Gambler's fallacy vs. Theory of Probablity

AN OBSERVATION ON STREAKS

On the face of it the probability of a win on one trade doesn't affect the probability of a win on the next trade (the gambler's fallacy).

But I don't believe this independence of probabilities to be strictly true in the real world.

Certain kinds of days have benign trading conditions which give rise to a high probability of successful trades on that day. A classic example is a strongly unidirectional day with well-ordered retracements. Given that all trades in such conditions have a higher than usual probability of success, it must necessarily follow that the probabilities of success on successive trades are not independent.

Another reason why the outcome of successive trades may not be independent relates to the current state of mind of the trader. We can not preclude the possibility that on certain days the trader will be more 'in tune' with the market. This will give rise to non-independent probabilities of success on a series of trades.

Just my 2 cents ... in the real world, the gambler's fallacy cannot be argued away through the use of statistics because of at least two extraneous factors:
1) benign market conditions on a given trading day
2) the state of mind of the trader
 
Seems like a "streak" would be due to either a change in one's probability of success (due to factors others have mentioned), or to dumb luck. Now you either know that your success rate will be different for a particular set of trades, or you don't, in which case you might as well be dealing with luck. Point is that you shouldn't be increasing your trading size unless capital has increased, or known risk of loss has decreased (or your risk tolerance has changed).

A short streak alone is a really bad reason to increase trading size (except to degree that capital is increased). This is equivalent to picking a fund manager based only on his past year's performance - you're very likely to get someone who succeeded by dumb luck. The few good one's will be hidden within the larger pool of all fund managers, with only "better than average" results.
 
Originally posted by huby
But trader two (I believe) can make more money (if he has a positive outcome system) by taking more risk with "market money" than by keeping shares the same.
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well, from purely mathematical standpoint, this is incorrect. optimum risk (measured as % of portfolio) is a function of expectancy (probability distribution of trade outcomes, to be more precise).

therefore - as others have pointed out - unless you have a reason to believe that your expectancy for the next trade is better, you should not risk more.

of course, from psychological perspective, "playing with market's money" makes perfect sense.

- jaan
 
Lets remember:

If these 2 items are tracked using a running total:

Win Rate
Winn Loss Ratio

Then the reasonable expectation is dictated by the above. That's it!....time is on your side.

The fact that you put your system on a spreadsheet and trade it the same as you always do is key here. If you do worse on your trades, well then of course these 2 items above will be lowered, thus affecting your bet size.

So not only will the random "losing streak" that defy's the above win rate affect your bet size but also the way you trade. Now remember a trader when trading REAL MONEY on A REAL TRADE could trade differently because of the large size of the trade.

For these mechanical theories to work, a trader must hold a constant. We are human and must train.

Have you noticed when a portfolio reaches 100k the equity curve flattens out....why is that?...really this is a serious question.

I am questioning these 2 numbers above that are maintained on a running total (win rate, winn loss ratio) As the runing total (sample size) grows larger, do the changes (rate of change) in those numbers above grow smaller? That is to say, that when the trader deviates from his constant the numbers above used in calculating bet size might be less responsive to his results. This would change the exponential pyramiding that these sytems cause.

Michael B.
 
For what it's worth, I've heard that U.S. coins are not symmetrical, and will yield "heads" a disproportianate number of times.

I'm hoping someone will test this with 1 million flips. I heard the number is closer to 65% "heads."

This sounds like a job for Harrytrader.
 
The problem with expectancy in the markets, as I see it, is that you never know if the past results of a system or methodology (either real or hypothetical), will match the future results.

For example, you may have a system that has had a 60% expectancy in the past, but you have no idea whether the performance will continue in the future. In fact, based on my experience, as well as comments I've heard over and over again, you should expect your system to stop working eventually as the edge it exploits becomes factored in to the market by others who recognize it as well.

This is why I believe that even if you are a system trader, you still have to use discretion as to whether or not you should continue to keep using it, modify it, or stop using it altogether when it stops working.

I tried Van K. Tharps "Secrets of the Masters" trading game free trial, where the first system had a 60% expectancy. I simply used a formula that invested and risked the same percentage of capital on each trade and I made a bundle. It was incredibly easy because I knew that the odds were programmed into the game. Not so in the market - even with a mechanical system. Those PhD's must have been a bunch of dopes, because when you have a positive expectancy like that, you will almost always win without even trying if you keep your bet size and risk (as a percentage of total capital) the same for each trial.

One other comment about increasing trade size when you are winning and decreasing it when you are losing - I think this is more important from a psychological/emotional point of view, rather than a statistical one. If I have had several losing trades in a row, I tend to get stressed out and start making poor decisions and stupid mistakes. Decreasing the number of contracts that I trade reduces my stress and anxiety and helps me to think more clearly again.

As far as increasing size when I'm winning, that doesn't work for me yet. What usually happens is that I start to do well for a while (several weeks, or a month or two), and then I try to increase my size and end up losing it all and then some. I'm not sure if it's because I'm doing something differently (most likely) or the market has changed (occasionally the reason), but anyway I'm still working on how to increase the size of my trades once I have something that works without having it all fall apart on me.

Anyway, just my 2 cents worth.
 
Thirty years ago a good friend and I had to write a thesis for one of our statistics classes - we were both engineers and finishing our MS in Operations Research. We knew that it was impossible to beat the house in the long run, but wanted to have some fun, especially since we were on nice expense accounts.

We met in Monte Carlo as we had the weekends off on our European tours, and decided to test our "best" theory and keep tabs on the results and run them through the IBM on our return (there were no PC's then).

We played roulette and only bet on black or red. We would wait until let's say black came up four times in a row and then bet on red. We doubled each succeeding bet - i.e. we kept betting on red and doubled up each time. The problem is that you loose regardless when you hit a zero or double zero, depending on the system used by the casino, but we knew that and wanted to see how long we could play on 500 dollars ( a lot back then).

The story is too long to tell, but we were ahead a considerable amount when all hell broke loose. They changed pit crews, lost chips and "replaced" them etc. The end result after four hours was a loosing streak of over 12 rolls, which the IBM tagged as a "cheat". I am sure to this day that the casino in Monte Carlo cheats - no wonder with the amount of money they see and the high expenses of the royal family. (Our luck was much better in the large state-run casinos in Nice and BadenBaden).

30 years later I took my wife to the Bahamas (only 60 or so miles form my home in Florida) and since I am not a gambler (obviously!) I decided to try the same "system" again while my wife was playing the slots - I usually pass the time with Black Jack.

Guess what - there was a bronze plaque mounted next to the roulette table that desribed the very "system" and forbid to play it - probably, because you are out of the game a lot and tie up access.

Now, it tought me a lesson early on - you don't win in gambling ( unless you are the house) and since there is $$$ at stake, a lot of cheating goes on. The best "sytem" I know and play is get out immediately when you have a bad day and get also out when you have a good winning streak - don't be greedy. Go take time out to enjoy your money. Go fishing, chase women (or men depending) relax or retire early as did. It worked for me.
 
Quote from Babak:

wanted to comment on "streaks":

in "Beyond Greed and Fear" by Shefrin, he talks about asking a class full of students to pretend they are flipping coins and to write down what they got, heads or tails. How do you think their imagined coin flips would differ from a real random coin flip?

The difference was that when the students pretended, they would stops streaks of H or T. So it would look like this: HHTHTTHTHHTTTHTHT

But a real random flip of a coin may actually contain a really long streak, like this: HHHHTHHHTTTTTTHHTTTTTTTTT

interesting, huh?
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Ok, not to split hairs, but how can we ensure that we are truly being random when flipping a coin in real life?

People tend to put the same amount of force into the flip, put their arms and hands into the same position when they flip, etc.

Wouldn't these factors increase the odds of having the same outcome when flipping?

To be truly random, wouldn't one have to put a random amount of force, randomize arm/hand technique, etc.?
 
Harrytrader,

This is actually true only for freshly minted/unhandled pennies, and i've seen it tested on 100 flips on three occassions and all three occassions yielded about 65% heads.

That is all.

BigMike
 
Do you have the exact quite before I kill Tharp :D I wouldn't like to misinterpret him :p. he is a great vendor sure. The way they lose have less to do with gambler's fallacy than it has to do with the risk of ruin.



Quote from Skiley:

In Tharp's "Trade Your Way to Financial Freedom", he talked about Gambler's fallacy. Using an example of a game played by 40 Ph.D.s,(each of whom were given $1,000 to play 100 trials and their winning chance is 60 percent), he got the conclusion that only 2 of them made money finally because of wrong position sizing. He said that suppose the first three bets are losers and you bet $100 each time. You would think :"Well, I've got three losses in a row and it's time for a win." So you bet more for the fourth time, which he said you've fallen into gambler's fallacy because the fourth trade still has the winning probability of only 60 percent. I was just wondering why probablity theory doesn't work here. According to probability theory, since each trade has two results--winning or losing, the prob. of the fourth consecutive loss should be (1-0.6)*(1-0.6)*(1-0.6)*(1-0.6) instead of (1-0.6). And honestly if I were in that game, I would also bet more after three losses in a row. Also, Tharp seems to believe that 10 losses in a row in the market is very natural, which again contradicts to prob. theory. Any thoughts or explainations will be greatly appreciated.
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