Fooled by Probability.

”The benefit of thinking in probabilities helps you quantify price movement into tradeable edges.”

Mark Douglas.

Recent Backtesting

Mark Douglas, author of one of the most acclaimed books in trading, ”Trading in the Zone,” died recently aged 67. Mark had been  working on his third book which is due for publication soon and there is to be an auction of some of Mark’s trading materials in October or November.

Although I have read the book, I will have to admit that I have never really found a way to think in probabilities like Mark suggests. For the learner trader you have to have a set of results, with a win loss ratio and a profit loss account to be able to start thinking in terms of probabilities, winning and losing runs and such. Now we could do some back-testing to come up with the necessary stats, however I’ve recently been attempting to do this and it’s been a struggle. Things like hindsight bias, indicator lag, broker spread and economic announcements cause problems especially for us short term traders for who these things matter. I’ve been recently testing Rob Bookers Knoxville divergence indicator on the 70 tick chart on Ninjatrader’s back-tester, to see if I could add it as a confirmation indicator to my counter trend strategy, however although on scrolling back through the charts there appears to be some nice angled red indicator lines indicating divergence, you have to actually walk forwards in time from the right side of the chart, to get the truer picture and you see in the chart below I’ve had to add my own entry arrows, as one divergence line actually includes 3 entries. The line just kept growing to cover the next. Also look at the time around 08:55am uk time.

08.53 09.50

Now look at the announcement list at the same time.


Yes some nice red announcements just at the same time. And here are my broker Oanda spreads;


The spread increased to over 4.5 pips at this time.

Now I’m not saying there wasn’t a trade somewhere there, but it just shows you some of the difficulties in gaining a useful set of back tested results, to use for thinking in probabilities. Adam Grimes in his excellent free course explains other difficulties in back testing, and so does back testing guru, Rudy Leder

The Hole In One Gang, Taleb and Spitznagel.

Where probabilities are concerned humans tend to have poor judgements when it comes to extreme events. We tend to put to the back of our minds the chance of extreme events as a sort of natural self preservation mechanism. It would do us no good to worry about death every day. However the closer we get to the extreme event the more time we spend thinking about it, and then it’s too late to do any thing to mitigate the effects. We can’t take out insurance once diagnosed with a terminal illness, like we can’t find a buyer when we want to short as the market crashes.

Having done their back-testing, in 1991 two Essex men, Paul Simmons and John Carter travelled around the UK and Ireland putting on bets with independent bookmakers at odds of over 100/1 on a hole in one occurring at five different golf tournaments (British Open, Benson and Hedges, Volo PGA, US Open and European Open.) They were able to place permutations of doubles, trebles, 4-folds and a 5-fold accumulator at the odds. To the shock of the bookies at least one hole in one was landed at each of the tournaments with the 5-fold accumulator being bagged when the Spaniard Miguel Angel Jimenez holed in one at the European Open, Walton Heath, Surrey. Simmons and Carter netted over £500,000 not including the welshers who refused to payout on the grounds it would bankrupt them. Even the crafty bookies have a hard time with long odds.

The ”Black Swan Protection,” hedging strategy utilised by Nassim Taleb at his firm Empirica Capital was brilliantly documented in Malcolm Gladwell’s ”What the Dog Saw,” which was a series of his articles he’d written in the New Yorker magazine and put into book form. The article can be found in the New Yorker archives, titled ”Blowing Up.” . Trading partner at Empirica, Mark Spitznagel set up Universa Investments in 2007 to which Taleb is adviser. In 2008 using the Black Swan type strategy Universa made one the biggest profits on Wall St during the financial crisis and again they produced gains of 20% (over $1 Billion) in the recent 2015 mini  ”Black Monday(China)” stock market crash. (Better not mention the allegations that he caused the 2010 crash.) Here’s Spitznagel in a short 5 minute talk on his ”Tail Hedge” strategy, about the paradox of higher returns with lower risk. Still it’s interesting that the market as a whole hasn’t yet adapted to the bubble and burst event. So much for efficient market theory. Swarm theory is more near the mark, as we all step over each other not to miss out on the big thing then panic and charge the other way like the ”Gadarene Swine” to get out, drowning in the sea of losses.

This is why I now like to look for the counter trend strategy to hedge the pull of the trend, with divergence as one of its indicators. If I can ever get my head around this back testing malarkey.

A History Lesson in Probability

Forward thinking French gentleman gambler Chevalier de Mere (1610-1685) had made a killing offering odds to fellow gamblers of even money against him throwing at least one six with an unbiased die in 4 rolls. He had calculated that the chance of a six was 1/6 and he had four chances, so the probability was 4/6. Due to his success he ran out of takers so he changed the bet to getting at least one double six with two dice in 24 rolls, after all a 1/36 x 24 chances was a probability of 24/36. The bet almost bankrupted him, so he asked his friend mathematician Blaise Pascal (1623-166) what was going on? Pascal consulted with another notable mathematician Pierre de Fermat (1601-1665) and together they produced what we know today as probability theory.

In de Mere’s first bet they calculated the probability of losing was 5/6 x 5/6 x 5/6 x 5/6 = 625/1296 =0.482253 so the probability of him winning was 1 – 0.482253 = approx 52%. A lot less than the 4/6 or 66.66% he’d calculated, but still a winning proposition.

In the second bet they calculated the probability of losing was 35/36 to the power of 24 = 0.508596 so the probability of him winning was 1 – 0.508596 = approx 49%. Much less than 24/36 de Mere had calculated and a losing bet at odds of evens . One more throw would have made a winning bet!

The eminent philosopher Jean d’Alembert (1717-1783), 100 years on, obviously hadn’t paid attention in class to the new branch of mathematics, called probability theory, because he got himself into trouble in a coin tossing gamble. Playing a simple coin toss game where a player tossed a coin twice and won if it came up heads on either occasion. He calculated odds of 2 to 1 (probability 1/3) of winning as he had decided he had one chance of winning on the first go and one on the second and he had one chance he would lose when they both came up tails. Listing the possible outcomes we have HH, TH, HT, TT, four outcomes not d’Alemberts three, so the odds should have been 3 to 1. As one of the foremost intellectuals of the time and a noted contributor to ”Encycopedie,” it just goes to show even the cleverest of us can be fooled by probability.

Moving on to the nineteenth century, what about mathematician and intellectual, Ada Augusta the Countess Lovelace (1815-1852) otherwise known as Lady Lovelace, the daughter of Lord Byron and chief assistant to Charles Babbage (1792-1871) in his research to design the ‘Analytical Engine,” who devised a gambling system that bankrupted her and forced her to sell the family silver to pay her gambling debts. Two hundred years after Pascal and we’re still being fooled by probability.

Well what about these days? Everyone must had done some sort of statistics and probability classes in school? How many of us at least had to think about, maybe started calculating the amounts and maybe even got suckered in, when first presented with the Martingale strategy? Go to a casino and double up after a loser betting on red or black, it’s a sure fire winner. What about trading? That has to be a 50/50 bet, lets do the Martingale here. Well anyone who has looked into it, knows how fast doubling up can build up to astronomical amounts and even if we had the unlimited reserves of an oil sheik, you’ve still got to find someone to take the other side of the bet or trade! Still if you can find a newbie to sell a system, try offering them the Martingale staking plan as a bonus, chances are they’ll be suckered as we all once were.

Hold on a bit. If we are fooled by probability what is the chance that there is some staking strategy that is out there, that is suitable for our trading strategy, but we are too foolish to see it.   Madame de Tecin (1682-1749) a nun whose brother was the bishop of Grenoble, a notorious  gambler and philanderer who was lined up for a Cardinals position, in 1717 gave birth to an illegitimate son, Jean le Rond d’Alembert (1717-1783). How about that then! d’Alembert was abandoned by his mother on the steps of a Paris church and then subsequently brought up by foster parents in the slums of Paris. d’Alembert even though he couldn’t calculate the odds on a coin toss as explained earlier, (yes it’s the same guy), crawled out of the gutter and made his name as a philosopher, physicist and mathematician and won a huge pile of money on the roulette tables to boot, using what is now known as the d’Alembert staking strategy. He did have one advantage in that the private gambling dens of Paris didn’t have a zero on the roulette table, you paid presumably to get in, or on a percentage of returns or on vastly inflated booze or on the sporting women.

Anyway for those that don’t know it this is his system. For a genuine even money bet, eg: a coin toss, red/black, odd/even, etc you start with an initial stake of five units, then following each loser you add 1 unit and for each winner you subtract 1 unit. Should you reach zero units you go back to 5 units. Ok you could go on a never ending losing run but you would be done for in any case with level stakes.

Here is a hypothetical run of 20 bets on heads on a coin toss:

No          Stake           H/T                Result          Total

1              5                   T                     Loss 5            -5

2             6                   T                      Loss 6           -11

3             7                    H                    Win 7              -4

4             6                    T                     Loss 6            -10

5             7                    H                     Win 7              -3

6             6                    H                     Win 6              +3

7             5                    H                     Win 5              +8

8             4                    T                     Loss 4             +4

9             5                     T                    Loss 5             -1

10           6                     T                     Loss 6             -7

11            7                    T                    Loss 7            -14

12           8                     T                    Loss 8            -22

13           9                     H                    Win 9            -13

14           8                     H                     Win 8             -5

15            7                    T                      Loss 7          -12

16            8                    H                     Win 8             -4

17            7                    H                    Win 7             +3

18            6                    T                    Loss 6             -3

19            7                    H                   Win 7             +4

20            6                    H                   Win 6            +10

The results produced 10 heads and 10 tails and when it does so it will always win. Try testing the Martingale strategy and see the huge figures you get up to on the same sequence. Putting 1 point on bet 8 and doubling up would leave you with a 32 point risk on bet 13 as opposed to the 9 points with d’Alembert!

Risk Management and Fred Craggs

In 2008 farm labourer Fred Craggs entered the Thirsk branch of William Hills bookmakers in North Yorkshire with horse muck plastered all over his wellies and placed a 50p eight-horse accumulator on the eve of his 60th birthday. All eight horses came in at a combined odds of 2800,000/1. For 50p his winnings should have been £1.4 million, however William Hills small print stated his winnings were subject to a limit of £1 million. On receiving his giant cardboard cheque from William Hills for £1 million, Fred’s poor risk management led him to make the following comment. ”I lost 10p on this one because I only needed 40p to get the limit up. That was an extravagance!” Actually under another rule William Hill had could have capped his winnings at £100,000, however given the potential PR disaster that would of occurred if they enforced it, he received the £1m.

One of the disciplines in trading has to be risk management. How much do we risk on the trade? Should it be the absolute minimum to preserve our psychi or should we max out mathematically using a full or half Kelly, or is there another way? Why risk more than we need, if it’s not going to get us any further any faster? One things for certain without knowing our win/loss ratios and profit loss account we have to go for the absolute minimum. But once we have gained confidence in our strategies and have our stats to back it up what then? Well as we are so easily fooled by probabilities as shown earlier wouldn’t it be possible to fool ourselves into thinking we are trading small when actually we are trading big? How about separating some of our small stakes winnings in an imaginary separate account and taking say 3 massive trades but only out of winnings, eg the account has gone from £1000 to £1300 with steady gains risking 0.5% (£5) per trade. Now we have £300 we can divide into say 6, put 3 stakes total back into the account so we now have £1150 that we will only ever risk 0.5% per trade (£5.75) then wait for the day we feel we’re in the zone and take a £50 risk trade 3 times. If we lose all 3, so what, it was an extravagance as Fred Craggs would say. Ok we would feel a bit miffed but we could easily shrug it off with some self talk and get back to trading 0.5% of our main account. If we had a winner or more than one, we could divide the winnings again, occaisionally adding to the main bank. Well it’s just an idea. In any case you have to have a winning edge or you won’t ever make the winnings to play with.

The Losing Run

A string of losers can see all trading discipline go out the window especially in the early stages of developing confidence in a strategy. Being au fait with probability theory is not enough as our confidence erodes. So what can we do? One of the best ideas, and a practical one as well, I read about in Robert Thornton’s  long candle course. It’s about regular exercise just tossing a coin and recording the results. It’s surprising how doing this can swing your emotions, as one side starts a winning run whilst the other is losing. You can really feel desperate waiting for chance to even out. After 7 heads, then 1 tails, then 4 more heads, then 1 tails, then 6 heads, you can start to understand what a 50/50 proposition really looks like especially after a 100 coin tosses. Do it daily and it becomes a mind exercise in preparing for the losing run. It does work, but you have to get into the routine of doing it.

The Win/Loss Ratio.

I’ve done my brains in up to this point and will continue on this point another time, if one person indicates to me they found something of interest here. Quite a lot of rambling waffle here. The sort of stuff I usually bore the pants off people down the local boozer with. I usually can clear a nice spot for myself at the bar with this sort of stuff, as the other customers try to avoid me.

Right I’m outta here and straight in the pub for a swift one, and a few coin tosses thrown in.

4 responses

  1. Hi Outlier. You make me laugh!

    I like the experiment with the coin. I will try to get into that. Probabilities is such an important thing to understand. See my most recent post in the blog about it. I’m working very hard on reminding myself when in position that the result of this trade doesnt matter.

    You have a very accurate point that the novice trader really can’t think in terms of probabilities because he hasnt developed an edge yet. Maybe I’m wrong but because I try to trade exactly like Volman, I believe that I have his edge and therefore I can (more) comfortably think in probabilities and not need immediate profit. Now – I must be honest with myself and only take the best setups with favorable conditions, as he does, or else my edge is gone.

  2. Very well written, thanks.

    1. Cheers Jon, thanks for following. I’ve got 15 followers now and you were one of the earliest along with dd and Shonn. My viewing figures are slowly increasing every month and although there is no financial gain it keeps me motivated to prove i can crack this game. All the best,hope your trading is going well.

  3. Hey there Outlier! I did your coin flip experiment just now and posted my thoughts about it on allen’s forum, under one of his threads entitles “state of mind”. Check it out. I think you’ll get a kick out of it.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: