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How advanced mathematics and gaming theory can help you as a trader


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How advanced mathematics and gaming theory can help you as a trader

  #161 (permalink)
 
Big Mike's Avatar
 Big Mike 
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Lampert View Post
The spreadsheet is too large to post (16 MB) but I can send if you PM me.


Len

Just zip it then attach it.

Mike

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  #162 (permalink)
traitor786
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nakachalet View Post
just curious, what kinds of setup do you use for your trading then? thx

I use Andrews pitchfork. Many dont like this kind of stuff but as it is all i have really learnt I love it, Its funny how when ever i see a chart some one posts price seems to just fly all over the indicator but with forks everything looks like its bouncing in the right place.

When I was trading in an office I remember listening to the squack. Here you can hear when Goldman Sachs makes a move. Many times I notice that they buy and sell at key points that i also use just they do so more selectively.

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  #163 (permalink)
traitor786
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Lampert View Post
I liked reading this thread, especially @Fat Tails rock-solid explanations about the gambler's fallacy. The summary in post #2 is also helpful.

If some still believe that strings of outcomes and progressive betting are beneficial for independent events, perhaps the following charts can help. I expanded on the spreadsheet provided by @worldwary in post #47.

This first chart shows 10 trials with a constant betting strategy (coin flips with 50/50 W/L). The initial capital is $100 and every bet is $10.




This second chart shows 10 trials with the same scenario, except that bets are increased by 50% after each win - ie. bets are increased during strings of wins. After each loss, the bet is returned to $10. The average bet is $13.34. This is the anti-martingale system or the "progressive string strategy" as described by the OP.




Just for interest, this chart shows one of the trials with three strings of 10 wins.




This last chart shows the distributions of final capital from 500 trials of each of the two betting strategies. Results from the progressive betting strategy have been normalized to match the bets used in the constant betting strategy (each final capital x 10.00 / 13.34). The binomial distributions are quite similar and their averages are close to the initial capital of $100. In other words, there is no benefit from the progressive betting strategy.




On the positive side, these charts show that one should be able to play a 50/50 game for a long time given a reasonable initial capital.

The spreadsheet is attached if anyone is interested.


Len



Your charts seem to disprove what i think fat tails is saying.

From my understanding Fat tails suggests that every toss is independent of the previous one. Yet he says that the odds of having 3 tails in a row is .5 x.5x.5

Maybe i havent thought about enough but it seems that as the string gets longer the "chances of having another head after a streak of heads is getting slimmer.

the chart where there is an increased bet placed after a string shows that it favours profit. from what i remember the negative was 2000 but the max positive was 3000, this could be luck but who knows. Even that one line that goes to the 3000 dollar line can be some thing that can be played. If you were to bet a chart like that over and over and favoured the buy side you'd end up really happy i think. In esence its a the "slight edge" we may all look for in trading. But yes it could be a big anomaly but in general there anomalies are wiped out over many runs.


also the other (i think last chart) shows something similar to my previous mentioned card flipping idea. and that is that there is a maximum to how big a string can get. which means that there is some form of "memory" as you call it.


Seems to me, some one who sah not really looked as deeply in to this as yourselves that you are backing up 2 opposing theories.

1. the odds decrease as strings go on (seen mathamatically) .5 x .5 x .5 = less then .5
2. solid objects dont have memory ?

and the second theory is where your logic seems to come from. There is no math or science there, the word memory was just used for lack of a better word and this makes it even more believable as only living things can have memory.

If things are not dependant on previous flips there would be no reason to revert back to the 50 50. if we do revert back to the 50 50 over many tries this indicates that previous flips must be accounted for in order to get back to the 50 50. That is to say the coin must keep a memory in order to revert to a certain percentage.

now again, i haven't really learnt all about this stuff, this is just my opinion which is usually wrong and not from any research. I'm sure some math genius has figured this all out. but untill i read it (when i have time as im very focused on trading right now) and i truely understand it then and find that the words used in the conclusion match the math ( this is usually where there is an issue in science) then Ill be happy to be better informed

randomness (50-50) can be charted and the randomness disapears as seen on your charts. step back they all look very symetrical (except the one where bet was increased).

I'll probably change my position on this as the convo goes on or i read past posts/links im sure

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  #164 (permalink)
 
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 vvhg 
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The answer is already in your post:


traitor786 View Post
1. the odds decrease as strings go on (seen mathamatically) .5 x .5 x .5 = less then .5

To arrive at the chance of three heads in a row you multiply .5 three times. If you now want to calculate the chance of 4 heads in a row you just extend the string by *.5. this proves that the single event has got a .5 chance in order to give the 4 heads in a row event the chance of .5*.5*.5*.5


vvhg

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  #165 (permalink)
traitor786
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vvhg View Post
The answer is already in your post:



To arrive at the chance of three heads in a row you multiply .5 three times. If you now want to calculate the chance of 4 heads in a row you just extend the string by *.5. this proves that the single event has got a .5 chance in order to give the 4 heads in a row event the chance of .5*.5*.5*.5


vvhg

yes but the last flip is a single event. even though it is part of the string. I imagine that the falasy would say state that the last flip has in a string has a 50 50 chance. the fact that the we mutiply the odds togeteher to get a smaller the 50 50 i would imagine is common sence?

I cant even tell what side your on.

the question should be.

if a coin is fliped 3 times , and 2 heads show up, what are the chances that the next flip comes a head also.

since the last flip has not been made, do we just assume it is an individual flip at 50 50 or do we look at the previous flips and say that it is .5 to the power of 3 ?

In order for it to be a falasy it should go against common sence to some respect and common sence would state that the last flip is not a 50 50.\

if you believe the last flip is a 50 5o, then all flips are 50 50.

if that the case then why do we even quote the formulae .5x..5 x .5 ?

maybe im just unclear on what side you are on or maybe im not understanding something here

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  #166 (permalink)
 
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 vvhg 
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traitor786 View Post
yes but the last flip is a single event. even though it is part of the string. I imagine that the falasy would say state that the last flip has in a string has a 50 50 chance. the fact that the we mutiply the odds togeteher to get a smaller the 50 50 i would imagine is common sence?

I cant even tell what side your on.

the question should be.

if a coin is fliped 3 times , and 2 heads show up, what are the chances that the next flip comes a head also.

since the last flip has not been made, do we just assume it is an individual flip at 50 50 or do we look at the previous flips and say that it is .5 to the power of 3 ?

In order for it to be a falasy it should go against common sence to some respect and common sence would state that the last flip is not a 50 50.\

if you believe the last flip is a 50 5o, then all flips are 50 50.

if that the case then why do we even quote the formulae .5x..5 x .5 ?

maybe im just unclear on what side you are on or maybe im not understanding something here

All tosses are .5, and that is not my belief, it is the very definition of a fair coin toss.
If the last toss was not .5 how could we then calculate the exact probability of the string by .5^n?
Doesn't this clearly prove that each individual coin toss is .5? Otherwise the calculation wouldn't work.

vvhg

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  #167 (permalink)
 
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traitor786 View Post
Your charts seem to disprove what i think fat tails is saying.

From my understanding Fat tails suggests that every toss is independent of the previous one. Yet he says that the odds of having 3 tails in a row is .5 x.5x.5

The charts do not disprove independency. The odds for having 3 tails in a row are .5 x .5 x .5 = .125, because the tosses are independent.


traitor786 View Post
also the other (i think last chart) shows something similar to my previous mentioned card flipping idea. and that is that there is a maximum to how big a string can get. which means that there is some form of "memory" as you call it.

This is a fallacy. There is no maximum. However, the probability for a long string is inferior than the probability for a short string. If you want to get 10 tails in a row, the probability calculates as 1/1024. This means that statistically you need to run 1024 experiments of tossing a coin 10 times to observe the event "10 tails in a row" once. Even with 1024 experiments, it is not sure that you will observe the event, as there are random elements that contribute to the outcome.


traitor786 View Post
1. the odds decrease as strings go on (seen mathamatically) .5 x .5 x .5 = less then .5
2. solid objects dont have memory ?

The odds do not decrease, the odds for a single toss remain at 0.5. The calculated probability for three tosses in a row is larger than the calculated probabilibty for 4 tosses. This means that the probability depends on the number of consecutive tosses, but it does not decrease.

Objects do not have a memory,. If you have somebody who cheats when throwing the coin - consider that guy has a memory how he manipulated the previous toss - then there may well be a dependency between 2 consecutive events.

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  #168 (permalink)
 
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 Lornz 
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All this discussion about coin flips reminded me of this:

https://www.espenhaug.com/ScientificCoinFlipExperiment.pdf

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  #169 (permalink)
 
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 Fat Tails 
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Lornz View Post
All this discussion about coin flips reminded me of this:

https://www.espenhaug.com/ScientificCoinFlipExperiment.pdf



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  #170 (permalink)
 
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But if you find the box, don't open it! You might half kill the cat...


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