stupid probability questions - Off-Topic | futures io social day trading
futures io futures trading


stupid probability questions
Updated: Views / Replies:7,181 / 56
Created: by stephenszpak Attachments:12

Welcome to futures io.

(If you already have an account, login at the top of the page)

futures io is the largest futures trading community on the planet, with over 90,000 members. At futures io, our goal has always been and always will be to create a friendly, positive, forward-thinking community where members can openly share and discuss everything the world of trading has to offer. The community is one of the friendliest you will find on any subject, with members going out of their way to help others. Some of the primary differences between futures io and other trading sites revolve around the standards of our community. Those standards include a code of conduct for our members, as well as extremely high standards that govern which partners we do business with, and which products or services we recommend to our members.

At futures io, our focus is on quality education. No hype, gimmicks, or secret sauce. The truth is: trading is hard. To succeed, you need to surround yourself with the right support system, educational content, and trading mentors Ė all of which you can find on futures io, utilizing our social trading environment.

With futures io, you can find honest trading reviews on brokers, trading rooms, indicator packages, trading strategies, and much more. Our trading review process is highly moderated to ensure that only genuine users are allowed, so you donít need to worry about fake reviews.

We are fundamentally different than most other trading sites:
  • We are here to help. Just let us know what you need.
  • We work extremely hard to keep things positive in our community.
  • We do not tolerate rude behavior, trolling, or vendors advertising in posts.
  • We firmly believe in and encourage sharing. The holy grail is within you, we can help you find it.
  • We expect our members to participate and become a part of the community. Help yourself by helping others.

You'll need to register in order to view the content of the threads and start contributing to our community.  It's free and simple.

-- Big Mike, Site Administrator

Reply
 12  
 
Thread Tools Search this Thread
 

stupid probability questions

  #21 (permalink)
 Vendor: www.traderwerks.com 
Taipei Taiwan
 
Futures Experience: Advanced
Platform: NinjaTrader
Broker/Data: Optimus
Favorite Futures: TW
 
Posts: 693 since Jun 2009
Thanks: 440 given, 440 received


Big Mike View Post


My head just exploded. You guys are way smarter than me, I hate math.

Mike

I am sure it would be easy for you, you are a pretty smart guy. I think math just LOOKS hard for most people. Once you use math in a practical sense, it all starts to make sense.

Then again people think I am weird because I do math problems for fun.


Last edited by traderwerks; October 31st, 2010 at 09:46 PM. Reason: spelling
Reply With Quote
 
  #22 (permalink)
Elite Member
Massachusetts (USA)
 
Futures Experience: None
Platform: NinjaTrader
Favorite Futures: YM
 
stephenszpak's Avatar
 
Posts: 778 since Jun 2009
Thanks: 144 given, 358 received


Big Mike View Post


My head just exploded. You guys are way smarter than me, I hate math.

Mike

I feel better now.
===========================================================
Hey, if anyone thinks they're being alive on earth is just by chance, trying
estimating the odds of your parents getting together AND a specific cell
of your Dad meeting a specific cell of your Mom. After you have that estimate,
(ha ha) go back to their parents and do it again. (S.S.)
===========================================================

Math quotes time:


If you think dogs can't count, try putting three dog biscuits in your pocket
and then giving Fido only two of them.
~Phil Pastoret

Pure mathematics is, in its way, the poetry of logical ideas. ~Albert Einstein

Black holes result from God dividing the universe by zero. ~Author Unknown

Arithmetic is where numbers fly like pigeons in and out of your head. ~Carl Sandburg, "Arithmetic"

If equations are trains threading the landscape of numbers, then no train stops at pi. ~Richard Preston


Can you do Division? Divide a loaf by a knife - what's the answer to that?
~Lewis Carroll, Through the Looking Glass

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. ~Albert Einstein, Sidelights on Relativity

If there is a God, he's a great mathematician. ~Paul Dirac

One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers... ~Heinrich Hertz


In the binary system we count on our fists instead of on our fingers. ~Author Unknown

The laws of nature are but the mathematical thoughts of God. ~Euclid

Pure mathematics is the world's best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It's free. It can be played anywhere - Archimedes did it in a bathtub. ~Richard J. Trudeau, Dots and Lines

Math Quotes, Sayings about Mathematics

Reply With Quote
The following 2 users say Thank You to stephenszpak for this post:
 
  #23 (permalink)
Elite Member
Paris
 
Futures Experience: None
Platform: NinjaTrader
 
Posts: 1,177 since Oct 2009
Thanks: 228 given, 4,097 received


Here's a few pages of "Cartoon Guide to Statistics" on binomial random variables and gaussian approximation

Attached Thumbnails
stupid  probability questions-p75.jpg   stupid  probability questions-p76.jpg   stupid  probability questions-p77.jpg   stupid  probability questions-p78.jpg   stupid  probability questions-p79.jpg   stupid  probability questions-p80.jpg   stupid  probability questions-p81.jpg   stupid  probability questions-p82.jpg  
Reply With Quote
The following 2 users say Thank You to gomi for this post:
 
  #24 (permalink)
 Vendor: www.traderwerks.com 
Taipei Taiwan
 
Futures Experience: Advanced
Platform: NinjaTrader
Broker/Data: Optimus
Favorite Futures: TW
 
Posts: 693 since Jun 2009
Thanks: 440 given, 440 received


gomi View Post
Here's a few pages of "Cartoon Guide to Statistics" on binomial random variables and gaussian approximation

I do recommend the book if you want to brush up on you statistics.

Reply With Quote
 
  #25 (permalink)
Elite Member
Massachusetts (USA)
 
Futures Experience: None
Platform: NinjaTrader
Favorite Futures: YM
 
stephenszpak's Avatar
 
Posts: 778 since Jun 2009
Thanks: 144 given, 358 received

I found this on-line book today. I really don't know if it's good
or not. Maybe it would have some value for some trader out there.

The Little Handbook of Statistical Practice

Gerard E. Dallal, Ph.D

The Little Handbook of Statistical Practice

=================================================

I quickly went back and checked out the replies on this thread.

Maybe there is something here I'm missing.
The link below seems important (maybe).

https://futures.io/off-topic/6430-stupid-probability-questions.html#post74008


How about this?

If a coin is flipped it has a 50:50 probability of coming up heads.

Someone flips a fair coin 9 times and comes up tails each time.
(This is NOT part of a larger number of flips, like 100 or 1000.)
The coin doesn't know about probabilities so it's not due, so to
speak, to be heads at the 10th flip.

This someone, flips the coin the 10th time. I don't get why the
odds of it coming up heads are still 50:50. Is it because of when
we ask about the probability of it coming up heads?

If we ask before the first flip...

What is the probability of 10 tails in a row? Then the odds are
greatly against. 2 to the 10th, or whatever.

If we ask after the 9th flip (remember, all previous flips were tails)...

What is the probability of 10 tails in a row? Then the odds are 50:50 ?!

Reply With Quote
 
  #26 (permalink)
Elite Member
Wodonga Australia
 
Futures Experience: Intermediate
Platform: NT, MT4
Broker/Data: tba
Favorite Futures: tba
 
Linds's Avatar
 
Posts: 290 since Jul 2010
Thanks: 348 given, 277 received

yes i see your thinking

but

each toss is 100% independent of every other toss

so its still 50/50 on the tenth throw.

the coin doesnt care about the previous 9 or 99 results

Reply With Quote
 
  #27 (permalink)
Elite Member
Berlin, Europe
 
Futures Experience: Advanced
Platform: NinjaTrader, MultiCharts
Broker/Data: Interactive Brokers
Favorite Futures: Keyboard
 
Fat Tails's Avatar
 
Posts: 9,653 since Mar 2010
Thanks: 4,226 given, 25,601 received
Forum Reputation: Legendary


stephenszpak View Post
I found this on-line book today. I really don't know if it's good
or not. Maybe it would have some value for some trader out there.

The Little Handbook of Statistical Practice

Gerard E. Dallal, Ph.D

The Little Handbook of Statistical Practice

=================================================

I quickly went back and checked out the replies on this thread.

Maybe there is something here I'm missing.
The link below seems important (maybe).

https://futures.io/off-topic/6430-stupid-probability-questions.html#post74008


How about this?

If a coin is flipped it has a 50:50 probability of coming up heads.

Someone flips a fair coin 9 times and comes up tails each time.
(This is NOT part of a larger number of flips, like 100 or 1000.)
The coin doesn't know about probabilities so it's not due, so to
speak, to be heads at the 10th flip.

This someone, flips the coin the 10th time. I don't get why the
odds of it coming up heads are still 50:50. Is it because of when
we ask about the probability of it coming up heads?

If we ask before the first flip...

What is the probability of 10 tails in a row? Then the odds are
greatly against. 2 to the 10th, or whatever.

If we ask after the 9th flip (remember, all previous flips were tails)...

What is the probability of 10 tails in a row? Then the odds are 50:50 ?!


Thinking in Conditional Probabilities

Just prior to the first flip the probability for the chain

tails -> tails -> tails -> tails -> tails -> tails -> tails -> tails -> tails -> heads

is (1/2)^10 = 1/1024. As for each of the flips the outcome head or tails has the same probability, this is just one out of 1024 possible events, which all have the same probability. For example, the probability for the event

tails -> tails -> heads -> heads -> tails -> heads -> tails -> tails -> tails -> heads

would also be 1/1024, as the probability for each of the 10 coin flips is the same again.

Stochastic Independance

If you ask about the probability for the 10th flip after the result for the first 9 flips is already known , it is 1/2 for both possible outcomes. Note that this is a conditional probability. The condition "9 flips with tails" has itself a probability of (1/2)^9 and you can calculate the total probability for the 10-flip result as

P = (1/2)^9 * (1/2) = (1/2)^10

This multiplication is only allowed if the single flips are independant from each other. And indeed, for a fair coin, the result of the 10 th flip will not depend on the prior results. It is important to understand that notion of stochastic independence.

Application to Trading

The Gaussian distribution which is assumed for the Black-Scholes formula and which is also used to calculate the probability that price will remain within a Bollinger Band using 2 standard deviations, assumes stochastic independance of consecutive changes of price.

This assumption is false, as we can find that consecutive changes in price show a - slightly positive - autocorrelation. The price action on your chart is represented by bars, and the 15:05 bar is not independant from teh 15:00 price bar, because traders are watching price and base their decision to buy or sell on the price action that could be observed before. This is simply feedback.

Whenever feedback is involved, the stochastic independance is lost.

Emotions, greed, fear, avalanches, panics produce typically positive feedback. Arbitrage traders create negative feedback. In both cases you are not allowed to multiply probabilities as for the fair coin flip. Strong feedback loops also invalidate probabilities that were calculated by arbitrageurs such as LTCM. The one-in-ten-thousand-years event happened after 4 years, because the (false) probability calculations were based on Gaussian distributions that did not apply. LTCM collapsed, because it was overleveraged, correlations between the different business models were underestimated and they did not fully understand the arbitrage risk resulting from positive feedback.

Reply With Quote
The following 2 users say Thank You to Fat Tails for this post:
 
  #28 (permalink)
Elite Member
Massachusetts (USA)
 
Futures Experience: None
Platform: NinjaTrader
Favorite Futures: YM
 
stephenszpak's Avatar
 
Posts: 778 since Jun 2009
Thanks: 144 given, 358 received


Fat Tails View Post
Thinking in Conditional Probabilities

Just prior to the first flip the probability for the chain

tails -> tails -> tails -> tails -> tails -> tails -> tails -> tails -> tails -> heads

is (1/2)^10 = 1/1024. As for each of the flips the outcome head or tails has the same probability, this is just one out of 1024 possible events, which all have the same probability. For example, the probability for the event

tails -> tails -> heads -> heads -> tails -> heads -> tails -> tails -> tails -> heads

would also be 1/1024, as the probability for each of the 10 coin flips is the same again.

Stochastic Independance

If you ask about the probability for the 10th flip after the result for the first 9 flips is already known , it is 1/2 for both possible outcomes. Note that this is a conditional probability. The condition "9 flips with tails" has itself a probability of (1/2)^9 and you can calculate the total probability for the 10-flip result as

P = (1/2)^9 * (1/2) = (1/2)^10

This multiplication is only allowed if the single flips are independant from each other. And indeed, for a fair coin, the result of the 10 th flip will not depend on the prior results. It is important to understand that notion of stochastic independence.


Ok...so it's (1/2)^10 = 1/1024 for the first idea and (1/2)^10 = 1/1024 for the second, correct?



Fat Tails View Post

The price action on your chart is represented by bars, and the 15:05 bar is not independant from teh 15:00 price bar, because traders are watching price and base their decision to buy or sell on the price action that could be observed before. This is simply feedback.

I can see there is feedback here, but is it random? Some trading systems are profitable on the day in question
and some are not. Some traders see the price going up and buy and others see the price going up and sell.
The price is, at times, going up and down simultaneously, as in the case when trader A using 5 minute bars
sees a higher close and goes long, yet trader B using 15 minute bars sees a lower close and goes short, on
the same instrument.

- Stephen

Reply With Quote
The following user says Thank You to stephenszpak for this post:
 
  #29 (permalink)
Elite Member
Berlin, Europe
 
Futures Experience: Advanced
Platform: NinjaTrader, MultiCharts
Broker/Data: Interactive Brokers
Favorite Futures: Keyboard
 
Fat Tails's Avatar
 
Posts: 9,653 since Mar 2010
Thanks: 4,226 given, 25,601 received
Forum Reputation: Legendary


stephenszpak View Post
I can see there is feedback here, but is it random? Some trading systems are profitable on the day in question and some are not. Some traders see the price going up and buy and others see the price going up and sell.

The price is, at times, going up and down simultaneously, as in the case when trader A using 5 minute bars
sees a higher close and goes long, yet trader B using 15 minute bars sees a lower close and goes short, on
the same instrument.

- Stephen

If there is feedback involved, it cannot be random. You would make the distinction between two cases

(1) Usually noise traders enter trades in a random way. Each trader may have a reason, but the overall effect comes close to a random movement as their reasons are arbitrary. If random movements prevail, prices will sit in a congestions or trading range. The price changes can be well approximated by a Gaussian distribution. In this situation you can enter mean reversion trades, if price moves further away from the center of the value area.

(2) Sometimes feedback - either driven by investor sentiment or by algorithms that try to exploit prices moves - may drive prices further away from value. This can be called a bubble, a crash, irrational exuberance, or it can simply be a trend. The trend relies on positive feedback, as one agent buying induces the next agent buying to participate in the price move. When this happens, the actions of the agents are no more independent. Price change does no more follow a Gaussian distribution. If somebody tells you that 95.4% of all price changes will fall into a band (Bollinger Band) with 2 standard deviations around the moving average, this only applies to Gauss distributions. When investor sentiment produces a collective action, the distribution changes, and the statement is no longer true.

If the 5 min trader sees something different than the 15 min trader, there need not be any contradiction. Positive or negative feedback is always temporary, before price finds back to random moves within the newly established value area.

Reply With Quote
The following user says Thank You to Fat Tails for this post:
 
  #30 (permalink)
Elite Member
Massachusetts (USA)
 
Futures Experience: None
Platform: NinjaTrader
Favorite Futures: YM
 
stephenszpak's Avatar
 
Posts: 778 since Jun 2009
Thanks: 144 given, 358 received



Fat Tails View Post
If there is feedback involved, it cannot be random. You would make the distinction between two cases

(1) Usually noise traders enter trades in a random way. Each trader may have a reason, but the overall effect comes close to a random movement as their reasons are arbitrary. If random movements prevail, prices will sit in a congestions or trading range. The price changes can be well approximated by a Gaussian distribution. In this situation you can enter mean reversion trades, if price moves further away from the center of the value area.

(2) Sometimes feedback - either driven by investor sentiment or by algorithms that try to exploit prices moves - may drive prices further away from value. This can be called a bubble, a crash, irrational exuberance, or it can simply be a trend. The trend relies on positive feedback, as one agent buying induces the next agent buying to participate in the price move. When this happens, the actions of the agents are no more independent. Price change does no more follow a Gaussian distribution. If somebody tells you that 95.4% of all price changes will fall into a band (Bollinger Band) with 2 standard deviations around the moving average, this only applies to Gauss distributions. When investor sentiment produces a collective action, the distribution changes, and the statement is no longer true.

If the 5 min trader sees something different than the 15 min trader, there need not be any contradiction. Positive or negative feedback is always temporary, before price finds back to random moves within the newly established value area.

I get it. I don't get it. I can see you've thought about this more than I.

There have been a number of mathematicians before the mid 20th century that actually flipped a fair
coin 10000 times or more. (I tried to find their actual recorded data of the flips but just can't.) Many years ago
I think I saw it briefly. Anyway each coin flip in the XX,XXX total is independent of all the others, yet there were
runs of >10 heads in a row and >10 tails in a row. There was no feedback, yet there were trends.

- Stephen

Reply With Quote

Reply



futures io > > > stupid probability questions

Thread Tools Search this Thread
Search this Thread:

Advanced Search



Upcoming Webinars and Events (4:30PM ET unless noted)

Jigsaw Trading: TBA

Elite only

FuturesTrader71: TBA

Elite only

NinjaTrader: TBA

Jan 18

RandBots: TBA

Jan 23

GFF Brokers & CME Group: Futures & Bitcoin

Elite only

Adam Grimes: TBA

Elite only

Ran Aroussi: TBA

Elite only
     

Similar Threads
Thread Thread Starter Forum Replies Last Post
High Probability Trades-My Journal Ronin Trading Journals 19 March 26th, 2011 02:50 PM
newbie stupid question!!!! bugsbunny NinjaTrader Programming 29 February 10th, 2011 10:19 AM
"It's a high probability trade" shodson Traders Hideout 6 September 4th, 2010 09:12 PM
Expectancy/Probability for zwentz steve2222 Psychology and Money Management 0 November 8th, 2009 01:59 AM
I feel so stupid :( Xzap Traders Hideout 3 July 21st, 2009 10:03 AM


All times are GMT -4. The time now is 10:30 PM.

Copyright © 2017 by futures io, s.a., Av Ricardo J. Alfaro, Century Tower, Panama, +507 833-9432, info@futures.io
All information is for educational use only and is not investment advice.
There is a substantial risk of loss in trading commodity futures, stocks, options and foreign exchange products. Past performance is not indicative of future results.
no new posts
Page generated 2017-12-14 in 0.19 seconds with 20 queries on phoenix via your IP 54.90.207.75