objective about the world and information flow around them. Written by one of the planet's certifiably smartest people, IQ rated at 228 (super genius level), this book is an eye-opener to the ways we're constantly misled into beliefs that seem intuitively correct on the surface. Advertisers and politicians take advantage of us everyday by spinning the truth, deceptions and misleading statistics. The more interesting parts of this book reveal how most people can be easily fooled into beliefs that seem correct, but are factually wrong. (For example, the better game wins the category.) One of the best parts of the books is when the author presents a series of puzzles that have counter-intuitive answers that are often hard to believe even when fully explained. Here's my favorite:

The Monty Hall 3-door puzzle: In the popular 60's - 70's game show, Let's Make A Deal, host Monty Hall would give the final contestant a chance to pick one of three showcase doors. He tells the contestant that behind one door is the big prize (maybe a car), behind another door is a runner-up prize (maybe a TV set), and behind the final door is a booby prize (often a farm animal, like a donkey). So, the contestant picks a door, let's say door #1. Monty doesn't open that door right away -- instead he builds excitement by first opening one of the two un-picked doors. (It's important to know that Monty knows what's behind each of the three doors. And he'll never open the door with the big prize during this stage.) Let's say Monty opens the door with the runner-up prize, revealing a TV set. That leaves two unopened doors, one with the big prize and one with the booby prize.

Now comes the fun part: Monty turns to the contestant, and says, "Well, there are two doors left, and so far so good -- you know the car is either behind the door you picked, or the door you didn't pick. Tell ya what...do you still feel like you made the right choice? If not, I'll give you a chance to switch your pick to the other unopened showcase door. Whachya wanna do?"

So, if you're that contestant, do you stick with the door you originally picked, or do you switch? (At some point I'll post the answer in the comments section.)

Okay, where are the game design books, I hear you screaming!? The truth is, I've read most of them (over 20) and there are only a few I'd recommend. I'll include them on my next book recommendation list.

Comments

[Simon Hibbs]

Logo, all your analyses of the probability tree are invalid because he hasn't opened the door and revealed the donky, he has revealed the TV. You are analysing the situation from the beginning of the game before you have chosen a door and before he has opened one of the ones you didn't choose. We are not in that situation, so considering situations like:

>1)Pick Car: shown donkey: stay: win

are irrelevent. You are wasting your time and confusing yourself by analysing all these situations that you are not in.

He has shown you a TV. You either chose the car or chose the donkey, and it's 50/50 which. No amount of analysis of irrelevent situations changes the fact that it's a 50:50 gamble whether you switch or whether you stick.

Simon Hibbs

[Logo]

The distribution is still the same though.

Lets say that he reveals the TV. Such an event occurs 1/2 of the time (1/6 for picking the car 1/3 for picking the donkey). The probability of picking the Donkey and seeing the tv is 1/3 of the time. Therefore using the equation of p(E|F) outlined in one of my posts higher up. We then have the probability of picking the donkey and seeing the tv (1/3 of the time) divided by the probability of seeing the tv at all (1/2 of the time). So thus we have (1/3 / 1/2) or 2/3. So 66.67% of the time you've picked the donkey to start and thus you should switch. The equation doesn't lie =).

[Scott Miller]

Logo, if you read Marilyn's book, she includes letters from major college Math professors who argue strongly that the answer is 50%, as if it's a new thesis for them. Some of them eventually come around. But, this puzzle, more than any I've come across, demonstrates the "hardening of the mind" I talked about in my original post. It also shows how people will nitpick little areas trying to spin things to their favor.

A fact of human psychology is that people do not like to change their minds. Among other things, it's an admission that their prior beliefs were wrong. And this leads back into the subject of positioning, as it recognizes this fact and purposely works around it. But advertising that tries to change people's minds will almost always fail. For example, even though New Coke was taste tested over 100,000 times in blind tests and proven conclusively to taste better than Original Coke, once the product came out people could not be convinced that it tasted better. And no amount of advertising would have ever changed that.

Changing people's minds is one of the most fruitless activities a company can undertake. Not too unlike counter-intuitive puzzles. ;-)

[Logo]

I should probably stop trying then. What about an answer for the third puzzle though?

[Peter Hatch]

"* pick a kid at random. report gender. pick a characteristic that this kid has ("plays soccer") - in other words, this gives no information. 33%."

No, this is 50%. Again, there are three possibilities, but the BG/GB possiblities are half as likely, because half the time they'll report boy and half the time girl.

Look at it this way: you have BB, BG, GB, and GG as possibilities. Half the time both will be the same sex, and half the time they will be different. Being told what one of them is doesn't change this.

Another puzzle to illustrate my point: A friend secretly draws one of four cards, an Ace, 2, 3, and 4. If he gets the Ace, he'll always yell Bingo, if he gets the 2 or 3, he'll yell Bingo half the time, if he gets the 4, he'll never yell Bingo. He draws a card and yells Bingo. What are the odds he drew an Ace?

[JP]

"A fact of human psychology is that people do not like to change their minds."

And yet, almost anything you could think of that has improved society and changed the world for the better required that at least one person change their minds about something. I think that's what people are getting at when they take umbrage at the smug self-assurance with which Scott preaches about perception-over-reality. Change *needs* to happen, but some people just want to make money - and of course they're welcome to. That's pretty much why I left the game industry - it's run by people to whom marketing and the bottom line are (understandably, given the stakes) infinitely more important than improving the overall quality of games, taking the medium in new directions, opening the market to new people (how many 40-something women are going to pick up Duke Nukem?), and establishing games as a valid cultural form, rather than a cheap amusement for overstimulated male adolescents. Of course, it would be insane to want to make money following any of those pursuits, so for now art and commerce are rigidly segregated in the games world. I'm convinced it doesn't always have to be that way, though. Will people not pay money to have their world view fucked with, their opinions challenged? Nobody, anywhere?

The ideas behind Positioning want only to keep people fat and happy and asleep, while the impulse to innovate rouses them from that state, often with upsetting results. Being fat and happy isn't necessarily bad, but I believe it was George Bernard Shaw who said, "all change depends upon unreasonable men". I'm glad that there are revolutionaries and artists in this world in addition to the bankers and marketers and floor-sweepers - really, they're all important.

[Eric von Rothkirch]

Charles E. Hardwidge wrote:

"Even though practice makes perfect it still won't tell you why something should be done. Issues of social and cultural responsibility aren't seemingly a high priority for most business today which is why companies like Disney and Coca-Cola operate as they do."

Why are we discussing moral obligation towards society?

Charles, the perception of your psuedo-intellectualism comes from obtuse references like David Bowie, Japanese glassmaking, and cryptic statements in Latin - each of which have very little to do with this thread, other than the fact that they represent thinly veiled attempts at appearing 'cultured'. The wit is irrelevantly dull, and so far hasn't contributed much to the conversation.

Also, criticizing a list of business books for being what they are is like criticizing a cow for being a mammal. What is the point?

You don't have to spend a significant amount of time writing abstracts about your favorite books. They either speak for themselves or they don't. They do not require mystification on your part. Or do they?

I'm genuinely interested in seeing a list of alternative recommendations.

[Charles E. Hardwidge]

Eric, the comments I've made have contributed as much as I feel or am interested in making, and so far I've made a handful of points some people have found worth acknowledging or commenting further on. Rather than seeing them as being opposed towards Scotts reading list, of which I've been broadly supportive, may I suggest there's more profit in viewing them as complementary. Given the huge interest in making better games, as opposed to what sells, (and building long lived businesses) I'm sure suggestions along those lines would fill a gap. What those suggestions might be is something I've only briefly thought about. Some candidates that might make such a list include:

The State We're In - Will Hutton.
The Third Wave - Alvin Toffler.
A History Of Western Philosophy - Bertrand Russel. (Out of print.)
Stalingrad - Antony Beevor.
Alan Clark - Diaries.
Legacy - Michael Wood.
Nelson - Christopher Hibbert.

Other material worth consideration:

Civilisation - Sir Kenneth Clark. (VHS).
The Victoria and Albert Museum. (London, United Kingdom.)

One of the problems I've had is working out precisely what I'd want to say with such a list and finding the right book to say it. Certain things are not necessarily best communicated with a book, hence the video and museum suggestions. Even though my hasty selection is far from perfect and contains glaring ommissions, each one contributes to a character building journey across society, history, and culture. I'd also like you to view the list as a personal selection to stimulate interest not a prescription. Where people go with it is entirely up to them.

[Scott Miller]

Someone pointed out this very good blog link to me, explaining the Monty Hall puzzle.

Charles, as far as book lists go, as this is a game industry blog, I prefer to stick with lists that are directly relevant and applicable to studios and publishers, from designers to developers to managers.

[Fungii]

I found this Monty Hall "puzzle" somewhat interesting, and very irritating. I think there are two problems here: odds and the rules of the game.

Firstly, odds. The odds BEFORE Monty opens the door are different from the odds AFTER he opens a door. A lot of people here are comparing apples and oranges.

Secondly, rules of the game: does Monty show the donkey ONLY when you pick the TV, or can he show the donkey when you pick the car as well? It alters the odds a bit.

Another thing is, what exactly are you comparing here? The always switch strategy, the always stay strategy, the "random" strategy or a simple "playing the odds" strategy? What do I mean by the last one? Well, I concede that if Monty shows the donkey, your odds increase by switching because of the situation where if you pick the TV, Monty MUST show you the donkey, as we all agree that he never shows the car. Your odds also increase a bit more if he only shows the donkey if you pick the TV, and NOT when you pick the car. Quite a bit, actually. [100%] If he can show the donkey when you pick the car, then your odds are still better when you choose to switch, it's just not a sure thing.

On the other hand, if Monty shows you the TV, then switching gains you absolutely NOTHING. Take these two strategies:

A. Always switch, no matter what. [Good move, it increases your odds]

B. If Monty shows the donkey, switch. Otherwise [TV] stay.

I submit that strategy B will be EQUALLY successful as strategy A. [Accounting for random error, of course.] The Monty Hall problem seems to be more a communication problem than a logic problem.

[Jeff (Be-gone) Smoley]

I would have to agree with Dan MacDonald on the car question. MPH is distance over time. In order for you to have an average of 60 mph you would have to do both laps in 2 mins. 2 miles / 2 mins = 1 mpm or 60 mph. If you do the first lap at 30 mph it will take you 2 minutes too complete the 1 mile lap. Which would leave you with no time left to complete the second lap meaning you would have to do the second lap instantaneously. So you can not have an average of 60 mph. You can come infinitely close but never reach it.

[Fungii]

I just read Scott's link. Ooops, I have to think about this, but I think I just realized why switching might be better. You're most likely to have picked the wrong the wrong door, 2-1. So if one door is eliminated, you can trade in your 2-1 pick in for a brand spanking new 1-1 pick. Got it, nevermind. *blush*

[Logo]

Haha that's a great link Scott. He goes into such detail about how sure he is that he was wrong and how 2/3rds is the right answer undeniably and he'd even bet blindly on it. Then the first comment... "No it's 50/50."

I think I have a new fear of getting older if my mind is going to become like that =).

[Logo]

sorry to double post but about #3:

Well my calculator has decided to give me a different answer now (so I must have made a mistake. I guess I am going to go with Dan's answer. You technically won't get to 60mph even from what I see but you will most likely get so close it's negligable. Of course that'd be close to 10k+mph. His answer did make a lot of sense to start but I felt like there should have been more to it (ie an answer) but I guess not.

[Simon Hibbs]

Scott,

Thanks for telling me I'm hard headed. I actualy couldn't give a flying monkeys what the answer is, I just want to know that the right one is.

Logo,

I'll concentrate on the second child problem because it's simpler.

In your first exposition of the P(E|F) calculation. I am familiar with this. It works where F is an as-yet undetermined probability, but in thisn case it is not undetermined. We already know what it's outcome is, so the probability of F is 1.

Furthermore you list the possible outcomes: (B-B, G-G, B-G, G-B) and analyse the probabilities based on them. But actualy we already know that two of those outcomes are not true. We can eliminate B-B and B-G because we know that the first child is a girl, so outcomes with a B in the first possition can be discarded. That leaves only G-G and G-B, which are the only outcome combinations that are relevent.

Please explain to me how the B-G and B-B combinations have anything to do with the problem, and have any place in the probability calculation?

Let's try another example: I buy a lottery ticket and win the big prize with million to one odds against. What is the sex of my second child? Plug those numbers into your equasion and see what comes out.

Simon Hibbs

[Logo]

The probability isn't 1 though. We we know in this case it is in fact true that one child is a girl. However the equation still uses the probability to determine p(E|F) meaning you use the p(F) if you didn't know F. Since it reads as the probability of E given F then under your logic the equation would be worthless because F would always be 1 (you are given F when you apply this equation, and you argue if you are given F its probability is 1).

Also you don't know which order the childern came in. The girl may be the younger one or the older one. Since this is such a case you can look at it like B-B doesn't matter but both B-G, G-B, and G-G do in fact matter.

Your other example is easy to solve. E (lottery ticket) and 2nd child's sex are independant events. p(E) = 1/1000000 and p(F) = 1/2 (for boy let's say) the chances of both occuring are 1/2000000 so P(E and F) are equal to P(E)*P(F) so there is no indication of your 2nd child's sex.

However lets apply this principal to the other problem. With 4 outcomes B-B, B-G, G-B, G-G we can calculate the probability of having 1 boy and the probability of having one girl. P(E) = 3/4, P(F) = 3/4. So P(E)*P(F) = 9/16. Now lets look at the probability of having both 1 boy and 1 girl. Well that leaves b-g and g-b so the p(E and F) is 1/2. As we can see P(E and F) does not equal P(F)*P(E) so our events are NOT independant so therefore it CANNOT be 50%.

[Simon Hibbs]

Logo:

>The probability isn't 1 though. We we know in
>this case it is in fact true that one child is a
>girl.

And this is the case under discussion, and no other.

>However the equation still uses the probability
>to determine p(E|F) meaning you use the p(F) if
>you didn't know F

But we do know F. Cases where we may not know F do not apply.

If the questions was: "A mother is picking up one of her children. She tells you that one of her children is a girl. What is the probability that the child she is picking up is a girl." then you would be right. However that is a very different question to the one we were posed.

I'm afarid I'm off on holiday now, so I won't be able to continue this. It's a shame. Please do reply though, I will certainly read any replies on my return after Christmass, and look forward to reading them. I do appologise if I am being brick headed, I'm perfectly aware that it is a possibility.

Many thanks for such an enjoyable discussion.

Simon Hibbs

[Scott Miller]

Okay, I wanted to let a few more people have a chance to comment before I revealed how fast Carmack would need to go around the track a second time in order to average 60mph for both laps. Dan got it right first. No matter how much Carmack souped up his Ferrari he wouldn't have a chance. As Dan explained, if the first lap took two minutes (which it would at 30mph), then the second lap would require the Ferrari to violate nature's own speed limit -- the speed of light -- in order to complete BOTH laps in two minutes, and thus average 60mph for the full two-mile run. This is as much a trick puzzle as a counter intuitive one. Most people will quickly give the answer for 90mph for the second lap, because 30 plus 90 divided by 2 equals 60.

Anyway, this puzzle thread was pretty fun so I'll likely do it again in a few months -- I used to post puzzles in my plan/finger files in the late 90's, so I have dozens of good ones ready to go. If anyone else has a good puzzle (and I prefer the kind that don't require a math-head to figure out), feel free to post it.

[Charles E. Hardwidge]

"Charles, as far as book lists go, as this is a game industry blog, I prefer to stick with lists that are directly relevant and applicable to studios and publishers, from designers to developers to managers."

When the research I'm aware of confirms the contribution I've made to this topic, you'll have to understand my difficulty in understanding how you consider it irrelevant. Perhaps you could explain your conclusion so that I may better understand why this might be so.

[Simon Hibbs]

I
Hi again, it turns out I actualy do have web access while I'm on holiday. Hurrah!

'm not realy sure about the three door problem Scott posed (with the TV) but I will accept that the one with a Car and two donkeys is interesting. You are better off switching in that game.

The way I think about it, what are the odds that Monty has given you information about where the car is? There's a 1 in 3 chance you chose the car and Monty has a free choice of which other door he opens to show you a donkey. There's a 2 in 3 chance you chose a donkey and Monty has no choice which of the remaining ones he opens. He has to open the one remaining door with a donkey behind it. That means there's a 2 in 3 chance Monty just showed you where the car is.

I am obstinate about the second daughter problem, because I am convinced the problem was miss-stated. Logo saying that "the lottery is E (lottery ticket) and 2nd child's sex are independant events" is revealing. The sex of every child on the planet is a seperate event from the sex of every other child on the planet. For the purposes of this discussion each is a seperate 50:50 chance, inunfluenced by all the others. I could as easily say "A woman has flipped a coin and has a child. Her child is a daughter, what are the odds she threw heads?".

Simon Hibbs

[logo]

I agree that the problem with 2 of the same prize, or equally as worthless prizes are a better representation of the problem. Many people are getting hung up on Monty stratigically opening doors (like TV instead of Donkey).

About the girl/boy problem though:

Simon the thing is you aren't looking at 1 child being born. You are looking at 2. If a couple has 2 children (thus a pair) then the 2 things are related. You don't know if the first child or the 2nd child is a girl so it's not simply an independant event.

To think about it in a larger scale if a couple has 1000 children and you know one is a girl what's the probability that at least one of them is a boy? You surely wouldn't say 50%.

The children act as a pair. If you knew a woman has 1 girl and 1 boy it could either be b-g or g-b. If you know a woman has 2 girls it can only be g-g. Since each sex of the child is 50:50 each outcome is equally as likely. However there are twice as many outcomes for having a mixed set (b-g, g-b).

My 3 recommendations to people who still can't see the answers clearly are to:

1) assume you wrong (mostly because you are) and assume the explainations are correct. Use the explainations to convince yourself that the answers are right and as you do that and fully come under the understanding of how and why you were wrong before. Don't act like you are right when you read the explainations. All you are doing in such a case is missing the point of the explanations so you can keep convincing yourself you are right.

2) Bet money on it. Are you so sure you are right to bet people money on it? I know that I am 100% confident in my answers (for #1 it would have to be car-donkey-donkey because of biases in the problem otherwise).

3) Make a computer simulation. Simulating such a situation (as long as you do it correctly, for example in the 2nd problem don't assume the girl is the firstborn or the 2nd born all the time). If you acurately program the situation it will undeniably return the proof that the counter-intuitive answers are infact correct.

4) Look around you. Scott has linked and talked about so many people doubting the correct answer and then eventually realizing how wrong they were. Including many many smart people. If so many people undeniably say that they were infact wrong and this is the correct answer isn't it at least possible. Especially when people are saying you are going to believe the intuitive answer (like doesn't matter if you switch, or 50:50 chance on the second child) but it's going to be wrong. You just read how Scott was saying these problems show how people's minds harden to certain answers and beliefs even when shown they are wrong and you do the same thing right after reading thing. It's something you really should think about without assumptions first.

[Charles E. Hardwidge]

Logo, your suggestions are exactly what I'd recommend, which is precisely why I've kept quiet about the probability questions since discovering the uncomfortable thought I may be mistaken. Given the effort required by statistical experts to overturn the weight of their own experience, I see no shame in admitting this.

With that in mind, I'd invite Scott to reexamine his conclusions about my earlier suggestions and explore the theory that lies behind them. It would be difficult pursuading me to provide further assistance so he might like to hunt down a friendly historian, sociologist, art critic, and economist. That way he might learn to better appreciate free advice.

[Simon Hibbs]

Logo,

>You just read how Scott was saying these problems show how people's minds harden to
>certain answers and beliefs even when shown they are wrong and you do the same thing right after
>reading thing. It's something you really should think about without assumptions first.

Yes I did, and I'm amazed that you can't see that introducing the TV does massively change the situation. I'm amazed you can't see this since you obviously reasoned through the two-donkey situation. Applying the same logical analysis, which gave me the correct answer in the two-donkey situation points out grave problems when you introduce the TV.

Regarding the child gender question:

>Simon the thing is you aren't looking at 1 child being born. You are looking at 2. If a couple has
>2 children (thus a pair) then the 2 things are related. You don't know if the first child or the
>2nd child is a girl so it's not simply an independant event.

I understand that, but surely you realise that the gender of one child does not affect the gender of another. This becaomes obvious when you substitute the sex of one of the children with a different 50:50 random event. I was just stunned that you can't accept this. What is it about gender determination that causes one event to affect another where a coin toss and a gender determination don't affect each other?

Have you read my alternate version of the question? You certainly haven't addressed it in your posts. That leads me to suspect that you're not actualy bothering to reason through my arguments independently.

It seems to me you're falling foul of the mistake you're warning against.

Simon Hibbs

[Scott Miller]

Simon, on the two penny puzzle, throw two pennies in the air 30 times. Whenever one of them is heads (either one, it doesn't matter), record how many times the other one is also heads. You will see they average working toward 33% of the time unless you get a freak streak going. Keep in mind, you don't record anything when both pennies are tails.

The same exact adds holds true when you're told a couple has two kids and one of them is a boy -- there's a one third chance the other kid will also be a boy. Keep in mind, of the set of couples with two kids, exactly 25% of those couples cannot tell you that one of their two kids is a boy, because they'll have two girls. So, whenever you're told that a couple has one boy, you're only working with 75% of all couples with two kids. Of this reduced population, two-thirds of those couples will have a girl as their second kid, and one-third will have a boy. That's because of this reduced population, the possible combinations are boy-girl, girl-boy, and boy-boy.

That's about the best I can explain this puzzle.

[Simon Hibbs]

Scott,

You're right. I first heard this puzzle from a friend that told me the puzzle and directed me to the site, but when he told me the puzzle he got it wrong. He said something along the lines of "You meet a woman taking her kid to play soccer. The kid is a girl, what are the odds the other kid is also a girl."

Obviously that's a different question to the one int he weblog, and i got it wrong.

If you read one of my posts p wthe way you'll see that I reverse-engineered logo's analysis of the problem and ended up with almost exactly the same question as your orriginal post. Doh.

Simon Hibbs

[Simon Hibbs]

Ok, you got me on the girl problem, but let's have another look at the game show problem that started this all off. If you spot me making a mistake, just point it out.

Firt of all, lets look at the classic version you linked to later : There's ne car and two donkeys.

This on is not controversial, I agree you're better off switchign because that gives you a 2/3 chance of winning the car. Here's why:

1. Suppose I chose the door with the car - Monty shows me a donkey. If I switch I lose.
2. Suppose I choose the door with donkey 'A' behind it - Monty shows me donkey 'B'. The only remaining door contains the car and switching wins me the game.
3. Suppose I choose the door with donkey 'B' behingd it - Monty shows me donkey 'A'. Again the only remaining door contains the car and if I switch I win.

That's two cases in which switching wins me the game and one in which switching loses me the game. I'm clearly better off switching.

Now let's look at the verion you stated in your blog. In this version there is a car, a TV and a donkey.

1. If I choose the door with the car behind it, Monty shows me the TV. If I switch I lose.
2. If I choose the door with the donkey behind it, Monty shows me the TV. He has no choice, because he can't show me the car. If I switch to the remaining door I win the car.
3. If I choose the door with the TV behind it - Oops. I'm not in that situation. Let's look at your statement of the problem:

"Let's say Monty opens the door with the runner-up prize, revealing a TV set. That leaves two unopened doors, one with the big prize and one with the booby prize."

So if Monty opened the door with the TV set behind it, I can't have chosen that door, right? I know I'm not in that situation. Therefore only two possible situations remain. In one of them switching wins me the game, in the other it loses me the game.

You can see that the way you have reconstructed the problem is distinctly different from the orriginal and yields a different result.

However let's approach this game differently again. Let's suppose Monty excercises a free choice every time he may do so. i.e. He will not open the door with the car behind it, but if he has a choice of doors to pen he will do so at random.

1. I choose the door with the car behind it. There is a 1 in 3 chance this hapens. Monty can either show me a TV or a Donkey and picks one a random. Therefore the 1/3 probability gets split in half. There's a 1/6 chance I picked the car and he shows me the TV, and a 1/6 chance that I picked the car and he shows me a donkey. In either of these situatons switching doors loses me the game
2. I choose the door with the TV behind it. Monty must show me the Donkey. Switching wins me the game. There is a 1 in 3 chance (2/6) I'm, in this situation.
3. I choose the door with the Donkey behind it. Monty has no choice, he must show me the TV. There's a 1 in 3 chance (2/6) I'm in this situation.

Let's look at those probabilities. Suppose Monty shows me the TV. This occurs 3/6 of the time. In 1/6 of those switching loses me the game, in the other 2/6 it wins me the game. Suppose Monty shows me the Donkey. This occurs 3/6 of the time too. In 1/6 of those switching loses me the game, but in the other 2/6 it wins me the game.

Clearly I'm better off switching.

So assuming Monty has a free choice we're back in the situaton wheer switching is the best strategy. The trouble is, this isn't the problem you posed on your weblog (I checked carefully this time).

Simon Hibbs

[Scott Miller]

Simon, I tried to use the TV as an example, not as a hard-coded part of the problem. I do see how it's confusing, though.

[Simon Hibbs]

No, I think I'm being dense again. I'm reading far too much into the specific way you presented the problem.

Simon Hibbs

[Simon Hibbs]

Actualy the girl problem does take advantage of an ambiguity in the english language to disguise the true situation a little. It states:

"...one of them is a girl..."

This could be interpreted in two ways.

1. "...THIS one of them is a girl..."

2. "...EITHER one of them is a girl..."

From the context I think it's clear that the second interpretation is intended, but it's oh-so-easy to interpret it the first way.

Simon Hibbs

[Kalvin Lyle]

Ignoring the topic of problem solving, are there any other books that people recommend?

I recently read Chris Crawfords latest book and was a bit disappointed that the majority of the books he recommended where out of print. I appreciate that Scott's list is more current.

If you haven't read Aristotle's Poetics or http://www.amazon.com/exec/obidos/ASIN/0060391685/qid=1073091801/sr=2-1/ref=sr_2_1/002-7619329-7808036'>Robert McKee's Story you should.

[Scott Miller]

Kalvin, if you liked McKee's book, then I highly recommend:

o The Writer's Journey, by Chris Vogler

o Story Sense, by Paul Lucey

o Creating Emotion in Games, by David Freeman

[Paul Jenkins]

This site is an incredible resource, Scott, and I greatly appreciate you taking the time to provide it for us. That being said, I wanted to provide a bit of context to Charles, who seems to be sinking a bit.

I don't think the problem is in Charles' assertions so much as the way in which he presents them. I wholeheartedly agree that it is incredibly important for developers to have an understanding of the business end of the industry, and at the same time, I absolutely encourage people to broaden their worldview, if for no other reason than to make them more marketable within the games industry.

On our development team we're including students of linguistics and history to help build an end product that provides both text and context for players. Similarly, my background as a generalist, having worked both as an engineer and a freelance digital artist allow me a great deal of flexibility in understanding customer needs. In saying that, "this reading list is not enough to assure success," Charles is 100% correct. However, the reading list you've provided is absolutely a wonderful place to start, and will serve to appropriately educate people in a critical part of life within the industry.

Those who believe that games are produced by the people who were willing to "sell out" are limiting their thinking in the worst way. It should always be realized that any product that goes to market does so out of demand created by the public. Determination of what is the "best" product is done at the buyer's end, but most consumers like to consider that marketing and sales are part of the product they are buying, sometimes moreso than the game itself.

Likewise, the statement that innovation is killed by playing to the market is absolutely false within the context of computer games. Any developer that doesn't innovate dies a quick death, which can be observed through numerous observations. The truth is that the market shapes the direction of innovation, often without realizing that innovation has occurred. One of the primary strengths of Scott's list is that it provides a good understanding of how, as a developer, one can learn to gauge the needs of the market and innovate to meet those needs.

In a recent article in Forbes, there's a quote that I found interesting. One of the former dotcom boomers was discussing the "new state of the market" and said, "The key to success in the new market will not be producing great products and selling them, but finding out what the customer wants, and reverse engineering it."

My first thought when reading that was, "It took you this long to figure that out, eh?"

Great job of providing a foundation, Scott. One topic that I think more dev's should be looking at is management strategy. If you're short up on information in that department, let me know... there are some incredible resources showing up recently for teaching software developers about how to organize projects and keep them flowing, how to gauge progress and anticipate needs, etc.

Warm Regards,
Paul Jenkins
Verite' Studios LLC (Registration Pending)

[Kristian]

I still dont understand how something being X or Y alters the fact that something else is X or Y

[I'm Never Wrong]

"I still dont understand how something being X or Y alters the fact that something else is X or Y"

It's the probability of both having a certain value rather than their direct effects on each other.

Consider the lottery.

Each number that you pick has a 1 in 50 chance of being picked. Say the winning numbers are:

12, 23, 31, 32, 45, 50.

I tell you that I picked 12, 23, 31, 32, 45, and I have one more to pick. If I asked you to tell me my odds of winning, you can't just disregard the overwhelming odds that had to be overcome to reach that point. Even though my odds of correctly picking the last number are 1 in 50, my true OVERALL chances of winning the lottery are still over 150 MILLION to 1.

If there are relevant values that must be considered, then you have to factor them into the whole equation even if they don't directly affect each other.

[Anonymous]

I picked yes..

I wrote this down on a piece of paper:

ABC
CBA

With A being the car, B being the TV, and C being the animal.

If you picked the car and the host were to open a door, he could open either the one with the animal or the one with the TV as none are the car.

If you picked the animal, the host would have to open the door with the TV behind it because the other one would reveal the car. So he'd have a 2x greater chance of opening the door with the TV in this situation than in the first(50% in the first, 100% here).

So you probably picked the animal and should say yes.