Things I hate

Ten things that make me scowl:


expanded polystyrene (a.k.a. Styrofoam)

candy sprinkles

country music

leaf blowers

motorcycles that are so loud that the sound literally hurts my ears

lies that are disproven yet keep coming back

movies that twist together romance and hatred, love and cruelty, sex and violence

waiting in a long line when someone cuts in line several places ahead of me and gets away with it

having to smile and say “I’m fine thanks, how are you?” to the grocery clerk when I’m feeling depressed and just want to pay for my groceries and go home



Missing song lyrics

Years ago, I heard the song “Johnny McEldoo” sung by The Clancy Brothers. One thing that struck me about it was the interesting rhyme scheme. It’s something like this:

And, sometimes, the x’s rhyme with A or C.

Allow me to illustrate. The first four lines are:
There was Johnny McEldoo and McGee and me
And a couple of two or three went on the spree one day
We had a bob or two, which we knew how to blew
And the beer and whiskey flew and we all felt gay

Now I’ll remove the words that don’t rhyme:
…….. McGee . me
…… three … spree . day
….. two .. knew .. blew
…… flew …. gay

I don’t think I’ve ever seen a rhyme scheme like that.

The lyrics are hard to understand, so I Googled them, and found that has a MISTAKE in the lyrics. There’s two whole lines missing!

Just look at the last word of every other line, which are supposed to rhyme:

*record scratch* Say what? “fire” doesn’t rhyme with “in”! Then it continues…


Clearly, “fire” rhymes with “liar” and then everything’s fine after that. So where did it go wrong? There must be a missing line that rhymes with “in”. It has to be either:

He swallowed tripe and lard by the yard, we got scarred
We thought it would go hard when the waiter brought the bill
We told him to give o’er, but he swore he could lower
Twice as much again and more before he had his fill
something something something something
something something something-that-rhymes-with-“in”
He nearly supped a trough full of broth says McGragh
“He’ll devour the tablecloth if you don’t hold him in”
When the waiter brought the charge, McEldoo felt so large
He began to shout and barge and his blood went on fire
He began to curse and swear, tear his hair in despair
To finish the affair, called the shop man a liar

or it could be…

He swallowed tripe and lard by the yard, we got scarred
We thought it would go hard when the waiter brought the bill
We told him to give o’er, but he swore he could lower
Twice as much again and more before he had his fill
He nearly supped a trough full of broth says McGragh
“He’ll devour the tablecloth if you don’t hold him in”
something something something something
something something something-that-rhymes-with-“in”
When the waiter brought the charge, McEldoo felt so large
He began to shout and barge and his blood went on fire
He began to curse and swear, tear his hair in despair
To finish the affair, called the shop man a liar

I think it’s the second option, but I’ll be damned if I know what the two lines are. This has been bugging me for a long time. The freaky part is that MetroLyrics has the SAME MISTAKE. And so does And I’ve listened to multiple recordings of the song, by different artists, and the lines are missing from ALL OF THEM. If this really is a traditional Irish song, the lines could have gone missing decades go, perhaps centuries.

Now, before you dismiss me as making something out of nothing, consider the tune itself, with no words. In 4:4 time, each line is two measures and the tune repeats every eight lines (sixteen measures).


So the number of lines in the song must be a multiple of 8 and the number of measures must be a multiple of 16. But it’s not. There are 38 lines and 76 measures. There should be 40 lines but two are missing. Q.E.D.

I’m afraid that these two lines are lost in the mists of time. I will probably never be able to solve this mystery. Add this to the list of reasons I need a time machine. *sigh*

If anyone reading this knows what the two missing lines are, PLEASE message me.

Things aren’t as bad as you think.

Pick just about any metric for the shape our world is in and chances are it’s IMPROVING.

Take violent crime. The rates of violent crime in America are at an all-time low, about half what is was when I was a kid. Total crimes are up, but as a percentage of the population it’s down. I’m safer now than I was 50 years ago. And other countries are also showing downward trends.

Take war. Worldwide, the number of people killed in wars each year, as a percentage of the population, has been going down for the last couple of centuries. Your probability of being killed in a war is lower now than just about any time in history. It’s true that the percentage of casualties which are civilians is up, but that’s mostly because the number of soldiers killed in war has dropped dramatically while the number of civilians hasn’t dropped as fast.

Take diseases. Despite hearing about outbreaks by Ebola and Zika, the fraction of people who actually die from such things is tiny compared to past outbreaks of typhoid, cholera, polio, measles, the plague, etc. We’ve made amazing progress against so many killers of the past, and we’re even making headway against Malaria now.

Take education. Even when you hear people complain that their schools aren’t as good as other schools, the fact that’s overlooked is that more people around the world are going to school than ever before in the history of the world. The global literacy rate is at an all-time high and it’s still going up.

Even when it comes to population growth, there’s good news. Our population is still going up but the number of babies being born has finally stopped growing exponentially and has stabilized. As one statistician put it, we have reached “Peak Child”. And soon we will reach “Peak Adult” too, and the population will stop growing, right around 11 billion is the prediction.

Take corruption in politics. We complain that our politicians don’t live up to our expectations but the truth is that’s because our expectations are much higher than they ever were in the past. The truth is that the average politician today is less corrupt and more responsible than the average politician of 100 years ago, let alone 1,000 years ago.

Take religious zealots and cult leaders. Even though you hear more about such things now because it makes for interesting news, the fraction of the population who fall prey to cult leaders is smaller now than it was in the past. And there are fewer and fewer people dying in holy wars started by religious leaders. The fraction of the population who say they don’t belong to any particular religion is higher today than ever.

Take transportation. Cars are safer now than ever. The number of fatalities per million passenger miles is about half now what it was 30 years ago, largely due to reductions in drunk driving and improvements in airbags and crumple zones. Airplane travel is amazingly safe now. in 2013, there were 31,000,000 commercial airplane flights, and there were only 6 fatal crashes. People say “one in a million” meaning something extremely rare, but that’s one in five million.

Take food and nutrition. The average human today is less likely to suffer from malnutrition or a vitamin deficiency than the average human did 100 years ago, or at almost any time in history. The percentage of children who develop blindness from malnutrition is lower than ever. The number of people who face starvation may be large, but it’s still a smaller fraction than during most of history.

You really have to look long and hard to find examples where things are actually worse now than in the past. One example I can think of is that fifty years ago it took fewer working days to earn enough money to buy a house. But even that one is a good-news-bad-news kinda thing. Housing is more expensive now but it’s also better. Our houses are more energy efficient than ever. They stand up better to natural disasters like hurricanes and earthquakes than ever. They catch fire much less frequently than they did in the past, and when they do catch fire we are much much less likely to be trapped in them.

There are a small handful of other trends that actually are getting worse, like global warming for example. But I don’t want to get into those today. I just want to focus on the fact that such things are a small minority.

We have the illusion that the world is falling apart because bad news spreads fast and far. But, in almost every way, the world is better now than it ever has been, and things are continuing to improve.

Pascal’s Wager

Rene DesCartes and Blaise Pascal lived in France about 400 years ago. They were colleagues and they were both mathematicians. Also, they both tried to prove the existence of God.

Rene DesCartes tried to prove it directly, arguing that nothing can exist without God. But his attempt failed; he only got as far as proving that you can’t ask questions if you don’t exist. This is usually summarized as Cogito Ergo Sum, which I discussed in my last post. If you ask me, his attempt was doomed from the start; it’s just too long a chain of ideas and each link in the chain can break very easily.

In order to justify a claim like “You need to believe in Jesus in order to get into Heaven”, you’d have to show all eight of the following: #1 There’s a law which says everything has to come from somewhere, e.g. if you see a shoe, there must have been a shoemaker (Let’s call this the Shoemaker Law). #2 The Shoemaker Law applies to the universe itself. #3 The Shoemaker Law does not apply to whatever created the universe. And whatever created the universe… #4 is able observe what happens as the universe unfolds, #5 cares deeply about the behavior of the creatures which inhabit the universe, and #6 has a plan for rewarding or punishing those creatures based on their behavior. Also, #7 You know what the rewards and punishments are. Finally, #8 You know specifically which behaviors are the ones to be rewarded and which ones are to be punished.

Cogito Ergo Sum doesn’t prove any of the links in that chain, let alone all of them.

In modern times, others have tried to build on DesCartes’s work by making the dubious claim that the Shoemaker Law applies not only to the universe, but to knowledge and logic itself. Their argument is basically “I think, therefore logic is real, therefore God exists”. At best, this allows them to bypass the first three links in the chain I described above. But they conveniently ignore the fact that it doesn’t even address the other five links. You often find such arguments under headings like “Christian Apologetics” or “Presuppositionists”.

Blaise Pascal took a different approach. He fell back on his formula for the Expected Value, which I discussed quite a bit in my three posts about playing the lottery. Here’s the logic which Pascal laid out.

Given the fact that (as we all know) believing in Jesus is what gets you into Heaven, and given the fact that Heaven is an infinite reward, and given the fact that the alternative is Hell, which is an infinite punishment, we can calculate the Expected Value for believing in Jesus. The formula will require some unknown quantities, but as you’ll see in a minute, their precise values don’t change the outcome. First, we need the probability that God exists. Let’s call that “g”. Like all probabilities, this is a number between zero and one. Because you can’t be 100% certain that God does not exist, that means g > 0. It might be 22% or 0.00000004% or it might be 0.000000000000000000001% but whatever it is, it’s not zero. Next, we need to ask the question what does it cost you to believe in a god that doesn’t exist. Let’s call this “c”. Pascal claimed that c was zero, but it still works if c is some other number, as long as c is finite.

EV for believing in Jesus = (g) x (infinite reward) –  (1-g) x (c)

Notice that, if g > 0 and c is finite, this result is always infinity, regardless of the specific values for c and g. Now consider the Expected Value for not believing in Jesus. For this calculation, we need one more number, the value of not believing in Jesus in a world where there is no god. Let’s call this “a”.

EV for not believing in Jesus = (1-g) x (a) – (g) x (infinite punishment)

Notice that, if g > 0 and a is finite, the result is always negative infinity.

Pascal’s conclusion from this is that, no matter how unlikely you think God’s existence might be, whether it’s 50% or 2% or 0.000000000000000001%, it doesn’t matter. When you multiply that probability times the infinite reward of going to Heaven, it’s always a safe bet for you to believe in Jesus.

There are so many flaws with this argument that there’s an entire page on Wikipedia devoted to explaining Pascal’s Wager and its flaws. I’m not going to try to repeat them all. I’ll just point out three which I thought of on my own.

Flaw #1: It uses circular logic.

The whole point of Pascal’s Wager is to try to decide if God exists and what you should do about it. The argument admits the possibility that God might not exist at all. Yet the argument is founded on the assumption that believing in Jesus gets you into Heaven and that Heaven is an infinite reward. If there is no god, then this assumption isn’t true at all. He started his proof for knowledge about God by assuming we have knowledge about God. That’s circular logic.

Flaw #2: It ignores alternatives (such as other religions).

Even if God does exist, that still wouldn’t prove that Heaven is real, or that Heaven is an infinite reward, or that believing in Jesus is what gets you into Heaven. Muslims believe that submission to the will of God is what gets you into Heaven, not belief in Jesus. Some religions believe that God has already decided whether you will get into Heaven or not and nothing you ever do has the power to change that decision. And Pascal conveniently ignored the possibility that there might be more than one god, and perhaps even different heavens. Then there’s one of my very favorite alternatives which I found on youtube: Keight’s Wager (“Keight” is pronounced like “eight”). Put yourself in God’s shoes for a minute. You’ve just created a universe. You’re lonely. You want to invite some people to join you in Heaven. What kind of people would you, God, want to hang out with? It’s easy to imagine that God is really into science. So maybe God would only invite into Heaven people who embrace the scientific method. Now, considering that there’s an amazing lack of evidence proving God’s existence, the only rational conclusion for a scientific-minded person to make is that God does not exist. Therefore, the perfect candidate for who God wants to invite into Heaven is…. an atheist! So, if you want the infinite reward of going to Heaven, your best strategy is to be an atheist. I’m not saying I actually believe Keight’s Wager. I’m just pointing out that Pascal’s Wager rests on unproven assumptions.

Flaw #3: The exact same logic leads to conclusions which are obviously wrong.

Suppose I show up at your door selling a bottle of water which came from the Fountain of Youth. Given the fact that (as we all know) drinking water from the Fountain of Youth bestows upon you the gift of immortality, and immortality is an infinite reward, let’s calculate the Expected Value for purchasing this bottle. We need the probability that I’m telling the truth about the water. Let’s call it “t”. You can’t be 100% sure that I’m lying, so t > 0. I didn’t specified the asking price for the bottle of water; let’s call it “p”.

EV = (t) x (infinite reward) – (1-t) x (p)

As long as p is a finite number and t is not zero, this formula always comes out to infinity. Therefore, you should definitely buy the bottle of water from me, no matter how much money I ask from you, and no matter how slim the chance is that I might be telling the truth. If the reward is infinite, then your only logical course of action is to hand over all your money.

Clearly, this is wrong-headed. Only a fool would hand over all their money to a stranger selling bottles of “magic” water. To suggest that logic demands that this must be the best course of action is just ridiculous.

.  .  .  .  .

Remember in my last post when I said that the Expected Value formula doesn’t work very well when you use very large numbers? Well, here’s a case where Pascal tried to apply the formula to INFINITE numbers, and it failed miserably. Frankly, he should have known better. But he was desperate. He knew deep down that he was 99.9% convinced that God doesn’t exist, but he badly wanted to keep clinging to some tiny scrap of hope. He couldn’t face the idea if giving up his belief. So he slapped together this appalling collection of bad logic and said he would keep on believing in Jesus anyway.

I can sympathize with Pascal’s situation. I struggled for years before I could finally give up my belief. After holding on to it for such a long time, it was very difficult to let go. I was a believer from childhood up until my early thirties.

I think that if I had started questioning my beliefs in my fifties or sixties, it would have been even harder to let go. I’m not sure if I would have been able to do it.

In conclusion… if you’re a believer who wants to try to bring me back into the light and you think to yourself “Hey! I know what to say to an Atheist. I’ll say what if you’re wrong? That’ll get him”… don’t even bother. I have spent way more time asking myself that very question than you ever will.

You can’t know anything with 100% certainty.

When people say “It’s impossible to know with 100% certainty that there is or isn’t a god.”, I respond that it’s impossible to know with 100% certainty ANYTHING. If “100% certainty” is your benchmark, then nobody knows anything about anything and we can all just give up on ever trying to find any knowledge at all. Obviously, in the real world, we have to make a judgment call and say “In this situation, 99% certainty is good enough for me to make a decision.” or maybe it’s 95%, or 99.999%, depending on the situation. It seems to me an awful lot of time gets wasted quibbling over whether someone who is 99.7% sure the aren’t any gods should be called an atheist or an agnostic.

Even scientific facts (like “water freezes at 32 degrees Fahrenheit”) are subject to change when more evidence comes in. For example, as recent as 20 years ago, it was considered a “fact” that male pattern baldness was caused by a sex-linked gene on the X chromosome. Now we know that the original study which made that determination was faulty. The “fact” that you inherit baldness exclusively from your mother’s side of the family turns out to be simply not true.

Even the example of water freezing at 32 degrees F isn’t 100% true. The truth is more complicated than that, depending not just on temperature but also pressure. The so-called triple point of water happens at .01 degrees C and 611.73 Pa (roughly .006 atmospheres). Around 2,000 atmospheres, water can remain liquid all the way down to zero Fahrenheit. Read the wikipedia article about “ice”.

Heck, even in an ordinary real-life setting, if you put a bowl of water outside and the meteorologist on the radio tells you that it’s 31 degrees outside, can you be 100% sure that the water will freeze? Of course not. The weather report could be mistaken. The water could have trace amounts of salt in it, which changes the freezing point. The bowl might be in direct sunlight, preventing it from freezing.

And in the bigger picture, the only reason that you think you know that water freezes at 32 degrees F is that you remember having been told this fact by other people. But you can’t be 100% certain that your memory is accurate. People forget things all the time and make mistakes. Maybe the correct number is 23 and not 32 but you have some combination of Alzheimer’s disease and Dyslexia. Sure, the chances of that being true are very very slim but it’s not zero.

Beyond faulty memory, there’s also the possibility that you are not who you think you are at all and everything you think you remember about your past is actually an elaborate hallucination. You could be lying in a hospital bed, in a coma, on some distant planet, dreaming that you’re an Earthling, and all the so-called facts you think you learned on Earth are just figments of your imagination. Sure this idea seems far-fetched, but you can never be 100% certain that it isn’t true.

I’m not saying that facts don’t exist, or that nothing is true. I’m just saying that, as a human being, our knowledge of the facts is never 100% certain.

The only fact I can think of that might come close to being 100% certain is Rene DesCarte’s Cogito Ergo Sum, “I think therefore I am”. But even that statement is very limited. It only applies to the person who is doing the thinking. And it doesn’t really explain what it means to exist. If I’m part of a simulation, living inside a computer, is it fair to say that I “am”? Cogito Ergo Sum doesn’t even prove that your brain has any physical substance, let alone the body which you believe contains your brain. It also doesn’t explain what I am. It just says that I am. And I’m still not entirely convinced that it’s 100% certain. Maybe there’s a flaw in the logic that we haven’t discovered yet.

But most of the time, in day-to-day life, it’s pointless to worry about this stuff. All you need is to be convinced that it’s probably okay and the risks are small. Could a speeding car kill you? That’s a sizable risk, so it’s prudent to take precautions like staying on the sidewalk and waiting for the signal at the crosswalk and looking both ways before crossing the street. But it would be overreacting to never leave your house just because you can’t be 100% sure that a car won’t drive up onto the sidewalk and kill you. There are no guarantees in life. Just accept the fact that, sooner or later, everybody dies, and make the best judgment calls you can in each situation. If you spend your life terrified of death, you miss your chance to enjoy the life you have.

Playing the Lottery, part 3

Now that we’ve discussed Pascal’s calculations of “expected value” and the various shenanigans the Lottery uses to make the prize look bigger than it really is, let’s talk about the end results of being a so-called winner.

First, ask yourself what money is good for. Seriously. There are things you can get if you have money which you can’t get if you don’t have money. For example, if you have $2 you can get a hamburger, which can mean a lot if you’re very hungry. If you have just $10 you can get a good meal at a restaurant. If you have $50 you can spend the night in a hotel room instead of sleeping on the street. If you have $1,000 you can rent an apartment for an entire month. With $10,000 you could buy a nice used car or an older motorhome. With $100,000 you could buy a small house or a really nice motorhome. With $1,000,000 you could buy a really nice house plus have enough money left over to buy food for yourself for several years. Each of these examples demonstrates the utility of money. With it, you can get something you need or want, without it you can’t. This might affect your happiness level (or might not) but it certainly can affect your health and your safety.

But how much utility can you get from $2,000,000 compared to $1,000,000? You can buy a house that’s twice as big. But will that make you twice as happy? Will it make you twice as safe? Will it make you twice as healthy? Certainly not. The difference between struggling to find food and shelter vs. having a nice house full of food is about $4,000 per month. Beyond that, having more and more money only adds a tiny amount to the list of things you can do and how healthy/safe/happy you’ll be.

Of course, if you got $10,000,000 you could give most of it away to other people. Then both you and 9 of your friends could each have a house full of food. But my point remains that $10 million in the hands of one person is not 10x better than $1 million.

Consider the following game. I’ll put 30 six-sided dice into a shoebox and shake it up. You buy a ticket from me for $1,000 and then we open the box. If all 30 of the dice have landed on 6, I pay you $1,000,000,000,000,000,000,000,000,000. That’s one billion billion billion dollars, also known as an octillion. It’s many many times all the money on Earth right now. If you had that much money, it would literally be impossible for you to spend it all because there simply isn’t enough stuff on Earth for you to buy. Let’s calculate the expected value for this game. The chance of rolling 30 sixes is 4.52337×10^-24, which is .00000000000000000000000452337 .

EV = (4.52337×10^-24)x($1 octillion) – (1-4.52337×10^-24)x($1,000) = +$3,523.37

As you may remember, any positive expected value at all means that the game is tilted in favor of the player and it’s a “good” bet. In this case, you are risking $1,000 and expect to make a profit of $3,523.37 which is a fabulous return on your investment. Would you do it? Would you actually pay me $1,000 for a ticket to play this game?

I submit that, even if you believed that I’d be able to follow through on the promise of paying out if you win the bet, it still would be foolish for you to spend $1,000 on a ticket. The amount of happiness you’d get from winning simply isn’t worth what you give up by having to pay me $1,000.

This demonstrates a fundamental flaw in the Expected Value formula. It assumes that getting 100x as much money has 100x as much utility or will make you 100x as happy, and that’s simply not true. The larger the numbers involved, the less useful the formula becomes.

However, there’s a positive result from buying a lottery ticket which has nothing to do with winning. Just buying a ticket gives you a chance to dream about changing your life. If the amount of happiness you get from dreaming about becoming a millionaire makes you happier than keeping the cost of that ticket, then it might be money well spent.


Playing the Lottery, part 2

In my previous post, I talked about a calculation called “expected value”, which helps measure just how fair or unfair a given game is. I also talked about “the gambler’s downfall”, which basically means that the player is much more likely to run out of money before the house does. In this post, I’ll talk about five ways the state lottery tries to trick you into thinking that the game is better than it really is.

#1 The prize might be divided among several winners. They want you to think about the size of the jackpot and ignore the fact that several winners may end up splitting the jackpot. A $72 million jackpot sounds bigger than a $24 million jackpot, but that’s just an illusion. The $72 million jackpot is much more likely to be split three ways, so each gets $24 million.

#2 They lie about the value of the jackpot. I’m not talking about taxes; that’s a whole other subject. Imagine a game where, if I win, you have to pay me right now, but if you win, I take 30 years to pay you. How fair does that sound? When they tell you that the prize is $24 million, that’s a deception. The truth is that they are essentially offering you a gift certificate which is only worth $14 million. You can trade it for $14 million in cash, or you can trade it for an annuity that pays $800K per year for the next 30 years. The problem here is the difference between Present Value and Future Value. $24 million is the Future Value, spread out over 30 years. But I don’t care what it will be worth in the future. What matters is what it’s worth right now. The Present Value is only $14 million, not 24. There exact ratio of Present Value to Future Value depends on interest rates, but right now PV is roughly 60% of FV over 30 years.

#3 They use huge numbers in order to confuse people. Most people can understand small numbers like $50 and $1,400 but they have trouble understanding just how big is a million, or a billion. The lottery takes advantage of this by offering what seems like a large prize and burying in the fine print the fact that the odds against you are even more astronomical. Sometimes it’s 14 million to 1 against, sometimes it’s 292 million to 1 against. Your brain sees both those numbers as just “really big”, even though the second one is twenty times higher.

#4 They make the game complicated. This has the double whammy of making it more fun (because it feels like you have some control) yet it also makes it harder to understand the odds. Even if you’re one of the rare people who learned Pascal’s formula for expected value, they are betting you won’t be able to apply it to such a complicated game. It has been said that the lottery is a tax on people who are bad at math. The truth is that even people who are relatively good at math have trouble understanding the lottery. Luckily, you have me to help you.

#5 The exact parameters of the game aren’t known until after it’s over. In order to figure out how much you might win, you need to know how many tickets will be sold. But that’s not known at the time you buy your ticket. And they are constantly adjusting their estimate of what the jackpot will be. In fact, the size of the jackpot also depends on how many tickets get sold.

Let’s try to estimate what the expected value of the lottery really is. First, it’s not guaranteed that someone will win. It’s very possible that there won’t be any winning tickets. The more tickets get sold, the greater the chance that someone will win, but that also increases the chance that the jackpot will be split. And remember that the advertised number isn’t the actual jackpot. Unfortunately, we’ll have to make educated guesses for some of the numbers. Suppose they advertise that the jackpot this week will be $18 million and we think there will be 30 million tickets sold. Suppose this is a standard $1 “pick six numbers from 1 to 49” lottery, with 13,983,816 unique combinations of numbers. Let’s call that last number n; you’ll see why in a minute. All things being equal, any ticket has 1/n chance of winning. But, assuming that someone wins, the best guess for how many winning tickets there will be is 30 million divided by n. The jackpot will be divided by this number, which means we’ll actually multiply the jackpot times n over 30 million. And lastly, remember that the actual jackpot is only about 60% of the advertised jackpot. And we need to multiply all this by the probability that someone will win. Given 30 million tickets, I’ll estimate that to be 75%.

EV = (75%)x(1/n)x(60%)x($18 million)x(n/30 million)-$1.00

Notice there’s an n in the numerator and denominator, so the n’s cancel. Same goes for the “million”. That just leaves…

EV = (75%)x(60%)x($18)x(1/30)-$1 = $.27-$1.00 = -$.73

This is a really bad expected value. It’s negative (of course) meaning the odds are tilted against the players. On average, each ticket costs $1.00 and loses $.73. That’s a huge profit for the house.

Well, let’s suppose that no one wins the jackpot this week and it rolls over to another week. Now they’ll another 30 million tickets and the advertised jackpot is $36 million.

EV = (75%)x(60%)x($36m)x(1/30m)-$1 = $.54-$1.00 = -$.46

This is better, but it’s still a large profit for the house, and that’s on top of all the profit they made last week when there were no winners at all.

Let’s take it one more step. Suppose that once again there are no winners and it rolls over again. This week they advertise the jackpot to be $72 million. Why such a big jump? Because they expect to sell more tickets! This week there will be 60 million tickets instead of just 30 million. Now it’s 90% certain that someone will win.

EV = (90%)x(60%)x($72m)x(1/60m)-$1 = $.65-$1.00 = -$.35

The house still expects to make a 35% profit this week, on top of all the profit they made last week and the week before. The only way that your EV becomes positive is if there’s a rollover followed by a week where very few people buy any tickets. But they’ve convinced everyone to buy the tickets because $72,000,000 sounds great.

Now, let’s use the real-world numbers from last week’s Powerball Lottery. The jackpot was advertised as $1.5 billion and they sold 371 million tickets.

EV = (85%)x(60%)x($1586m)x(1/371m)-$2 = $2.18 – $2.00 = $.18

Amazingly, we’ve actually found a game with a positive expected value, which means it favors the players (slightly). Players could expect a 9% return on their investment. This leads to another question. If you could buy one of every single ticket, would it be worth it? First, consider that n=292,201,338 for Powerball, so you’d need to buy that many tickets. And you’d have to hire an army of 120,000 people to help you buy them, which would cost around $50 million to pay their salaries for one week, bringing your total investment to $634 million. You’d be increasing the number of tickets sold to 663 million, and the jackpot would go up another 200 million or so. Also, you’d be guaranteeing that there would be at least one winner.

EV = (100%)x(100%)x(60%)x($1786m)x(292m/663m)-$634m = $471m-$634m = -$163 million

So that would be a really bad business plan. It’s not smart to invest $634 million when you expect to lose $163 million of it. The EV changed when you altered the game by buying so many tickets.

Anyway, what actually happened last week is there were 3 winners, so each of them got $328 million (Present Value), which isn’t nearly as big as $1.586 billion but it’s still huge. But is it really all that great? Will it make you happy? Will it solve your problems? That’s the topic for part 3.

Playing the Lottery, part 1

There was a lot of talk last week about the huge jackpot in the Powerball Lottery. Many people were wondering… is it true that this Lottery was somehow better than other Lotteries? As a former math teacher, I find such questions interesting. I’m going to tackle this in three parts. Part 1 will be about how to judge the fairness of gambling games in general. Part 2 will talk about strategies the Lottery uses to try to trick you. Part 3 will discuss the complicated question of how winning and losing affects your happiness.

First, let’s look at a simple way to judge whether games are fair.

The simplest game I can think of is a coin flip. I flip the coin, you call it heads or tails. If you guessed right, you win. Otherwise, I win. But what, exactly, do we “win”? Suppose we each put up a dollar and the winner gets to keep all the money. I think you’ll agree that this is a completely fair game. Neither of us has an advantage over the other.

But that’s not generally how gambling works. The person who sets up the game (called “the house”) can adjust the game to give themselves an advantage. As the saying goes, “the house always wins.” But there are varying degrees of just how lopsided the game might be.

Let’s consider a slightly more complicated game. I’ll roll a six-sided die underneath a cup and invite you to guess what number is showing on the die. But you have to put down $3 before you guess. If you guess the number, I’ll give you $12. How fair is this game? Fortunately, a very smart man called Blaise Pascal came up with a way of calculating this, 400 years ago.

Imagine yourself playing the game many times (or many copies of yourself playing the game together). On the average, do you come out ahead? Consider the six-sided die game described above. Clearly, you’ll lose this game most of the time. But it might be worth it to play, if the amount you win is sufficiently large compared to the amount you lose. Imagine playing the game six times and winning just once. You lose five times. All together, you’ve won 1x$1=$12 and you’ve lost 5x$3=$15. So you’re down by $3 after six games. That’s an average loss of 50 cents each time you played. This gives us a measure of how fair the game is. Your “expected value” is -.50 , which is roughly 18% of what it costs you to play the game. From the house’s point of view, they expect to make an average of 18% gross profit from each game.

This isn’t precisely how Blaise Pascal did it. He suggested that you should consider all the possible outcomes, calculate the probability of each, and multiply each probability times the win/loss associated with that outcome, and add up those values. Let’s try it his way.

You probability of winning is 1/6. Your probability of losing is 5/6. Multiply 1/6 times the $12 win and you get $2. Multiply 5/6 times the -$3 (negative because it’s a loss) and you get -$2.50. Add together $2 and -$2.50 and the result is -$.50, which is the same expected value we calculated above.

Note: when the house has the advantage (which is nearly always), the expected value will be negative. If you ever find a game with a positive expected value, that means the player has the advantage over the house. Such games are very rare.

Let’s compare that game to another one. In this next game, I’ll write down a single digit, anywhere from 0 to 9. You have to guess the number to win. I sell you a ticket for $2 and you write your guess on the ticket. If you guessed right, you win $17. Let’s calculate the expected value for this game. There are 10 choices so your probability of winning is 1/1o. Multiply that by $17 to get $1.70. Then multiply 9/10 by -$2 and get -$1.80. Add together $1.70 and -$1.80 to get -$.10, which is the expected value. But wait. There’s a mistake there. Did you catch it? I said I’ll sell you a ticket for $2 and you write your guess on the ticket and maybe you win $17… but you don’t get your $2 back! So even when you win, you really only came out ahead $15, not $17. So really we should have added together (1/10)x($15)+(9/10)x(-$2) = -$.30.

So the six-sided die costs $3 to play and you expect to lose $.50 (about 18%) but the 0-9 game costs $2 to play and you expect to lose $.30 (which is only 15% of $2). So you lose 18% of your money in the first game but only 15% of your money in the second game. Hence, the 0-9 game is a better bet for you. Of course, better for you means worse for the house.

Generally speaking, if the house takes less than 10%, that’s pretty good for the players. If the house takes more than 20%, that’s bad for the players. If the house takes more than 50%, that’s terrible for the players.

So now let’s look at a game where the house takes more than 50%. It’s a charity fundraiser. They walk around the room selling tickets for $1. At the end of the night, they count how much has been collected, put 1/4 of the money into a big glass jar and then randomly draw a number to see who wins. If your ticket matches the number, you win what’s in the jar. Suppose they sell 600 tickets, taking in $600. $150 of it ends up in the jar. So if your ticket wins you come out $149 ahead. The chance that your ticket wins is 1/600. The expected value is (1/600)x($149)+(599/600)x(-$1) = 149/600 – 599/600 = -450/600 = -.75 which means that, for each $1 ticket sold, the house keeps 75 cents. That’s great for the house, but bad for the players.

Let’s go back to the 0-9 guessing game for a minute. We calculated that, on average, you’ll lose 15% of your money. Imagine that you start with $100 and you use it to buy 50 tickets. On average, 5 of those tickets will be winners and 45 will be losers, so you end up with $85. What happens next? Suppose you buy 42 more tickets. You’d expect 4 of them to win and 38 to lose. Now you have $69. I think you can see where this is going. If you keep using your winnings to buy more tickets, eventually you’ll end up with no money left at all. The point is that recycling your winnings back into more tickets causes you to lose even more money than what the expected value says.

Of course, there’s a tiny tiny chance that you’ll have a lucky streak, winning game after game, until the house runs out of money (called “breaking the bank”). But honestly, who do you think will run out of money first, you or the house? This is called “the gambler’s downfall”.

Let’s talk about roulette. You pick a number from 1 to 36 and hope that the ball will land on that number. The “odds” are 35 to 1, but there are 38 spaces on the wheel. So if you bet $10 you have a 1/38 chance to win $350 (and keep your $10 too), plus a 37/38 chance to lose your $10. The expected value is (1/38)x($350)+(37/38)x(-$10) = -10/19, approximately -53 cents. That’s barely 5% of your bet, so this is a good game from the player’s point of view. But think about what would happen if you recycle your winnings. Suppose you walk in with $500 and you say “I’m going to bet $10 on my lucky number fifty times”. We don’t know precisely what will happen, but you’ll probably win once, maybe twice, and walk out with either $360 or $720. Not bad. But if you take those winnings and keep on betting it, you will eventually run out of money and walk out with nothing.

On the other hand, Suppose you walk in with $500 and say “I’m going to bet $10 on my lucky number until I run out of money or until I win, at which point I’ll stop”, then you have almost a 50-50 chance to walk out with more money than you came in with. You might even walk out with $850 if you win on the very first spin. As Kenny Rogers sang, “Know when to walk away.”

From the house’s point of view, it’s still a win for them. Suppose it takes you forty bets until you eventually win one and quit. Imagine you and 1,000 other people all making forty $10 bets. According to the expected value, the house predicts an average profit of 53 cents times forty bets times 1,000 people, which comes to $21,200. On a good day, the house might make $30,000 profit at that roulette table. On a bad day, they might only profit $10,000. But the house always wins.

That’s all for Part 1. In Part 2, we’ll discuss state-run Lotteries and how they trick you into thinking that the game is better than it actually is.


Star Trek Pagh

I just got through watching “A Matter of Honor”, the Star Trek TNG episode where Riker is temporarily posted to a the Klingon ship Pagh. At the end of the episode, he takes command by deposing the Klingon captain and says to the Klingon crew, “I’m your captain now”.  With weapons armed and a crew which is ready for a fight, he hails the Enterprise and orders Picard to lower their shields and surrender. So I started thinking… what if the Klingon weapons officer had fired a photon torpedo at that moment?

Suppose the Enterprise were destroyed by the hit. Kargan was aboard the Enterprise at that moment. That leaves Riker as permanent captain of the Klingon ship Pagh. His first office is now Lt. Klag. Naturally, Captain Riker would chastise the weapons officer, possibly kill him. But it would be too late to undo the damage.

Neither Troi nor LeForge appeared in that episode, so it’s possible that they were not on board the ship at that moment. Also, Beverley Crusher was at StarFleet Medical during season two, so she would have survived as well. Maybe some strange twists of fate would get Troi, LeForge, and Crusher transferred to the Pagh as well, and then Captain Riker and his mostly Klingon crew could travel the galaxy having adventures aboard the Pagh.

I think this is an interesting though experiment.

And, according to Rule 34, somebody somewhere has made porn about it.

Bring out the popcorn!

ten crazy theories you can’t disprove

Everything you know is based on information you gather with your senses, compared to memories that are stored in your mind. You believe that this knowledge comes from your interaction with the real world and the objects and people which inhabit that world. Plato pointed out that a person who lived their entire life in a cave, seeing nothing but shadows and never seeing the objects which cast the shadows, would think the shadows are real, just like we think the world we see is real. But what if that’s all an illusion? Could you prove it?

Here are ten crazy theories about the universe which cannot be disproved.

#1 This life is really just a dream you’re having while you’re lying in a hospital bed somewhere, in a coma.

Every detail of your life, and every memory you think you have of it, is really just a highly detailed dream you’re having. None of it is real. Any minute now, you might wake up and find yourself lying in a hospital bed, in a world with a completely different history, and say to yourself “Oh, it was all a dream.” Right now, you think you’re a 32-year-old real estate agent with 2 kids but the truth is that you’re a 60-year-old school teacher who never got married, having a dream about being a 32-year-old real estate agent with 2 kids. Some dreams can seem very real when you’re in them and you never know for sure until you wake up.

#2 This life is really just a dream and Earth doesn’t exist at all.

Similar to #1 above, you’re in a coma having a dream but the hospital bed is on an alien planet which is very different from Earth. In fact, Earth doesn’t exist. You just dreamed it up. You think you’re a Homo Sapiens but you’re not. As the philosopher Chuang Tzu asked, if a man can have a dream about being a butterfly, how do you know that you aren’t really a butterfly who’s having a dream about being a man?

#3 The entire universe doesn’t exist, except for you.

This world is a dream all right, but you aren’t lying in a hospital bed on Earth or any other planet because there are no planets. You dreamed the very concept of stars and planets. The truth is that your mind is the only thing that exists in the cosmos and everything else (even your body) is just part of this dream you’re having. Rene DesCartes famously said Cogito Ergo Sum ( I think therefore I am ) but the only person you know for sure to be thinking is yourself, so you exist and maybe that’s all there is. Just you. Thinking and existing.

#4 The universe is real but it was created five minutes ago.

For reasons unknown, an omnipotent god decided to create a universe with you in it, complete with galaxies and stars and planet Earth, and everything on Earth, including other humans. But this god didn’t have the patience to spend 6 days creating the universe and then wait 6,000 years for history to unfold gradually, leading us to this exact moment in time. This impatient god decided instead to create the entire universe, just as you perceive it to be right now, five minutes ago. Any memories you have of things that happened more than five minutes ago are false memories. Those memories were created five minutes ago. Any artifacts you find which appear to be more than five minutes old were actually created five minutes ago, complete with features which give them the illusion of being much older, and those features were created five minutes ago.

#5 The world as we know it is just a computer simulation.

Remember the game The Sims? If computers keep getting better and better, it may become possible to program a simulation which is so detailed that the characters in the simulation become self-aware. The world they inhabit seems very real to them. It’s the only world they have ever known. It’s perfectly consistent for them, even if the rules are slightly different from those of the world inhabited by the programmer who wrote the simulation. Now, given the idea that there could be thousands of such simulations running on thousands of different computers, and only one real world, what are the odds that this world, which you think is real, is actually the one real world? Isn’t more likely that it’s one of the many many simulations? Perhaps it was created by a programmer in the far off future who wanted to see what life might have been like here in our time, which is the ancient past from the programmer’s point of view.

#6 You’re in a simulation which is running parallel to the real world, on trial for a crime you haven’t committed yet.

Similar to #5 above, you’re in a simulation, but it’s not the ancient past, it’s present day. There’s the real you who inhabits the real world, and there’s a thousand simulated yous who inhabits a thousand simulations. The real you has been arrested by the thought police who suspect you are about to commit a crime. They’ve programmed a thousand computers with a simulation of the real world, and put into each one a highly detailed simulation of you and your personality. They are monitoring the simulations to see what you’ll do. In each simulation, there will be a situation where simulated you will have an opportunity to commit a crime where simulated you thinks no one will ever find out. If the majority of the simulated yous go through with the crime, then the real you will be punished with horrific torture. So, dear reader, you think you’re real but actually you’re just a simulation and the real you is handcuffed in a police station awaiting the results of this test. If you, the simulation, commit a crime (which crime? impossible to say…) then the real you will be tortured for a very long time. So watch yourself.

#7 You’re in a parallel simulation, accused of treason and being tested for loyalty.

Similar to #6 above, you’re one of a thousand simulated yous whose actions will have dire consequences for the real you which is handcuffed in a police station. This simulation is your chance to prove your loyalty. The problem is… loyalty to whom? You don’t know. Perhaps the programmers are Nazis who are giving you this chance to prove your loyalty to the Nazi Party. If you denounce the Nazis in this simulation, the real you will suffer for it. Or maybe the programmers are Communists fighting the Nazis who are expecting you to denounce the Nazis and demonstrate your loyalty to Communism. There’s no way to tell what it is they want you do do or say. But if you make the wrong choice, the real you will tortured for a very long time.

#8 You’re in a simulation which appears to be 14 billion years old but really it was created just 6,000 years ago and you’re being tested for… something.

Is the simulation real, or does it just seem real? Either way, you find yourself on planet Earth, surrounded by people, a few of which are desperately trying to tell you that the universe is only 6,000 years old. You laugh at those people but actually they’re right. And you’re being tested. The creator/programmer wants to see how you will act. Certain actions will prove your loyalty and the real you will be rewarded, other actions will show your disloyalty and the real you will be tortured. But which actions are which? The creator/programmer has deliberately put false clues into the simulation regarding the age of the universe. What if there are other false clues telling us to do certain things and not do others when really that’s precisely what condemns us to torture? Does the creator reward people for being gullible? Does the creator reward people for being skeptical? There’s not way to cover all the bases. No matter what you do, there’s a risk that you’ve chosen the wrong answer. In the words of Bill Hicks, “Does that bother any of you? That God might be fucking with us?”.

#9 You are immortal.

The world is real, you are real, but you can never die. You see other people dying around you and you believe that some day you will die but the truth is that you’ll keep avoiding death, somehow. Every bullet fired at your head will miss by a few inches. Every disease you catch will just fail to kill you. You’ll keep getting older, of course, but no matter how bad your health gets, you never… quite… die. The only way to disprove this theory is to actually die but then if and when that happens you aren’t conscious anymore so you never have that “Aha!” moment where you can say “Look, I’m dead!”. So there’s no way to know for sure that you aren’t immortal.

#10 Everyone is immortal.

According to the many-worlds interpretation of quantum mechanics, every event splits the world into two worlds, one where it happened and one where it didn’t happen. Suppose the real you branches into this world and a ghost you branches into the other world. This happens millions of times each second. At every single branch point, there is at least one branch which leads to a world where you survive. For example, someone points a loaded gun right at your head and pulls the trigger. Will the gun misfire, yes or no? That event splits the world into two worlds, one where you are alive and one where you are dead. The real you follows the branch into the world where you are alive and in the other world it’s just a ghost you. The ghost is dead. But the real you is still alive, in another world. So the real you is immortal, because every single event has some possible way that the real you could survive (even if the odds are astronomical), so the real you always will survive. In those other worlds, other people see you die but it’s not the real you, it’s a ghost you. And the same thing is true about other people! Their real selves always branch to a world where they survive, but it may not be the same one that the real you is in. So you see people dying, but it’s just ghost them. The real them is still alive. And they see you dying, but it’s not the real you either. Everyone is immortal. Again, the only way to disprove this would be to have an “Aha!” moment after you’re dead. But if you’re dead, it’s too late to have that moment.

None of these theories can be proven false. There aren’t any experiments that you could conduct whose outcome would confirm or deny the truth of these theories.

But hey, there’s probably nothing you can do about it anyway, so don’t waste time worrying about it.