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droesparky Jul 25, 2009 10:08pm | Post# 21

I did a coin toss on another forum, and I can tell you it comes out about 50/50.
you seem to get on a roll for a while them it takes away the profit and maybe your down for a while.
I changed the TP and SL a couple times.
I believe youll find that it comes out a 50/50 result over the long run.

I have been giving some idea to doing a weekly coin toss and going that direction all week and see how it comes out.

I really believe you need something with more of a varible out come. odds and evens type thing not sure what. If price is down a certian hour go lomng if its up a certian hour go short or visa versa. Use a pivot or a suport and resistance line. all of these can be back tested even a coin toss but it takes time to do it.

I used 115 tp and 55sl with a move to +20 if it was ever up 75pips.

The wheel goes round and round but to nowhere!

Rabid Jul 26, 2009 12:57am | Post# 22

Exactly. It always breaks even, or if you add transaction costs it's always a loss.

The trick is to find a time when things aren't 50/50, and get good at recognizing when the odds change back.

hanover Jul 26, 2009 1:02am | Post# 23

My attempt to explain Gambler's Fallacy
 
If you were to go over each tick and sum up the number of heads and tails, then wait for one to be 2 deviations from the norm, you could trade that as a "regression to the mean" since you know that it will eventually regress back to equal numbers of heads and tails.
Agreed, but a lot of folk misunderstand this and end up believing in Gambler's Fallacy.

Supposing that yesterday I tossed a coin 1,000 times, and 75% of the tosses were heads (i.e. 750 heads, 250 tails).

If I go ahead and toss 1,000 times today, the expected outcome is likely to be somewhere around 500 heads and 500 tails. Let's assume that's what in fact occurs. So the total heads over the 2 days = 750 + 500 = 1,250 out of 2,000 tosses, or 62.5%.

If I then toss a further 1,000 times tomorrow, then another 500 heads and 500 tails would bring the total heads to 1,250 + 500 = 1,750 out of 3,000, or ~58.33%.

So there is our "regression to the mean", the % of heads has fallen from 75% to 62.5% to 58.33%. With each subsequent day, as the number of tosses approaches infinity, the % of heads will continue to approach 50%.

But here's where Gambler's Fallacy fools many people. When it comes to considering today's (prospective) tosses as an independent sample, yesterday's are irrelevant. As we stated, we expected something approaching 500 heads and 500 tails from today's tosses, i.e. the 50/50 probability means that one is no better off statistically by betting on tails now, even though we know that over time the number of heads across the total number of tosses will eventually regress to the 50% mean.

So whether you have an edge or not depends on the type of bet:

(1) If the bet in question is "do you expect that the % of heads from all tosses to date, at the end of today, will be closer to 50% than it was yesterday?" then the correct answer is YES (i.e. regression to the mean provides the punter with an edge).

(2) But if the bet in question is "do you expect to toss more tails than heads today?" then the correct answer is NO (i.e. to believe that one has an edge is to succumb to Gambler's Fallacy).



Application to trading

Let's now attempt to apply this to trading. The question inherently being posed by the market (or its mediator, your broker) is effectively (2) ("i.e. do you expect price to rise more than it will fall in the immediate future?"), as opposed to (1). If (hypothetically) price movement was random (i.e. probability of an uptick is exactly the same as that of a downtick, at all times), then, you would have no real edge, and the presence of costs would mean that ALL trading methodologies would eventually fail (just as it's impossible to beat the casino long term at Roulette).

But price movement is not random. Economic influences and drivers, government intervention to rectify preceived imbalances, heavyweight trader agendas, bullish and bearish sentiment amongst speculators, technical 'conventions' like support and resistance, .... , and so on, all lead to 'trends' and patterns that are qualitatively different to those generated by a coin toss. In other words, there are reasons for price to "regress to a mean" other than purely statistical ones. Discover one of these "inefficiencies" that's capable of overcoming costs, and you have your potential edge. (Like waiting to roll a 6 before betting in Rabid's "9 or better game" (see post #8)).

One final point: if "regression to a mean" was able to offer an exploitable statistical edge, then of course everybody would cash in on it, and become a forex millionaire. But hopefully it's obvious that markets (where there must ultimately be a willing buyer for each willing seller) simply don't work that way.

_________________________________

Second attempt to explain Gambler's Fallacy

(just wanted to include this, in case anybody was unconvinced by my first attempt )

Let's suppose that I happen to toss 75 consecutive heads, followed by 20 consecutive tails, followed by 5 consecutive heads.

Now, my last 5 tosses have been heads, (and the probability of 6 consecutive heads is 1/64), so the next toss is likely to be a tail, right?

But wait, 20 of my last 25 tosses (80%) have been tails, so I'm more likely to toss a head now, right?

But wait, 80 of my last 100 tosses (80%) have been heads, so I'm more likely to toss a tail now, right?

Then, to extrapolate, we'd need to consider all the tosses I'd ever made in my entire life. And what about all the tosses that everybody else has ever made. Do they count also?

Hopefully it's obvious from all this that the outcome of the next toss can't be determined from previous tosses, because - for one thing - it's entirely arbitrary as to which sample of tosses we selectively choose to base our (flawed) probability analysis on. This illustrates the flaw in the logic that the past has some bearing on the present. While the % of heads will always regress toward a 50% mean with every toss, the probability of the outcome of the next toss being a head (or tail) is always exactly 50% (assuming a "fair" coin).

gbppip Jul 26, 2009 10:25am | Post# 24

If you always guess "heads", then over the long run, you should break even.

If you change your guess, there is a ( ever so slight ) chance that you will lose every time.

If you hit a hot streak, know when to leave the game and cash in.

Rabid Jul 26, 2009 1:22pm | Post# 25

(1) If the bet in question is "do you expect that the % of heads from all tosses to date, at the end of today, will be closer to 50% than it was yesterday?" then the correct answer is YES (i.e. regression to the mean provides the punter with an edge).

(2) But if the bet in question is "do you expect to toss more tails than heads today?" then the correct answer is NO (i.e. to believe that one has an edge is to succumb to Gambler's Fallacy).
I understand what you're getting at, but in both situations the answer sorta works out.

If you have someone tossing 750 heads and 250 tails, it would be wise to bet that the next day will have more tails than 250. Why? Because 1000 trials is enough to regress to a mean, so if the bet is "will there be more tails today than there were yesterday?" you could make that bet provided it cost you nothing to make.

If the question is "do you expect to toss more tails than heads today?" well then the answer is always going to be no, since it's even odds. Just because yesterday was skewed doesn't mean today will be skewed the other way, in fact that should be a relatively rare occurrence.

So there's a 3rd question: "Will there be more tails today than there were yesterday?"

That's the point of waiting for a 2nd stdev.

But all of this falls prey to another area: Variance.

Just because tomorrow will likely have more tails than yesterday in the above situation doesn't mean that it necessarily will. There could be a 100 times right in a row where that hypothesis fails, and then later those odds themselves will regress.

So in the situation where a coin flip determines price direction we have no way to know how far price will move away from the mean before it regresses. In a real market situation that's fatal to margin.

But price movement is not random. Economic influences and drivers, government intervention to rectify preceived imbalances, heavyweight trader agendas, bullish and bearish sentiment amongst speculators, technical 'conventions' like support and resistance, .... , and so on, all lead to 'trends' and patterns that are qualitatively different to those generated by a coin toss. In other words, there are reasons for price to "regress to a mean" other than purely statistical ones. Discover one of these "inefficiencies" that's capable of overcoming...

Nod. Auction market theory explains this perfectly. Effectively there are different styles of traders, and a certain set of traders tends to buy when the price goes up and vice-versa on down. These "initiative" or "positive feedback" traders tend to drive price trends. Price moves up, draws in more buyers, moves up more, draws even more buyers, the process reinforces itself getting stronger and stronger and stronger. These traders tend to be "long term" and are driven by those factors. If you map the layout of price with this it forms a skewed bell curve, clearly not the kind of market you'd want to fade.

The opposite of that is a responsive market, where people fade the latest high and low. This creates a tightening range, basically a bell curve that gets smaller and smaller. A market like that makes a great fade.

Learning how to read the effects of "feedback" in the market tells you which way to go. Wait for the most clear results and trade, stand aside the rest of the time. All of this is why I say that the market is clearly not random, and why I say that a quick study of the distribution of price over time proves that fact.

If you always guess "heads", then over the long run, you should break even.
In a random market, yes. Assuming that each "trial" is a single tick. In a real market, obviously not.


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