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Coin Toss Experiment (Strategy)
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Coin Toss Experiment (Strategy)

  #21 (permalink)
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Hi Fat Tails,

(Firstly, apologies for drifting away from the OP's intention for the thread.)

Thanks for the input, I'm glad for the opportunity to learn. I get the theory and agree that it's a dead end (thanks for the nudge on the search terms, some I was aware of some not, so I'm richer tonight for that). But I love to wrestle with an idea and all I am doing here is thinking aloud...

Say on an imaginary day I start trading and get a run of wins and up my size on each successive bet - no one knows the outcome of each I just happen to get a run of 5 winners. I think after the fifth "that's been a nice run, I'll stop and read a book for the rest of the afternoon." On the following (imaginary day) the opposite happens with 5 losers where I cut size each time and after teh 5th loser decide time would be better spent finishing the book.

On balance for the two days - and given that the trades were identical with only the position size differing , and ignoring for the sake of this thought experiment any transaction costs, slippage etc - I have in fact made money, as I made more on the winners than I lost on the losers.

If this is true then is is not possible to 'snap' the cycle by stepping out of winning and losing runs at a predetermined level (3 in a row, 5 in a row, n in a row), and resetting the position size to a starting level each trading period.

So whilst overall it shouldn't work, can the system be gamed by snapping it?

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  #22 (permalink)
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The Gambler's Fallacy Again


mokodo View Post
Hi Fat Tails,

(Firstly, apologies for drifting away from the OP's intention for the thread.)

Thanks for the input, I'm glad for the opportunity to learn. I get the theory and agree that it's a dead end (thanks for the nudge on the search terms, some I was aware of some not, so I'm richer tonight for that). But I love to wrestle with an idea and all I am doing here is thinking aloud...

Say on an imaginary day I start trading and get a run of wins and up my size on each successive bet - no one knows the outcome of each I just happen to get a run of 5 winners. I think after the fifth "that's been a nice run, I'll stop and read a book for the rest of the afternoon." On the following (imaginary day) the opposite happens with 5 losers where I cut size each time and after teh 5th loser decide time would be better spent finishing the book.

On balance for the two days - and given that the trades were identical with only the position size differing , and ignoring for the sake of this thought experiment any transaction costs, slippage etc - I have in fact made money, as I made more on the winners than I lost on the losers.

If this is true then is is not possible to 'snap' the cycle by stepping out of winning and losing runs at a predetermined level (3 in a row, 5 in a row, n in a row), and resetting the position size to a starting level each trading period.

So whilst overall it shouldn't work, can the system be gamed by snapping it?


You are still falling prey to the Gambler's Fallacy.

The point is that you look at the day with the 5 winners and the 5 losers with hindsight. If you cut your size back after the first loser, than you do not know, whether the first loser will be followed by another loser or another winner. In fact, if you enter 5 trades every day, the are 32 (2 to the power of 5) outcomes possible. Each of this outcomes has the the same probability.


An Example

Now let us arbitrarily assume that you start with 5 contracts and that you up your size by one contract, after a win, and that you reduce your size by one contract after a loss. Now you cannot selectively study the impact of this procedure on 2 out of 32 possible outcomes and ignore the impact on the other 30 ones! You would need to apply your idea to each of the 32 outcomes and calculate the result. Thanks to the copy and paste tool this can be quickly written down

W W W W W = + 5 + 6 + 7 + 8 + 9 = 35
W W W W L = + 5 + 6 + 7 + 8 - 9 = 17
W W W L W = + 5 + 6 + 7 - 8 + 7 = 17
W W W L L = + 5 + 6 + 7 - 8 - 7 = 3
W W L W W = + 5 + 6 - 7 + 6 + 7 = 17
W W L W L = + 5 + 6 - 7 + 6 - 7 = 3
W W L L W = + 5 + 6 - 7 - 6 + 5 = 3
W W L L L = + 5 + 6 - 7 - 6 - 5 = -7
W L W W W = + 5 - 6 + 5 + 6 + 7 = 17
W L W W L = + 5 - 6 + 5 + 6 - 7 = 3
W L W L W = + 5 - 6 + 5 - 6 + 5 = 3
W L W L L = + 5 - 6 + 5 - 6 - 5 = - 7
W L L W W = + 5 - 6 - 5 + 4 + 5 = 3
W L L W L = + 5 - 6 - 5 + 4 - 5 = - 7
W L L L W = + 5 - 6 - 5 - 4 + 3 = - 7
W L L L L = + 5 - 6 - 5 - 4 - 3 = - 13
L W W W W = - 5 + 4 + 5 + 6 + 7 = 17
L W W W L = - 5 + 4 + 5 + 6 - 7 = 3
L W W L W = - 5 + 4 + 5 - 6 + 5 = 3
L W W L L = - 5 + 4 + 5 - 6 - 5 = - 7
L W L W W = - 5 + 4 - 5 + 4 + 5 = 3
L W L W L = - 5 + 4 - 5 + 4 - 5 = - 7
L W L L W = - 5 + 4 - 5 - 4 + 3 = - 7
L W L L L = - 5 + 4 - 5 - 4 - 3 = - 13
L L W W W = - 5 - 4 + 3 + 4 + 5 = 3
L L W W L = - 5 - 4 + 3 + 4 - 5 = - 7
L L W L W = - 5 - 4 + 3 - 4 + 3 = - 7
L L W L L = - 5 - 4 + 3 - 4 - 3 = - 13
L L L W W = - 5 - 4 - 3 + 2 + 3 = - 7
L L L W L = - 5 - 4 - 3 + 2 - 3 = - 13
L L L L W = - 5 - 4 - 3 - 2 + 1 = - 13
L L L L L = - 5 - 4 - 3 - 2 - 1 = - 15


No Edge

Now let us calculate your edge

35 + 5*17 + 10*3 - 10*7 - 5*13 - 15 = 0

If you look at all the possible outcomes, you have gained an edge, if you compare the two extreme outcomes (+ 35 and - 15), but you pay with the 20 results that are neutral, as you lose 40 points.

This is the stochastic equivalent of a long condor. But it does not make you money as there is no such thing as stochastic volatility.

Just went through this exercise to show you that your idea does not work, and that you cannot base your expectancy on 2 out of 32 possible outcomes.


Be aware of the Gamblers Fallacy!

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  #23 (permalink)
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Yes, all this talk about probability is pretty easy.. but where do the edges come from? How do you push your chances above 50% ? And how can you be sure that you are?

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mikusha View Post
Yes, all this talk about probability is pretty easy.. but where do the edges come from? How do you push your chances above 50% ? And how can you be sure that you are?


This thread is about a coin toss experiment.

You cannot push your chances above or below 50% with a coin toss experiment.

It is impossible.


If you want to find an edge in trading, you have to

-> analyze time series of trade data
-> relate them to time series of other instruments
-> develop an approach to trading
-> backtest the idea on part of the data
-> use the other part of the data for a forward test
-> make a Monte Carlo simulation to study the drawdown in order to optimize position sizing
-> be lucky and hope that the edge still exists when you start trading

But this is not the subject of this thread. With a regular coin toss you cannot make money.

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  #25 (permalink)
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Yeah with a fair coin there is no edge. However, whether the experiment is valid or not, it can show that most people don't even need to bother with strategy. Most people are probably no better than a coinflip anyway, yet due to variance they can delude themselves for years thinking that they are great traders.

It seems your (any many others) approach to finding an edge is using statistics over relevant past samples. Is that the only way? Analyzing past data, backtesting, forward testing, ???, profit.

Do you believe any of the normal discretionary methods are valid? Obviously people looking at random indicators and formations on a chart and expecting them to work cannot honestly be passed off as an edge. Are there ANY people that trade successfully (and with an edge) that do not base their decisions on past historical stats? I have a hard time articulating it, because I don't even know what it would be like. Can people reliably read the price action on a chart and get a > 50% accuracy? What about people reading the tape? What other methods are available?

I suppose if you KNEW that ExxonMobile was gonna be buying many oil contracts, you could just go long in anticipation. That would be a pretty good edge. But that edge is derived from inside information. I don't think the normal retail trader would have access to that..

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  #26 (permalink)
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Fat Tails,

A comprehensive response, thank you. Now what if...

Only kidding

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  #27 (permalink)
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I am just fighting the idea of progressive betting


mokodo View Post
Fat Tails,

A comprehensive response, thank you. Now what if...

Only kidding


I just went through the pain of explaining this to show that progressive betting is not possible, if there is no correlation between consecutive bets.

Progressive betting works for card games, as a card that was played is no longer in the stack. The counting of card values while playing Black Jack as it was explained by Edward O.Thorpe in his book "Beat the Dealer" is a progressive betting system with an edge. But the card decks are correlated, as the cards remaining in the stack depend on those that have already been played.

For a coin toss there is no such relationship.

In trading usually there isn't either. However, there is a parallel between a card stack and the whole lot of investors. If all speculators are already long, there is no more speculator to initiate a new long position, and you may conclude that the odds are now in favour of a short.

This is not false, and you can in fact use the COT (Commitment of Traders) reports published by the CFTC (US Commodity Futures Trading Commission) to study the relative positions of traders. On a smaller timeframe this concept does not work as well, because the positions of smaller time frame traders can be offset by larger timeframe traders. This is what happens when price breaks out of a consolidation area after a few days.

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  #28 (permalink)
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Exactly


mikusha View Post
Yeah with a fair coin there is no edge. However, whether the experiment is valid or not, it can show that most people don't even need to bother with strategy. Most people are probably no better than a coinflip anyway, yet due to variance they can delude themselves for years thinking that they are great traders.

It seems your (any many others) approach to finding an edge is using statistics over relevant past samples. Is that the only way? Analyzing past data, backtesting, forward testing, ???, profit.

Do you believe any of the normal discretionary methods are valid? Obviously people looking at random indicators and formations on a chart and expecting them to work cannot honestly be passed off as an edge. Are there ANY people that trade successfully (and with an edge) that do not base their decisions on past historical stats? I have a hard time articulating it, because I don't even know what it would be like. Can people reliably read the price action on a chart and get a > 50% accuracy? What about people reading the tape? What other methods are available?

I suppose if you KNEW that ExxonMobile was gonna be buying many oil contracts, you could just go long in anticipation. That would be a pretty good edge. But that edge is derived from inside information. I don't think the normal retail trader would have access to that..

You have hit the nail on the head. There is NO edge, only experience or INSIDE information.

Stastistical Analysis. Most statisticians work for governments. What does that tell you!!!

If you sand down one edge of a coin, very slightly, you increase the probability of it coming up heads.

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  #29 (permalink)
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I certainly agree with the assertion that no statistical edge can be gained from a coin flip scenario. But the financial markets are not coin flip scenarios. Human psychology and crowd behaviour become factors and it is my belief that these can manifest as patterns in price data that can be detected with greater than 50% probability.

I also believe that the idea of 'discretion' in trading is simply a rule or series of rules being executed subconciously and can theoretically be automated if one thinks hard enough about the actual reasons that are contributing to this discretionary 'vibe' to open or close a trade. I say theoretically as certainly some rules around pattern recognition are pretty darn difficult to encaspulate in code.

Anyway, slightly off topic, but this thread has been thought provoking for me!


dee50 View Post
You have hit the nail on the head. There is NO edge, only experience or INSIDE information.

Stastistical Analysis. Most statisticians work for governments. What does that tell you!!!

If you sand down one edge of a coin, very slightly, you increase the probability of it coming up heads.


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  #30 (permalink)
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HitTheCity View Post
I certainly agree with the assertion that no statistical edge can be gained from a coin flip scenario. But the financial markets are not coin flip scenarios. Human psychology and crowd behaviour become factors and it is my belief that these can manifest as patterns in price data that can be detected with greater than 50% probability.

I also believe that the idea of 'discretion' in trading is simply a rule or series of rules being executed subconciously and can theoretically be automated if one thinks hard enough about the actual reasons that are contributing to this discretionary 'vibe' to open or close a trade. I say theoretically as certainly some rules around pattern recognition are pretty darn difficult to encaspulate in code.

Anyway, slightly off topic, but this thread has been thought provoking for me!

Not at all off-topic. I fully agree.

If the financial markets did behave like a coin flip scenario, there would be no point trading at all. You would simply engage in a random walk.

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