In *Probabilities in* *Trading – How Your Mind Is Tricking You*, I introduced some errors people make in regards to probabilities–namely, availability bias and attributing increased probabilities if we can come up with more reasons to back our claim. Both of these tendencies will lead us astray. In this article, I discuss these concepts a bit more, but also get into the relevant factors of how market move…in other words, what to base trading decisions on.

At the end of Probabilities in Trading – How Your Mind Is Tricking You, the following question was posed.

- A man likes two women and is going to ask both of them out via a text message. For each woman, there is a 50% chance she will say YES and a 50% chance she will say NO (like flipping a coin). Neither woman knows of the other, and the answer of one woman in no way affects the answer of the other woman. Our man wants to know what the odds are he will get only one date? Since it could lead to complications, he also wants to know what the odds are he will get
at leastone date?- Given that either one says YES, what are the odds the other one will as well?
The woman may respond at different times, so he does not know the order in which he will receive the text replies from the women.There are no tricks here. The probability for each scenario is our only concern.

When looking at probabilities it can be of great help to create what is called a “sample space.” From the sample space, it is easy to see what the odds of a potential outcome are.

To create a sample space we write down all the potential outcomes. In this scenario there are 4 potential outcomes, based on each woman saying YES or NO. The potential outcomes are as follows, set up as (woman 1 response, woman 2 response):

(YES, YES), (YES, NO), (NO, YES), (NO, NO).

Using the sample space we can answer our questions:

-The odds he will get one date: 50% (only two outcomes out of four have only 1 YES in them)

-The odds he gets AT LEAST one date: 75% (we include all outcomes with 1 or more yeses – three outcomes out of four).

-The odds of the other saying YES if one woman said YES is 1/3. We know one woman says YES so include all those sample spaces (Yes,No), (Yes,Yes) and (No,Yes). Only one of these satisfies both woman saying Yes, so 1/3.

Ok, so this doesn’t exactly relate to trading…at least not on the surface. But, since very few people get these answers correct, it is likely decisions are being made in trading which are not based on accurate information. How our minds function (are we looking at the correct information and interpreting it properly?) in trading can greatly affect performance, and not understanding probabilities in trading can mean what you think you are doing is very different from what is actually occurring.

### Sometimes we make things too complex…

Find the highest probabilities in trading means simplifying when we need to, asking the most basic questions and working from there. Such as: is the market moving higher or lower, overall? If that is the case, based on the price oscillating up and down (but moving higher overall), where is the best place to buy and sell? And then asking which is likely to be trigger first, my stop loss or profit target? These questions can get as complicated as *you* want to make them, but keep them as basic as possible at first, and then (if needed) introduce more advanced techniques to hone in.

Can you keep it simple (keep in mind our brains are not wired for probabilities, so don’t be discouraged if you struggle with these)? Consider the following question:

In university me and friend got drunk one night in a nearby city and failed to make it back for our statistics exam the following morning. We hatched a plan not to tell the professor we were out drinking, but rather to tell him I got a flat tire on the way to the exam (my friend in the car with me). Me and my friend went to the professor’s office and said we were sorry for missing the exam, but we got a flat tire on the way to exam and that missing the exam was unavoidable. We asked if we could write another exam at his convenience. To our surprise he said “OK…wait outside for 5 minutes.”

We sat outside and a few minutes later he came out and handed us both a sheet of paper and sent us to separate rooms. There were only two questions.

On the first side of the page was a statistics question worth 5 points (similar to the one above).

On the other side of the sheet was a second question worth 95 points: “What tire was it?” In order to get the 95 points we both had to identify the same tire.

What are the odds that, not having discussed which tire went flat, *me and my friend* both pick the same tire? My friend insists there is a 1 in 16 chance; is he correct?

Take a moment and ponder what the odds are we both pick the same tire.

My friend failed statistics. The odds are 1 in 4. After creating the sample space you will see that many cancel each other out, because in this case order does not matter. We either pick the same tire or we don’t.

Traders often make trades much more complicated than they have to be. They see so many variables, like my friend seeing 16 potential outcomes, instead of reducing the trade down to relevant factors. They hear things on TV, read something in the newspaper, or read an article online and believe it will impact the market or will affect the odds of a trade they are considering. They fail to realize almost all these factors are irrelevant and complicate the trading process, but do not increase the odds of success.

As discussed in the first article, the market is going to move in a certain direction regardless of how many arguments I present for or against that move–piling on arguments and indicators to prove a point does not improve odds. This means we must *focus on analyzing only factors that affect price.*So what are the relevant factors that affect price, and how do we calculate probabilities in trading?

### Probabilities in Trading: Relevant Factors

To me, there are only two primary relevant factors that drive my trading decisions. Then there are a few secondary factors which can aid in the analysis.

The primary relevant factors are Trend and Magnitude (see Impulse and Corrective Waves and Velocity and Magnitude). The Trend affects price (and is price), because humans are emotional and trends create greed and fear to various extents depending on where in the trend we are. Trends may also include Chart Patterns, which are created and break based on human emotion. Magnitude determines the volatility, velocity and projected price targets of a move. Price move in waves–sometimes smooth, sometimes choppy–but since we know markets always move in waves, and those waves provide us with information on the extent to which the market is moving, magnitude is also very relevant.

Secondary factors include analysis tools used to determine trend and magnitude. For some this may include, trendlines, cycles moving averages, Fibonacci retracements/fans, an ATR indicator, RSI, etc. No matter the tools used, focus should be given to trend/chart patterns and magnitude. These secondary tools just help us see what we may have missed looking only at the price chart. Typically I don’t like “out of the box” indicators or tools. You are far better off analyzing the charts and coming up with your own settings for indicators (that help you see the trend and magnitude) or simply researching your charts and finding the common tendencies in trends and magnitude. Only use secondary factors to help you clarify what you already see based on trend and magnitude (price action).

So what are the odds of scoring a winning trade? Each trade is different, but the odds increase by trading with the trend and being aware of market magnitude. Trade against the trend and your odds decrease. Don’t account for magnitude and you are basically gambling on whether your stop loss or profit target will get hit first. Trading with the trend doesn’t mean randomly buying when the price is in an uptrend…it means looking at how the price oscillates and entering at opportune times. Examples of this are covered in How to Spot Trend Trading Opportunities, How to Day Trade Forex and this Swing Trading Forex Trends video.

So why should you only focus on trend (and chart patterns) and magnitude? Because they tell you everything you need to know, especially when short-term trading. If the price is rising, that is all you need to know. The news doesn’t matter, and who cares what this or that analyst says. If the price is rising, it is rising. Use your strategies to take advantage of that. There is no reason to figure why it is rising, or why it may fall. Trade the rise, and if it starts to fall, get out and trade the falling price. Use the analysis of trend and magnitude to help isolate these trades (and a few tools if needed). I actually avoid news trades, until after the news has come out. Often we can’t predict what a news event will be, or how it will impact the market…but we can trade the trends that ensue afterward. I discuss why I exit trades before news events, like stock earnings, in my Stock Market Swing Trading Video Course.

Also, if something totally random happens, like the stock plummets on bankruptcy concerns or skyrockets on buyout rumors….could that be predicted? Often the price moves prior to such moves…the stock is already trending lower before the company’s financial hardships are fully disclosed, or the stock is rallying before the buyout is announced. If this is the case, just focusing on trend and magnitude would have saved or made you money. If there was no prior indication that the price was going to tank or skyrocket, then the event is random, and you couldn’t have known about it anyway (unless you acted on insider information, which is illegal). Random things happen too…that is why I only risk a small percentage of my account on any single trade.

In terms of long-term investing, I use the same tools. I don’t look at fundamentals too much…although I do a bit. I have found that a low Price/Earnings ratio, around 5 or so, is typically a good value. P/E ratios range, on many stocks, between about 5 and 25. So buying around the 5 P/E mark typically produces a long-term gain. I also make sure that the company is not over-leveraged and can meet all their financial obligations without hardship.

Combining this with trend and magnitude, I look to buy stocks when they are cheap…which means after they have declined. I use magnitude to determine how far prices typically fall before moving into an uptrend…and then I buy them there. I then use trend analysis, and magnitude (looking at historically how far prices rise, and for how long) to determine how long I stay in the trade during the uptrend, or if I need to get out because it moves into a downtrend. Another way of looking at it is that even though I am buying after the price has declined, by zooming out on the chart to a longer time frame, I am buying because a much longer trend is up (and magnitude indicates the pullback within that longer-term uptrend is likely over). Or the much longer chart is moving within a huge range, and I am buying near the low of that range. The rules still apply–I am still trading off trend and magnitude–I am just looking at a much bigger picture than what may be immediately apparent if just looking at the price tumble on a shorter-term chart.

*If a trader’s reasoning for market moves only works in hindsight, but can’t help them make better trades in the future, their reasoning is fruitless and will likely cause more problems that it solves. Focus only the relevant factors, and give leeway for random events which will occasionally occur without warning.*

### Do I Need to Calculate Actual Probabilities in Trading?

If you can find a system that allows you trade with the trend, and then you account for magnitude in determining where to place stop losses and profit targets you will have already placed the odds in your favor. Losses will still occur, as that is part of trading, but over the long run you essentially become “the house” in Vegas–gaining an edge over other market participants.

*So before you place a trade ask yourself two simple questions: Am I trading with the trend? And does the magnitude (movement) of the market dictate that I am likely to be able to get out at my profit target (before my stop loss is hit) within the time frame I want? *

Analytical tools may be used to aid in these assessments. As you trade more, you will continue to ask yourself these questions, but they will basically become spot checks for your trading. Over many trades, you will see the true probability of your system. For example, over the last 500 trades you won 61.3% of them, and made 2.37% on account equity per winning trade, and lost 0.84% account equity on losing trades. That is specificity, and it tells you exactly what you can expect from your system over many trades. As market conditions change, those stats may change slightly as well, but at least you know you are working with something that has a probabilistic edge…and that is far more powerful than just *making up reasons* for why the market will do what you think it should.

If you can’t answer the spot check questions, don’t trade. If the answer to either question is No, then don’t trade. Only when the answer to both questions is Yes (and once you know the statistics of you and your strategies) are the probabilities on your side.

How you determine Trend and Magnitude is up to you and your trading system, but keep it simple to keep the probabilities on your side.

By Cory Mitchell, CMT

I believe if three people were in the car and all asked which tire–the odds would have been 1/16.

Hi Cory:

Thanks again for your very quick reply to my second post in the first part.

Since you told me about the answer to the two women quiz in the second part, I came here.

I agree with the two first answers (50% and 75%).

But I don’t understand the third answer.

I think the correct and PRACTICAL answer should be just 50% (1/2).

Because if one women has said yes, then we have only two possible outcomes: the other woman saying yes, or the other woman saying no.

We shouldn’t include the first woman saying yes as one of the outcomes (and so have 3 possible outcomes), because her answer is something that has happened. It was a past event, not a future event (a possible event that may occur in the future).

So we should consider only two possible (or future) outcomes: the other woman´s answers: Yes or No.

So the probability should be 1/2, or 50%.

Now, if the question is: what is the probability that one woman says yes, AND THEN other woman also says yes:

In this case, we do have 4 possible outcomes. And the answer should be 1/4.

But it is not 1/3 either.

I really don’t understand why the answer is 1/3 in any case.

I think it should be 1/2 (or 1/4 if we interpret the question other way as I explained above).

I never studied probability or statistics. So I could be “wrong” according to the probability theory.

However, if for some reason, and according to the probability theory, the correct answer is 1/3, I would very respectfully say: “Ok, this is the correct and very academic answer. But I think this academic answer is not practical nor useful in the real life. Because if one woman has said yes, then the probability of other woman also saying yes is just 1/2, because we only have to wait for her answers, and she will have only two possible answers”.

Please correct me if I am wrong. But again, even if I am wrong according to the probability theory. In real life, if I would do some betting in similar situation, I will use 1/2 probability to base my bet, and not 1/3 even if a professor showed me a detailed formula or calculations giving 1/3 :=)

Great response. As you pointed out in a prior comment, the words used are very important, and create different answers. In this case though, the word “either” is important. You have to include the three scenarios where there is a Yes, because you can’t ASSUME a chronological order. What if he asks woman 2 first? or Woman 1 first? Or sends a text to both at the same time? The questions asks… if “either” one says Yes, what are the odds the other one will as well. There are three scenarios with a Yes, which is either woman saying Yes, [(YES, YES), (YES, NO), (NO, YES)], but only one scenario where they both say Yes, so the odds are one in three for that question.

Also, the overall question states that he is “going” to ask two women out, so he is calculating odds before any actual results are available (he is assuming one woman will say yes–‘given that’–but it has not happened yet).

You are correct though in terms of your interpenetration. If it was specified that woman 1 says Yes, and that event has now taken place, then the odds are 1/2 that woman 2 will say Yes, because your sample same is reduced to (yes) and (no). In this case, woman 1 doesn’t even need to be included in the sample space. But this was not the question asked, which you answered in your comment.

It may seem practical to say that the odds are 50%. But it is a miscalculation. If our friend is trying to decide what are the odds he will end up with two dates on one night, and the odds are 1/3 (which they are), he may be willing to role those dice and go and ahead and ask out both women. But by your odds–50%–he may not take that risk and therefore miss out on meeting his soulmate 😉 So the practical and correct answer is still 1/3. But I do see where you are getting your answer.

It is mostly about paying attention to language (or a situation in the financial markets or in life) and being able to apply the right statistic at the right time and in the right context. It is a skill, just like answering those brain teaser puzzles. Our brains are not wired for probabilities, so it takes practice to get good at picking the right statistic for the right situation, and we still often get it wrong. There are many cases where wrongly accused people went to jail because a statistic was misused and no one caught it. There are also examples where the wrong statistic was used to help get someone off on charges, because no one spotted the error. A couple occurred in the OJ trial.

Writing down the sample space (like what I did in the article) is very important when working these sorts of things out, because if you just try to rationalize it, you will never come up with 1/3 via that approach…your mind will default to 50% or maybe 25% because there are two woman, and so our minds will eliminate odd fractions as possibilities.

Cheers,

Thanks again for your fast and detailed response.

Just one more (and last) question:

“If our friend is trying to decide what are the odds he will end up with two dates on one night, and the odds are 1/3 (which they are)”

I think I didn’t explain well in my second interpretation (when I said the probability was 1/4).

Actually what you said above is my second interpretation: both women say yes.

If, BEFORE asking any woman, he wants to know the probability of getting two yes, then the possible (future) outcomes are 4: (yes, no), (yes, yes), (no, no), (no yes). So the probability is 1/4, not 1/3.

Why 1/4? Because there are 4 outcomes, but only one (yes, yes) is the answer.

Finally, I think I shouldn’t ask so many questions about this issue (so I said this was my last question about it). Actually it is not so important to my trading skill.

I will ask you other questions about your day trading strategies, so I can learn more and improve my trading skill.

Hope getting your quick and detailed answers (as you did now) when I ask you question about your strategies (I think they are great) 😀

Thanks!

I was speaking in relation to the third question, and the answer is still 1/3. I can’t be 1/4 because the questions states either woman says yes, so we can’t have No,NO as an option.

Questions like this are important for trading skill in the sense that it is attention to detail, and applying the right method at the right time. The day trading articles ARE more applicable to actual trading skill though 🙂

I do try to respond to most questions on the site.

Hi Cory:

This is not another silly question.

Just want to thank you for your time and patience!

Finally I understand the concept.

I learned a lesson: many thing are not like I think. And what looks very obvious or evident to me, actually are not so.

Really appreciate your help!

I updated this page on August 13, 2014, replacing the third question (about dating the women) with a new one….so check out the new question near the top for a new challenge.

The old question was: He then decides that maybe he will see how it goes with the first woman, before he asks out the second one. If the first woman says YES, what are odds the second woman will also say YES?

In my original text I gave the wrong answer saying it was 25%, which is the odds of both woman saying Yes. But my wording didn’t reflect that, and so with how it is worded the correct response is actually 50%. Why?

The “if” or the inferred ‘given that’ gives us information which allows us to eliminate anything from the sample space which doesn’t begin with the first woman saying Yes. That only leaves us with (Yes,No) and (Yes,Yes), so the probability is 50% (1 out of 2) that we end up with a Yes,Yes.

I thank Jamie M for calling me out on this.

Great article Cory … you make total sense!

I just found you on google, to my luck !

So looking forward to reading more from you on forex & winning probabilities …

Correct me if i’m wrong but would you agree that casino players understand more about odds and probabilities than the average forex trader?

Hi Avi,

Thanks for the feedback. As for you question, I think that casino odds in general are easier to understand for most people, but despite this everyone still thinks they can beat the house. Odds in trading are a bit more murky and harder to grasp.

Professionalcasino players, just likeprofessionaltraders, will have a good understanding of when the odds are in their favor. I believe a large part of being a professional trader or casino player is knowing when the odds are in your favor–knowing when to hold, fold or tilt so to speak. The average person doesn’t know this and therefore applies the same strategy all the time, or folds when they should hold etc.Like anything, I believe we can train ourselves to be better. We can recognize when we are being biased by influences which may be hidden to others. Even in trading though we are never likely to completely overcome all our hidden tendencies, but by making things simply, and striving to make a few adjustments when we see we are not making logical decisions, it is still possible to succeed in the markets.

what your words reflect is trading-truth in purest form and humans are not wired to digest it .. are they? but it was real eyeopener for me..