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monkey_n+1 Guest
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monkey_n+1
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Tue Aug 13, 2002 7:59 pm
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Is this a banana which I see before me, the peel toward my hand? Come, let me clutch thee. I have thee not and yet I smell the still. Chomp chomp, small fruit. My belly is becoming a large walking shadow, it will rumble a few more hours and then be heard no more. All with peels is not gold. Out bruised spot, out I say! One two! I'm taking this back to the supermarket. Bubble bubble boil mush mubble, sorry to squabble but these still aren't good enough for banana bread my dear courtesy clerk. Is it better to pray for them or just bury them? Day old one day sale-o indeed! Gross! Alas Chiquita, I knew her well. Yes we have no more bananas? Friends and fellow roaming monkeys, lend me some pears. Skylark, a pound of plantains please. Mellow, for they are bound to be the very next phase. Bruised ones, they are dangerous. My love is like a yellow yellow banana. Ooooogaaa Chugga oogaa chugga
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Scrooge Famous Grouse
Joined: 16 Dec 2001 Posts: 6966 | TRs | Pics Location: wishful thinking |
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Scrooge
Famous Grouse
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Wed Aug 14, 2002 3:33 pm
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Tom and company: I know you're right, mathematically, about past events not counting and the next time odds always being 50-50; but we've an intuitive sense that the real world doesn't work that way - else movie directors couldn't build so much tension into their gambling sequences.
The lucky crapshooter rolls, and rolls, and rolls again. Will he quit in time and walk away with his winnings? Or will he crap out? The drum beats get more insistent; the brow begins to sweat; we know the end is near. - In the real world it does make a difference how often you've tried before. or perhaps, just that you have tried before.
Maybe the problem is in the math. Maybe statistics needs its own version of chaos theory, a mathematics to describe real world events that traditional mathematics can't handle?
Excuse me. I'm in way over my head.
Something lost behind the ranges. Lost and waiting for you....... Go and find it. Go!
Something lost behind the ranges. Lost and waiting for you....... Go and find it. Go!
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MtnGoat Member
Joined: 17 Dec 2001 Posts: 11992 | TRs | Pics Location: Lyle, WA |
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MtnGoat
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Wed Aug 14, 2002 4:32 pm
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The mathematics of probability, when matched with empirical data anyone can gather using good method, will bear out probability theory 100%. These things *are* tested in the real world.
The problem is the human mind and it's tendency to infuse situations with emotion. What something *feels* like when you're standing at a crap table has no bearing whatsoever on what the odds are each time you roll. The feeling that past rolls do matter is merely an intuitive awareness of the reality of cumulative probability, instead of single event probability, IMO.
Diplomacy is the art of saying 'Nice doggie' until you can find a rock. - Will Rogers
Diplomacy is the art of saying 'Nice doggie' until you can find a rock. - Will Rogers
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Tom Admin
Joined: 15 Dec 2001 Posts: 17853 | TRs | Pics
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Tom
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Wed Aug 14, 2002 6:02 pm
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It's funny you guys bring up the craps table example. Being a mathemetican and statistician, I know that each roll of the dice is independent of the last roll regardless of which dice are thrown, who is throwing them, whether they fell off the table on the previous roll, whether they hit someone's stray hand, etc. given fair dice and no foul play. I am fascinated whenever I go into a casino and watch the superstitions come alive, even in my mind. The thing about randomness, however, is that these wild "streaks" are in fact expected to occur. If they did not, things would not be random. Every possible combination must eventually play out, even "streaks" that do not look random. Flip a coin 5 times and there is actually a 6% chance you'll get a streak of 5 heads or 5 tails. When it occurs does it mean the "real world" isn't random? Nope, it's just randomness at work.
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MCaver Founder
Joined: 14 Dec 2001 Posts: 5124 | TRs | Pics
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MCaver
Founder
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Thu Aug 15, 2002 11:47 am
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I was good at math once, but I have computers to do it for me now. Logic is my cornerstone, and it seems logical to me that someone that flies often is more likely to die in a plane crash than someone who flies infrequently, due to the sheer number of flights taken, i.e. it's cumulative. Does math say that's not the case?
I tried following all of the above posts, but I'm afraid I need the monkey answer as well.
Quote: | Is this a banana which I see before me, the peel toward my hand? |
Great line! I haven't laughed this hard is a while.
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Scrooge Famous Grouse
Joined: 16 Dec 2001 Posts: 6966 | TRs | Pics Location: wishful thinking |
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Scrooge
Famous Grouse
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Thu Aug 15, 2002 7:59 pm
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MtnGoat wrote: | The feeling that past rolls do matter is merely an intuitive awareness of the reality of cumulative probability. |
Chris, I think that's pretty much what I said, except that I added that we don't seem to have a math that will let us quantify that reality. And Tom, I do think I'm comfortable with idea that randomness and streaks are built into reality. It's just the math that I never understood.
Tom, in your elegant explanation of how a repetitive event is increasingly likely to result in one particular outcome (or another), I believe you said you couldn't treat a series of past events in the same way. I think that's what's bothering us "intuitive" types.
Let's try another example. Say the M's are on a 20 game winning streak. What are the odds that they'll extend that streak to 40 games? What are the odds that they'll win their next 5 games? Are those odds really as good as the odds of winning 5 games in a row starting from a loss?
I don't think so. Not in the real world. We know that that series of past events matters. The more events there are in the series in the past, the sooner the series is going to come to an end in the future. The world works that way. Perhaps it's only the mathematics that doesn't?
Something lost behind the ranges. Lost and waiting for you....... Go and find it. Go!
Something lost behind the ranges. Lost and waiting for you....... Go and find it. Go!
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polarbear Member
Joined: 16 Dec 2001 Posts: 3680 | TRs | Pics Location: Snow Lake hide-away |
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Tom Admin
Joined: 15 Dec 2001 Posts: 17853 | TRs | Pics
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Tom
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Thu Aug 15, 2002 11:10 pm
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Scrooge wrote: | Let's try another example. Say the M's are on a 20 game winning streak. What are the odds that they'll extend that streak to 40 games? What are the odds that they'll win their next 5 games? Are those odds really as good as the odds of winning 5 games in a row starting from a loss? |
Yes, the odds are the same assuming the previous win streak or loss does not influence the team's motivation for winning the next game(s).
If you're really bored you can prove it to yourself. Take a coin and flip it until you get a streak of heads or tails (say 4 in a row). Once you reach that point, start counting the number of times you make another 4 in a row. If you do this enough times you'll notice the odds of it happening again are no better or worse than at any other point in time.
Think of it this way, if past streaks had any influence on future streaks you would have casinos going out of business left and right since someone could easily arbitrage this at the craps table by playing the pass or don't pass, or at the roulette table by betting red or black.
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