Thread: Probability Paradox!?!

Originally Posted by ;

Yeah smittens, I was really talking about a game with 50% chance. Then let's just flip a coin when you have problems with a physical coin getting flipped a couple of times.
Now, that which you don't appear to get is, that also totally random events may have extensive streaks, but the irony is that just because the computer hit head a thousand times or more, it doesn't mean the next time tails is going to appear.

I think he has it, but he is just talking about real life. In the actual world, there's a chance that any coin is unfair.

In reality in the real world that the coin is much more predictable than men and women assume.

Originally Posted by ;

But with high speed cameras and equations, Diaconis and colleagues have now found that although humans are largely unpredictable coin flippers, there's still a bias built in: If a coin starts out heads, it ends up heads when caught more often than it will tails.

http://www.npr.org/templates/story/s...toryId=1697475

Originally Posted by ;

Yeah smittens, I was really referring to a match with 50% chance. Let's just flip a coin with a schedule, if you have problems with a physical coin.
Now, that which you do not appear to get isthat totally arbitrary events may have extensive stripes, but the irony is that simply because the computer hit head a million times or more, it doesn't signify that the next time tails will seem. The chance is 50%. And now do not come up with something which the computer is programmed blabla or wrong.
I'm talking...

I get it, I think our misunderstanding comes in where we start-- my base premise for this theoretical example is that we're given a coin, or perish, or cards, or any other chances match, and we assume (but do not know) that the chances are mended evenly, i.e. heads in a coin toss is 1/2, six-sided expire is 1/6, etc.. But after repeated observation, our premise that the chances are fixed equally may have to be revisited. If we know the chances are fixed in a level, they're fixed, no matter if it is 1000000000 or 1000000 successive strings. However it's worth considering that the chances are fixed -- just maybe not where you think they are if 1000000 sixes rolled in a row on a die.

Not especially interesting, I am bored at work, bare with me

Originally Posted by ;

I get it, I believe our misunderstanding comes in where we start-- my base premise for this theoretical case in point is that we are given a coin, or die, or cards, or any other chances game, and we assume (but do not understand ) that the chances are fixed equally, i.e. heads in a coin toss is 1/2, six-sided expire is 1/6, etc.. However after observation, our premise that the chances are fixed equally may need to be revisited. If we know the chances are fixed at some degree, they're fixed, whether or not it is 1000000 or 1000000000 successive...

Smittens,
you're spot on in every one your replies. The issue is that after people get that, then they take it to the opposite extreme, without attempting to understand the viability of it. That is why I countered the one million reverse streak comment. Glad to see somebody really gets it.

It's kind of like zeno's paradox. Would someone let an archer goal and discharge an arrow five feet away from their heart because a few mathematician assured them it would'theoretically' never reach them? I hope not.

For those men and women who keep chiming in about the 50% assumption, yes, we still get it. And you also agree with bayesian revisions and the pragmatic world. Given a computer and boundless time, one could struck on a streak of 10 trillion heads in a row and another throw would be 50/50. Yes that's perfectly true, but not well grounded in reality.

Btw. You probably already know it, but Ed Thorp and Claude Shannon really used the roulette wheel imperfections to earn money!

Believing in probabilities amazes me.but I believe that those monte carlo simulations take it too far.
Just try to imagine the fact that in 100 years we shall all be dead,in fifty years over half will be waxed.given the typical trading life is seldom a decade ,some of this scenarios will happen only in the event that you reside a milllenium.
The likelihood of losing money is so high thats its foolish for a sensible person to attempt.if 10% make it try?
But we're all here,united by greed,regardless of fancy characteristics of why we exchange.

Therefore it appears to me we all live on trust and downplay the odds.in other words that the choices we make are not plausible but based on chance and not probabilities.

This thread is pretty interesting. I thought it'd be interesting to bring in some of Kahneman and Co's views from their forays in plogy/behavioural economics.

The concept of the thread instantly reminded me of heuristic - shortcuts our brain takes instead of performing dull and rigorous manual calculation.

A significant and appropriate prejudice caused by heuristics is that the Law of Small Numbers and the Gambler's Fallacy

- Toss of a fair coin should yield approximately 50% heads - 50% tails after the law of large numbers
- With 10 tosses, we are wired to erroneously think that the sequence of 10 tosses needs to be representative of the underlying Bernoulli supply
- One would come across a series of H,T,H,T,H,T,H,T,H likely than T,T,T,T,H, T,H,T,H,T despite the fact that they are equally likely!
- This clarifies the erroneous belief in the roulette table of'mean-reversion'

On the other side of the coin (excuse the pun) would be the fallacy of Hot Hands where we erroneously form beliefs about trends on things That Are actually just random - e.g. lottery numbers

Lottery makes a Fairly fascinating illustration as one can fall into egories of erroneous beliefs

Originally Posted by ;

quote Reactor, You are right about the lottery, however Agro's remarks about roulette in post #35 are right. With one 0 on the wheel, the house chances are constantly 2.7% against the participant, irrespective of whether he bets on red/black, a whole row, a whole column, 4 numbers in a square, and a single number, etc . Here is what you are missing. He will be incorrect 36 times, and time in 37 When a player bets on a single number. You're right about the likelihood being 3 percent, or 1 in 37. But let's...

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