The stupid AA thing continued. Warning: This is long.
Just for fun, and just because I have way too much time on my hands, Iíve put together a little story.
Lets have it be a dialog, I like them. And letís use characters from a book I once tried to read called GŲdel, Escher, Bach: Couldnít understand it but it may make me seem like I know what Iím talking about and Iíll take all the help I can get. And oh yeah, any similarities between the characters in this story or the events depicted within is purely coincidental.
Achilles: Hey, a friend of mine lets call him Diablblanco wants to know what his chance of getting dealt AA is.
Achilles: What do you mean when? Whenever.
Achilles: What are smokiní man? Thatís nuts.
Tortoise: Somethiní from Brazil. Want some?
Achilles: No, no I mean the 100% thing, thatís nuts.
Tortoise: By whenever, if you mean ever, the 100% is correct; assuming your friend actually plays poker of course.
Achilles: OK, I see your point, and yes Iíll have some. What is his chance of getting it on the next hand?
Tortoise: Oh, let me pull out my HP-48GX and run the numbers. Aha, 4Ö52Ödivide 3Ö51 divide, multiply, invert and presto! 221:1
Achilles: Just what my good friend Icepari said it would be.
Now, Diablo heard from some asshole, letís call him Bpazjr, that the odds would be something crazy like 48,841:1 to get AA back to back. But that make absolutely no sense. If itís 221:1 once, itís 221:1 twice and forever after. Tell me Tortoise; since youíre so smart, just what are the odds of that happening?
Achilles: Excuse me.
Tortoise: You said are. You meant is.
Achilles: Are we talking math or grammar here I may be a little punk but I think I know what the definition of the word are is.
Tortoise: Apparently not because you see, Mr. Jr., although an asshole, is correct, getting dealt AA is a single event, and getting them back to back is also a single event that is exponentially less likely to happen.
Achilles: No you stupid turtle its 2 consecutive but separate events that should have the same likelihood of happening. WHY CANíT YOU SEE THAT?
Tortoise: Iím a tortoise.
Achilles: Whatís the difference?
Tortoise: I canít swim.
Achilles: Oh sorry. But WHY CANíT YOU SEE THAT?
Tortoise: We tortoises have bad eyesight. But anyway, it gets worse. What if I told you that it doesnít even matter if it happens back to back?
Achilles: Iíd say you should go back to chewing lettuce Ďcause this Brazilian shit is turning you into a fruit cake.
Tortoise: You Greek heroes have never been known for your brains, Odysseus excepted. I can see Iím going to need some visual aides to demonstrate my point.
Tortoise momentarily disappears into his shell and after a protracted period of rummaging sounds and slamming drawers, reemerges with a dime bag and 10 crisp, mint in the box, decks of Hoyle cards.
Achilles: Whatís that for?
Tortoise: Donít worry, Iíll share.
Achilles: I meant the cards.
Tortoise: Thatís the visual aide. Howís your math?
Achilles: Itís always been my Achilles heel.
Tortoise: Very funny. Do you know the odds of getting dealt a pair, any pair?
Achilles: That jerk Bpaz says itís 16:1 but I donít believe anything he says. Did you know he got kicked outa here for being such an a-hole. Besides, I keep getting 17:1.
Tortoise: Yes, well, once again thatís why youíre a dumb Greek and Iím a proud member of the Chordate Phylum. Itís 16:1. Weíll save that math for later.
Tortoise breaks the seal on the cards and with deft fingers uncharacteristic of his kind, proceeds to lay out all 10 decks on the table in front of them. Did I mention theyíre in a pub? Itís a big table. And oh yeah, they must be in Amsterdam. This curious behavior has now caught the attention of the patrons who have, up to no, been bickering amongst themselves about stupid things like ďthe dangers of playing unsuited pairsĒ and ď why itís better to fold when you can checkĒ. They consist of a secret agent, some hick from Tennessee wearing a crimson t-shirt, four condescending looking dogs sitting at a table by the door, and the bartender Nick who, while happy about the amount of beer heís selling, has become increasingly annoyed by the demeanor of those involved.
Tortoise: OK you demi god you, pick a card, any card.
Achilles: Very well, Iíll play your game. I choose this card from deck #1. Wow, what do you know, itís the ace of spades. What were the odds of that happening?
The crowed erupts in laughter save for one man who rises from his chair disgusted, insisting that the game is rigged. Tortoise himself cracks a smile at this.
Tortoise: Well, I wouldnít have bet more than a buck against your 13 of it, and speaking of bucks, hereís one of mine. What would you bet that the next card you draw from this deck will be one of the 3 remaining aces?
Achilles: Certainly not more than 7 or 8 cents.
Tortoise: Alright! 16:1 odds. Not too shabby for a dumb Greek. I think Iíll make out in the long run, but all-in-all, not to shabby. And what did we say the odds were pulling them out of this single deck together?
Achilles: Címon Tortoise, weíve been through this already. The odds are 221:1.
Tortoise: And may we call the act of drawing 2 consecutive aces from a single deck a single event?
Achilles: I guess so. Yes. Getting dealt pocket aces is one event.
Tortoise: With the same probability of drawing a single ace?
Achilles: Please Tortoise donít treat me like a complete idiot. Anyone with half a ganglion of intelligence can see that the odds of getting 2 aces are less than one.
Achilles: Well, there are more of them for one thing?
Tortoise: By the same logic, if youíre willing to treat the pocket pair as one event, which is really just the combined act of getting the same card twice, and you donít argue the math, then it should follow that getting dealt 2 consecutive pocket pairs is just a more extreme example of the same thing.
Achilles: Not at all. The odds will be the same forever, and besides, 48,841:1 is such a big number that it should never happen and I met a guy that says he saw it happen not 2, but three times in a row. Explain that!
The crowd now erupts in applause for Achilles flawless yet circular logic. The Secret Agent shouts out that he knows what he means.
Tortoise: This is going to be tougher than I thought.
Nick the bartender comes over and asks them all to keep it down as he refills the empty mugs.
Achilles: No prob Nick, just trying to keep it fresh whatever that means. Hey Tortoise what about the other 9 decks you got out?
Tortoise: I was going to demonstrate how consecutive hands donít matter, but it seems pointless now.
Achilles: Oh come on, donít be a sore ass. As you can see were all completely enthralled by your complex explanation of what to everyone here seems so simple. I am perfectly willing to admit when Iím wrong, but so far you havenít been able to demonstrate anything to convince me that I am.
Tortoise feels like withdrawing into his shell but never one to run from a fight decides to give it one more try.
Tortoise: OK, the whole thing has nothing to do with the specific cards or the fact that theyíre drawn back-to-back.
Achilles: This is gonna be good.
Tortoise: And for me to do this you must pretend to accept my numbers for the sake of argument.
Achilles: Yeah, OK whatever.
Tortoise: Instead of looking at each stack of cards as a separate deck, letís look at them as separate hands. Now, what are your chances of pulling a pair from deck 1?
Tortoise: And deck 5?
Achilles: The same.
Tortoise: How about if youíre looking for something specific say, AA from deck 3.
Tortoise: Good, I agree.
Achilles: Iím so glad. Continue.
Tortoise: What if I ask you to pull AA from Decks 3 and 4?
Achilles: Still 221:1.
Tortoise: Humor me.
Achilles: OK. Like 48,000:1, cause there back-to-back.
Tortoise: No. not because theyíre back to back, but because theyíre preselected.
Achilles: What does that have to do with it?
Tortoise: Youíre making a prediction before youíve seen any cards as to their value. Now how about AA from deck 3 and 7?
Achilles: No idea, theyíre no longer back-to-back.
Tortoise: Doesnít matter its still 48,841:1 because youíre predicting an exact pair of cards in an exact order. One last question. What are your chances of pulling 22 from deck 10 and 77 from deck 5?
Achilles: How the hell could anyone figure that out you stupid old fossil? Now weíre not even using the same pair for cryiní out loud!
Tortoise: Stupid, thatís pretty funny coming from a guy who couldnít even figure out that you should at least cover the one spot on your body where you could get hurt. Listen, the cards donít matter, the order doesnít matter, itís just the act of predicting when and where it happens you dumb shit!
This nonsense is too much for the crowd to take and they start brandishing their pitchforks. Not liking any sort of controversy, Nick has Tortoise banished from the Pub forever along with his friends Galileo and Copernicus. Achilles, ever the hero is lofted onto the shoulders of the patrons and forever hailed as a great visionary with the likes of Ptolemy and Malthus.