Help - Probability in the Context of Streaks Theory

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Jul 9, 2017
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#1
Dear Community

Could someone help me out.

I keep reading that when you toss a coin 10 times if it comes up heads all 10 times then there is still a 50:50 chance that on the 11th toss it could be heads or tails because the probability is still the same.

However when I study the law of streaks it shows me that for a sample size of 11 where the probability is 50:50 of a head or tail that the percentage of getting an 11th head in a row is 0.05%.

This means for that 11th coin toss the probability of getting a head is not 50% but 0.05%

In fact the law of streaks comes up with the following for a sample size of 11 tosses.

a streak of 2 heads = 88.62%
a streak of 4 heads = 27.25%
a streak of 6 heads = 5.47%
a streak of 8 heads = 0.98%

Therefore to say that every flick of the coin for any sample size is always a 50:50 probability is false because the law of streaks confirms that the chance of another head and another head and another head decreases as the streak of heads gets longer which is obviously why when you are going through a streak you expect at some point the streak to end.

Am I missing somethere here or do gurus repeat in parrot fashion a myth about the 50:50 being a constant in a coin toss scenario because unebelievably they fail to take into account the law of streaks. Hardly anyone talks about the law of streaks yet I am finding understanding the science and probability of streaks is like another layer of insight regarding probability.

The thing about its always 50:50 whether its the 2nd or 5th or 9th coin toss is normally used to address what is called gamblers fallacy. Where if you hit 5 heads in a row gamblers will increase their position size that the 6th toss will be a tail because they believe the streak has to end at some point.

Look forward to seeing your comments.

Mel
 

seekingTruth16

Active member
Nov 25, 2016
149
24
28
#2
Hi Mel,

Welcome to the forum.

You are missing something. Your misunderstanding is based on the difference between probability and conditional probability.

Conditional on you already having got 10 heads, the 11th toss is 50% likely to be a head again. That's not the same as saying the chances of getting 11 heads are 50%. It is two different questions you're asking.

The probability that a person is a millionaire, given that they earn 1 million a year, is a lot higher than the probability a random person is a millionaire.
 

tomorton

Well-known member
Feb 28, 2002
6,982
893
173
62
Exeter
#3
A lot of traders trade in the way described in the coin toss scenario. Believe it or not, they look at a price trend, and let's say its been going up for 10 hours or days or weeks or whatever. They will say that it is very unlikely to continue to go up for, making 11 hours or days or weeks. So they short it.

As we all know, 95% of traders lose.
 

seekingTruth16

Active member
Nov 25, 2016
149
24
28
#4
A lot of traders trade in the way described in the coin toss scenario. Believe it or not, they look at a price trend, and let's say its been going up for 10 hours or days or weeks or whatever. They will say that it is very unlikely to continue to go up for, making 11 hours or days or weeks. So they short it.

As we all know, 95% of traders lose.
Some things trend, like you say. Others can be mean-reverting (interest rates in the long term for example).

Important to have an idea of the statistical distribution of whatever you're trading.
 

barjon

Well-known member
May 6, 2003
9,995
1,446
223
78
#5
Hi

The fallacy is that the odds must change the longer a streak goes on. That's how casinos make their money on the roulette wheel.
 

Lee Shepherd

Well-known member
Feb 12, 2008
2,165
570
123
#6
Hi all,

Ive read a few of these posts and many like it before.

Probability and possibility are two separate things. Regardless of how many heads have come in or blacks on a roulette wheel, the possibility of another black or heads coming in remain 50/50. With exception of roulette which is around 48%. Taking in to account the single green for Europe and double green (zero) for U.S. However the probability is reduced (or increased depending on bet).

Over time it will equal 50/50.

So, in theory I could win the lottery, if I don't buy any tickets it's only a theory, however, if I buy just 1 ticket it then becomes possible... But highly improbable. Buy 10 million tickets and the possibility of me winning remains the same but the probability is far greater.

The clear difference between the markets and a coin toss (or roulette), is that the markets won't ever go to zero(or continue in one straight direction forever). Downside is limited to 100%, the upside is theoretically unlimited.

Not everyone will understand this and some will even challenge it.
Regards,
Lee
 

postman

Well-known member
May 20, 2005
20,642
2,186
323
#7
Dear Community

Could someone help me out.

I keep reading that when you toss a coin 10 times if it comes up heads all 10 times then there is still a 50:50 chance that on the 11th toss it could be heads or tails because the probability is still the same.

However when I study the law of streaks it shows me that for a sample size of 11 where the probability is 50:50 of a head or tail that the percentage of getting an 11th head in a row is 0.05%.

This means for that 11th coin toss the probability of getting a head is not 50% but 0.05%

...
Look forward to seeing your comments.

Mel
A coin has no memory, it doesn't know that the last time it was tossed it landed heads so when it is tossed it has a 50 / 50 chance EVERY time!

The statistical probability over 'infinity' is 50 / 50 heads and tails, as infinity is a very big number there will be a wide variation of 'streaks' over that time. Indeed over infinity tosses it is possible that the coin will land heads 2,000 times in a row. If you are planning a trading strategy based on a coin toss then factor that in to your equations otherwise you WILL go bang!

However, markets are not coins. :)
 

piphoe

Well-known member
Oct 31, 2015
9,957
194
123
#8
A coin has no memory, it doesn't know that the last time it was tossed it landed heads so when it is tossed it has a 50 / 50 chance EVERY time!

The statistical probability over 'infinity' is 50 / 50 heads and tails, as infinity is a very big number there will be a wide variation of 'streaks' over that time. Indeed over infinity tosses it is possible that the coin will land heads 2,000 times in a row. If you are planning a trading strategy based on a coin toss then factor that in to your equations otherwise you WILL go bang!

However, markets are not coins. :)
Now tell us a little about markets :D