Am I Missing Something - Probability and Streaks

[lmf21734]

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 that the percentage of getting an 11th head in a row is 0.05%.

In fact the law of streaks comes up with the following

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.

Am I missing something here or do gurus repeat in parrot fashion a myth about the 50:50 being a constant in a coin toss scenario because unbelievably they fail to take into account the law of streaks.

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 you increase your position size that the 6th toss will be a tail.

But I dont think this gamblers fallacy in the sense that whilst we cannot predict with certainty what the result will be for a new toss we do know that if in a hot streak of heads then as that streak continues so does the chances diminish of that streak being able to sustain itself.

Look forward to seeing your comments.

Mel

 

[stepandfetchit]

I have a Dividend trade that I would like to sell you! Pick a security that has profited the prior 8 Dividend periods, and assume the next will be profitable!
The fallacy is you snare yourself in your ill-conceived reasoning! <-- Note if the prob is 50/50, it is actually 50/50, regardless of history!
Just re-think and work out what you are stating here. It is easy to go in circles!
<AKA: Can you say "Curve fitting"?>

BTW: My reference to a Dividend trade strategy is a personal one, where I entered the similar rabbit hole.

 

[eganon69]

Question: You pick up the coin for the very first time and flip it.....what is the chance of heads or tails??? 50% right..?

Now what if I told you that someone else flipped that coin 10 times before you. Did their flips impact yours? NO

Your analysis of streaks is just saying that it is a small probability to have that many losses in a row and the longer the streak to lower the probability it will happen,.... but with fairly high probability (>5% of the time over 100 trades) you will have 6 heads in a row based on your own stats. This also says that 88% chance you will have 2 heads in a row. So if heads is a loss then you have several losses in a row. This is where a MC Analysis shows that it is these streaks of losses that can greatly impact a trading account because of drawdown. If every trade is 2% risk then 6 losses means 12% drawdown on your account. That means you have >5% chance that you will have your account drop to 88% of its total even if you trade your coin flip system PERFECTLY. You have to figure out where your coin flip system drawdown is acceptable for you. Is 12% drop ok or what if you had a 10 loss in a row,...rare as it may be. Now you are down 20%...

These streaks just show that its important to understand that prior trades do NOT impact future trades because even when you trade them perfectly you could end up with several losses in a row just based on the laws of streak distribution of the trades (coin flips). This also strengthens the arguement for lowering risk to 1% or less. Now 6 losses or 10 losses are 94% or 90% of the account respectively. Much easier to handle and recover from.

 

[dumpdapump]

Yes, the gurus (and educated) repeat in parrot fashion that each outcome of a fair coin toss amounts to 50% probability of happening. But to understand this (rather simple) concept you would need to drop your arrogance and pride. Arrogance can sometimes be a huge hindering block to knowledge and understanding.

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 that the percentage of getting an 11th head in a row is 0.05%.

In fact the law of streaks comes up with the following

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.

Am I missing something here or do gurus repeat in parrot fashion a myth about the 50:50 being a constant in a coin toss scenario because unbelievably they fail to take into account the law of streaks.

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 you increase your position size that the 6th toss will be a tail.

But I dont think this gamblers fallacy in the sense that whilst we cannot predict with certainty what the result will be for a new toss we do know that if in a hot streak of heads then as that streak continues so does the chances diminish of that streak being able to sustain itself.

Look forward to seeing your comments.

Mel

 

[Mtrader]

If you compare trading and probabilities in trading with flipping coins you should stop trading immediately as trading has NOTHING to do with flipping coins.

So don't break your head on something irrelevant to trading.

 

[lmf21734]

dumpdapump

Not sure what you mean by arrogance. I am trying to relate is there is something called the law of streaks then why does it give a different percentage outcone for an event compared to the traditional 50:50 probability expectation.

 

[lmf21734]

Thanks eganon69

appreciate your clarification. So streak science is more there to give us an idea of what potential streak losses we could be exposed to with our strategy so that we can use this data to properly apply the right position size and minimise the risk of ruin. correct?

 

[dumpdapump]

...but if you don't even understand basic probabilities of coin flips then you equally have no business trading...(unless of course you want to set yourself up for a painful, money-losing, episode).

If you compare trading and probabilities in trading with flipping coins you should stop trading immediately as trading has NOTHING to do with flipping coins.

So don't break your head on something irrelevant to trading.

 

[Xela]

Am I missing something here

Yes; you are.

What you're missing, in the examples and "explanation" you offer above for your theory about the "law of streaks" is that at the moment of the 11th toss, the chances are 50/50, and the reason for the 11th consecutive toss producing a run of 11 consecutive heads being so unlikely arises only when viewed from the perspective of the original probability of encountering a run of 11 consecutive heads.

You're therefore confusing two different things: ab origine chances and current chances.

After 10 consecutive heads, when you toss for the 11th time, something extremely unlikely (10 consecutive heads) has already happened, and the chances of the 11th toss coming out the same as the 10th toss did are exactly the same as the chances were for the 2nd toss to come out the same as the 1st toss did.

At every point in a sequence of consecutive "heads outcomes", the chances of the next toss also being heads are 50%.

Long experience of trying to explain this to people labouring under a misconception caused by the confusion of ab origine and current probabilities has taught me that I'm very unlikely to be successful in explaining it to you, but "it is what it is".

if you don't even understand basic probabilities of coin flips then you equally have no business trading...

I'm afraid this comment, stark though it is, is entirely correct. This is absolutely fundamental.

 

[birzos]

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 that the percentage of getting an 11th head in a row is 0.05%.

In fact the law of streaks comes up with the following

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.

Am I missing something here or do gurus repeat in parrot fashion a myth about the 50:50 being a constant in a coin toss scenario because unbelievably they fail to take into account the law of streaks.

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 you increase your position size that the 6th toss will be a tail.

But I dont think this gamblers fallacy in the sense that whilst we cannot predict with certainty what the result will be for a new toss we do know that if in a hot streak of heads then as that streak continues so does the chances diminish of that streak being able to sustain itself.

Look forward to seeing your comments.

Mel

Yes, your winning streak is based on an exponential curve or evolutionary, a coin toss is binary, whereas the markets have every combination of everything. There are various books about confidence and winning streaks especially in sports, which is why it is smarter to start slow and build up, any mistake and you start again from the beginning until you find the perfect combinations to keep the streak going. The largest rewards are at the end of the curve benefiting those who keep going the longest via incremental gains without any mistakes, simple economics.