Showing posts with label probability. Show all posts
Showing posts with label probability. Show all posts

16 September 2009

Death From the Skies!

Philip Plait, PhD
Grade: A

Death from the Skies! Oh sweet Lord, we're all gonna die. How?, you might be asking. The answer is easier if you ask, What in the universe is not trying to kill us? The answer is nothing, nothing wants us to live; everything in the universe is out to get us.

I repeat, we're all gonna die.

(Here’s what I took from each chapter, these are by no means meant to be summaries. The ratings express in general how terrifying I find being around for it to be. It’s a scale of 1-5)

Target Earth: Asteroid and Comet Impacts

Apophis. I want you to go write that name down right this minute. Why? Because on April 13 2029, Friday the 13th and I am so not making that up, Apophis will pass closer to earth than some of our satellites. That’s right, Apophis may get closer than the T-Mobile satellite powering your future wrist-phone. And while it may miss us this time around, if it passes through the wrong spot, it will most certainly hit us in 2036. That’s nine years to try and move a rock big enough to basically set the planet on fire. Yay.

This was my favourite chapter as it was the easiest to actually wrap your mind around. B612 Foundation: I can haz Science? Also, thanks for the “There’s not even enough time to worry” there Dr Plait, I think I shall begin right this minute. Put that in your metaphorical pipe and smoke it.

Paragraph of Dissension: When did an asteroid/comet hit become the accepted theory for dinosaur extinction? Back when I was studying on dinosaurs there was still a lot of disagreement over what caused what and when. Now I turn around and everywhere is all “Yeah, dinosaurs got knocked off* by an asteroid, where have you been?” I’ve been doing very important things! Also, admittedly, the last time I was really into dinosaurs was when Jurassic Park came out so that’s nearly twenty years. I concede that a lot can happen in that time.

*Please note that getting knocked off by an asteroid is totally different than getting knocked up by an asteroid.


Sunburn

So “death” by sunburn isn’t so much death by sunburn as it is “total collapse of the world’s economies and perhaps even civilisation” by sunburn. Strangely, in light of later chapters I found this oddly comforting. The wave of radiation from the sun would be mildly annoying here on earth. At the ISS we get the Fantastic 7 – yeah, you know that bit at the beginning of Fantastic 4 before things got interesting, that’s pretty much what would happen to the ISS crew. Only quite likely way less cool. The crew actually have a special place they hide to avoid getting mutant powers. This is why I could never be an astronaut.

Actually, a solar phenomenon is what brought down SkyLab (I’d mark this as “Things I did not know” but that list grew extensively during this book), the solar flare caused the earth’s atmosphere to puff up then drag it down. One can only presume it happened in slo-mo while SkyLab’s partner screamed “Nooooo!”.

He also brings up a good point. I remember all through school learning that Sol was only an “average sun”. Not huge, not tiny, just kind of there. Dude, even an “average” sun is a pretty freaking awesome sun.

FYI: Looking at the sun with the naked eye = not as bad as people have been telling you. I’ve done it while watching a sunrise (although admittedly, the sunlight is going through a lot more atmosphere then and not quite so bad for you). Look at the sun directly through any kind of helpful magnifying equipment = boil the fluid in your eyeball. Let’s not do that, kay?


The Stellar Fury of Supernovae

The awesomeness of this is somewhat tempered by the fact that it is really unlikely to happen to us. Here in our solar system. That’s not to say we might not go exploring at some point in our future and be very very unlucky.

Also learned that all the elements as we know them had their start in supernovae. That’s kind of cool. Also, also learned that supernovae is the plural of supernova. Even my spell-checker recognises it.


Cosmic Blowtorches: Gamma-Ray Bursts

Aw shit. I don’t care how “unlikely” Plait says this is, next to black holes *shudder* this is the absolute scariest thing I can imagine happening. Later chapters are pretty scary, but totally mind-boggling and as such, don’t carry the same shazam! Also, massive stars, black holes, twin beams of death, this is totally how they should have destroyed Romulus. Supernova, shmupernova.

We’re talking about an event occuring 100 light years away. A place so far away it takes light, something that travels so fast it took us thousands of years to notice it travelled at all, 100 years to get here. And that event is powerful enough heat roast you and instantly destroy our ozone layer. Three cheers for gamma-ray bursts! May you always be so terrifying.


The Bottomless Pits of Black Holes

ad infinitum

Just go read this chapter. If you’re too tight on money to buy it, see if you can convince Amazon to help you out with the ‘Look Inside’ feature. Note: spaghettification may be my new favourite word. Also note: I’ve had black hole based nightmares for the last three days.

This did cause me to think of two questions:

  1. Can planets orbit a small black hole? I know that galaxies can (and do) but it seems that with a sufficient source of matter to feed the black hole, a planet could conceivably orbit it as one might a star. Since the black hole will be giving of light, this planet could also conceivably support life. This would have the added benefit of making it the coolest form(s) of life ever, and the winner of every ‘rough childhood’ storytelling game for all time.

  2. Could a sufficiently large star swallow a sufficiently small black hole? It seems that this should be possible, but given the nature of black holes may be a total nonsensical statement. If it is, I apologise – but then again, can a black hole cannibalise another black hole? What happens when two black holes meet?

I totally should have gone into astronomy. Stupid archaeobotany.


Alien Attack!

Plait makes much of, if there is suitably intelligent life out there, theory states that we should have met them by now. Sure, but maybe we’re the first to advance to this stage. Also, given the Drake Equation (which he doesn’t explain, maybe he just assumes everyone is familiar with it. I was, but I’m special like that) it’s quite likely that given the other variables, life could evolve countless times, just not in time to meet each other. Both myself and my great-great grandparents existed. But we never got to meet each other. (NOT an insinuation that alien life will be descended from earth life, or vice versa. Just an analogy. A bad one actually.)

I’m only going to leave you with this: either we are alone in the universe or we are not. Both ideas are overwhelming.


The Death of the Sun

This would be way more scary if we weren’t going to have a lot of prep time when it happens. I give it two skulls because the fact that it won’t happen in my lifetime is balanced out by how pants-wettingly terrifying it would be if it did.


Bright Lights, Big Galaxy


That black hole sitting at the center of our galaxy? Worrisome. That black hole sitting at the middle of the Andromeda galaxy? You know, the one that will one day merge with ours in an apocalyptic scenario that makes me weep? WTF? We’re gonna get eaten by another galaxy? The Milky Way is going to eat another galaxy? Either way, I’m very disappointed in you Milky Way. Eating your own kind... bad galaxy, bad.


The End of Everything

?

I could not wrap my head completely around this chapter. Moments of lucidity were punctuated by the knowledge that I had no grasp whatsoever of the scale of what was eventually going to happen. That’s how the universe is supposed to work. I do however, love Plait’s venturing that we might get an ‘infinite do-over’. Was that meant to be reassuring?


What, Me Worry?

I harbour a fantasy where I had gone into astronomy or astrophysics or some other ‘astro’ related field. In my fantasy, I spend a lot of time looking at stars, doing math and discovering heretofore unknown laws of the universe. Yes, in my fantasy I am Albert Einstein. What I did not imagine was that I would spend any portion of time contemplating doomsday scenarios and worrying about being hit by a giant rock.

Part of me wants to move to another planet. This will not, however, solve the problem of black holes, gamma ray bursts, supernovae, asteroids, or well virtually anything. In fact, moving may in fact increase my risks. So I shall stay here on earth and keep an eye to the heavens. When the day comes, I shall be aware... not that I can do much about it...


17 August 2009

Roulette

Remember when we talked about Blackjack a while back? The main theme of the post was that, unlike most casino games, the odds in blackjack are continuously changing. Every card that is dealt in blackjack changes the overall odds in the game of your pulling any specific card.

Today we we will talk about games where the odds are fixed; which is a fiendishly difficult concept for some people to grasp. To do this, we'll use a very popular casino game, roulette (I'd use craps, but it deserves a post all its own). On any given roulette wheel there are 37 numbers. One through thirty-six and a '0' number. Some will also have a '00' (most American ones do), but for our purposes we will use a 37 number wheel.

Okay, it's payday, you got a decent bonus, you're heading to the casino to try your luck. At the roulette table, you notice that your lucky number, '4', has just landed. Being a mathsy kind of person, you know the chances of a the same number coming up twice in a row on a roulette wheel is 1 in 1,369. So, you bet your birthday instead and lo and behold, a '4' lands again, defying all the odds. It's a mathematical miracle!

Isn't it?

Well, sort of. Before any spin, the chances that any given number will come up twice in a row is in fact 1 in 1,369. However, once the number lands the first time it has no effect on the next spin. To put it more simply, every spin has a 1 in 37 chance of hitting any given number regardless of what the previous spin was.

Let's put it in more extreme terms. The chance that a number will be spun nine times in a row is 129,961,739,795,077 to 1. Or, if you like words, a bit over 129 trillion to one. Those are some pretty high odds. To put it in perspective, your chances of winning the lottery are about 200 million to one; or 645,000 times better. In my hypothetical, this has just happened. The world is abuzzing with the news. So, what are the chances of a number being spun ten times in a row? Well, from a fresh start, the chances are 4,808,584,372,417,849 to 1. So after our nine spins, the chances of the next spin being the same are 4.8 quadrillion (a word I had to look up) to one... right? No, the chances are 1 in 37. Previous rolls have no effect on the next one.

[Actually, at this point, there is a reasonable suspicion that the game has been compromised and there is a statistically higher chance of the same number rolling. We'd have probably shut the game down by the sixth roll or so.]

In the long run... all numbers will come up equal amounts of time; but this is in the life of the game. Just becuase the last twelve spins have been red does not make it statistically more likely it will spin black next. In the long run, the red and black spins should average out to about 48/48 (not 50/50 because the '0' number is green, which throws the red/black odds off). The odds one any given number is 2.7%. The odds of red/black (or odd/even) are 48.6%. Odds on the green '0' are (again) 2.7%.

These odds (say it with me) do not change.

So when you do head to Vegas and hear someone prattling on about how they've been keeping track and a '14' is due... well, in a way it is. But it may not show up until next week and do so fourteen times in a row.

17 July 2009

Blackjack Probability

My life experience, let me show you them.


At one point in my moderately shady past I worked as dealer on a Louisiana riverboat casino. I’ll take a moment here to let you bask in the fact that my past rocks. Done? Okay, this is to anyone who has ever played Blackjack – I would like to offer you a crash course in luck v. probability vis-à-vis card counting.


The difference between blackjack and the games I will go into later is simple, in blackjack your odds are constantly changing. Discarding suits, and I know of at least three variations on Blackjack that offer varying odds on certain suited sets of cards, there are thirteen different cards you can pull [A2345678910JQK]. Assuming a full deck, you have approximately a 7.6% chance of pulling any given card. However, in the game of blackjack, there are four cards that are considered to be ‘ten cards’ [10JQK]. All of these have the same value on the table and are interchangeable within the gameplay. You could take out all of the Jacks, Queens and Kings in a deck and replace them with 10s and the game would play the same. Thus, while the probability of drawing any single card is 7.6%, the probability of drawing a ten card is in fact 30%.


Let’s play with that for a moment. Let’s say I have a table with six players who all, on the first hand, receive natural twenties (two ‘ten cards’). I also receive a natural twenty. On the table there are now 14 ten cards. A six deck shoe (common for the area I dealt in) contains 312 cards. One is ‘burnt’, or discarded if you will, before the first hand is dealt. At the end of the first hand there are 297 cards left in the shoe. The shoe stared with 96 ‘ten cards’ and now contains 82. After the first hand, the total probability of pulling another ten card is now 27%. Until more cards are pulled, the probability of pulling a ten has dropped three percent. After one hand. If that doesn’t make you pause for a moment then I don’t know what will.


So how do we get back to a 30% probability of pulling a ten card? It seems easy. Pull 14 non-ten cards to balance it out. If we do this, however, our probability only rises to just shy of 29%. In fact, to return to a 30% probability, you’d need to pull nearly thirty non-ten cards from the shoe.


The above math is what card counters are attempting to take advantage of. As cards are pulled, the odds for that type of card appearing again will fluctuate in relation to other cards pulled. By keeping a count of what cards have already been used, you can make a guess at what cards are likely to appear.


So how do casinos combat this? The easiest way is in the cut. Ever notice the dealer doesn’t deal all the way to the last card? Instead, they deal to a special yellow cut card, finish the hand, then shuffle all decks. At my casino, procedure was for the dealer to cut at least a deck and a half to two decks from the end of the shoe. If you had a suspicion the player may be counting cards, you cut straight in the middle, three decks from either end. While this doesn’t change the overall odds, at any given time a significant portion of remaining cards will never be used or seen. In theory, with a deck where 156 of the cards will never be used (a halfway cut), all ten cards and aces could be on the other side of the cut card. While the odds of pulling one of these will grow closer and closer to 100%, knowledge of this is ultimately useless as there is literally no way to access these cards.


The more cards a counter sees, the better informed they are as to what their next card will be. If a dealer dealt to the last card, a person card counting would know with 100% probability what that last card will be. (This is actually giving counters a little too much credit. For the most part, the systems used merely give the counter a ‘best guess’ at what the nature of the next card will be [High/ Low/ Neutral] rather than the specific type of card [A23456789‘10’].)


So the moral of the story is, if you ever see a dealer cut a shoe halfway then they or their pit manager suspects a card counter at the table. And honestly, trying to count into a six deck shoe while nearly a third of the deck remains unknown is a little silly. You only gain a measurable advantage for the last two or three hands. Stick to basic strategy, you’ll probably work out better in the long run.


Math!

Probability of any type of card: 1/13 or .076923… (repeating)

Probability of 'ten card': 4/13 or .307692… (repeating)

Probability of 'ten card' after first hand: 82/297 or .276094… (repeating)

Probability of 'ten card' after fourteen non-'ten cards are removed after the first hand: 82/283 or 0.289752 (non-repeating)