Article / 12 October 2016 at 13:00 GMT

The real odds of success in any game of chance

Hypothesis Testing
United Kingdom
  • The zero on a roulette wheel means the odds of a win on red are not 50/50
  • History shows that markets rally or move sideways  53.1% of the time
  • Markets can throw a sideways day whereby long and short day traders can fail
  • Beware of distribution data that gives the house an edge

By fxtime*

Throughout my trading ''career'', I have come across many whom believe that trading is just a pure gambler's heaven. And that the markets are a random process of buyers and sellers seeking their own goals, irrespective of market fundamentals.

So let's consider if we are really all individual players at the world market casinos. Perhaps the easiest casino game that isn't totally rigged by casinos is the ubiquitous roulette table. In Europe and other parts of the world, there are numbers from 1 to 64 in red and black and a single green zero within the roulette wheel, while in the US tables have two zero slots in green.

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Anyone trading at high levels of leverage is really playing roulette,
a game in which the house always wins. Photo: iStock


The roulette table permits a selection of trades; sorry I mean "games" to us traders. We can opt for all or nothing by wagering on a colour, that is, red or black. But we encounter a problem similar to all traders. We can go long or short just as the casino players can have red or green, but the odds most definitely aren't 50/50, because of the existence of that green number. That is, there are 65 slots containing numbers 0 to 64 and only 32 of the 65 numbers on a European table are red which is slightly less than 50% odds.

The markets can also throw a sideways day whereby long and short day traders can fail. In fact history over any timeframe will show that for a magical 53.1% of the time, the markets rally or move sideways, and thus 46.9% of the time the are short. So if you are randomly trading red or black in your positions, the odds are in favour of keeping long positions, as you should make your casino account grow, as the worst case is a sideways day which is neutral to you.

So now we need to improve our casino gaming profits/margin(s), but how? Let's go back to the roulette table. We can select a single number including that zero and our payout would be akin to having a trade account with immense leverage. But if you don't win, then consider that your entire stake (or deposit on the number) is lost. Those trading 400 times leverage really are playing roulette with their money and you must always remember the ''house'' always wins because the game is skewed at all times in its favour.

So let's assume we visit our casino with less leverage and have a solid grasp of money management. Is it our skill in trade entries that gives us our profits, or is it our money management? How can individuals beat the casino at literally their own game?

Life is a lottery


When you buy a lottery ticket, do you randomly select numbers hoping you will win something? Is it better to select the same numbers again and again? Do we look at all low numbers or all high numbers? Or do we keep a record of all numbers selected and then choose the numbers with the least or most popular numbers, on the expectation that the law of averages will secure a win?

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Lottery number choices are not truly random, but biased, with many
punters influenced by birthdates and other preferences. Photo: iStock



The law of averages and large numbers do occur, but it takes at the very least 100,000 tickets to be generated to gainsay a 98% even spread of numbers selects (that is, within two standard deviations). So far the UK generates two tickets per week, which implies 50,000 weeks of ticket selections before this idea would come to fruition. This ''frequentist'' approach for statistical advantage clearly has limitations here.

As for choosing only high or low numbers; most people spread their numbers, based on birthdays and age, for example. So all that would occur with high and low number selections is that any winnings would be greater, as fewer people choose these numbers. But the odds of these number selections winning are lower, because distribution data has a sting in the tail which gives the house an edge. Again we cannot rely on frequency for making profitable trading transactions or consistent revenue with lotteries or the markets in general.

So how do we improve success rates? The Lottery has a flaw like all random-generated number games, even roulette. In big casinos where the mega casino can give high returns much like the trading platforms that give stupendous leverage they rely on ''usual practice'' to occur but when they see untoward strategies the casino will reduce max stake size permissable or close down the game entirely.

Trading platforms with high leverage are no different — they can slow fills as there is always a risk officer or programme that can assess the implication of a trade being opened against the market makers/trade platforms overall values at risk and can decline the order for requote etc. Usually before you have your order confirmed, there is an algorithm embedded into the trade platform that will make the risk assessment in milliseconds before permitting/declining your trade request.

The first flaw of a casino is that it permits multi-faceted strategies and game plays. It has to permit various types of card players just as lotteries permit syndicates. Usual practice implies the vast majority will play randomly like anyone else. But there is a big prize available with a lottery and the UK certainly discovered that the law of large numbers may require the equivalent of 50,000 weeks worth of results to average numbers appearing on a winning ticket but the lottery can be manipulated.

The Bernoulli Law shows that games of chance have a distribution curve like anything else and that in the old 49 numbers draw of the UK, you could add all the permutations of a ticket and determine where the most frequent number of six-drawn numbered balls totals occurs. Or to put it another way, what is the minimum and maximum success rate for a total of six balls randomly chosen in the UK lottery.

The number value of 177 and above proved to be the most successful range. Professional syndicates quickly determined that there were more permutations of a win with 6 balls numbered 1 to 49 having an aggregate sum value of 177+ is where the maximum permutations available for a win. Probability then moves into the syndicates favour.

Roulette also has a similar issue where an aggregate score will rapidly show where the greatest success rate strategies occur. Even better with roulette as opposed to lotteries is that you can trade a roulette table much the same way as you would with option trades eg strangles/straddles etc. You look to gain the house margin for the consistent profit stream.

So now we know chance is a measurable factor can we benefit from it? Lets consider any liquid market that has volume and liquidity. SP500/forex majors are the obvious candidates. Bernoulli permits a plotting of a classic standard distribution curve but with a different interpretation to the old Gaussian model so beloved with statisticians.

Firstly we know where the greatest number of permutations for successful trades occur and where the least are just as option traders look at implied volatility as a measure against the annual rate of volatility. We know with the Volatility Index too that extremes in volatility is unsustainable and trading at these extremes in a contrarian manner is safer as we know ''normality'' will occur over any given period of time. Basically we are looking at the marketplace just like the syndicates that traded against the lottery....we know where the highest frequency of success would occur.

Secondly we can measure over three trading days what is considered usual at any given point whatever the current here-and-now trend for the market place happens to be. A simple three-day trading range and a central pivot point would show if we are trading above the three-day pivot and thus in a bullish bias or we close below it suggesting the bias is about to change to the bearish side of things. A break of the three-day trading range would also be a confirmation of the bullish/bearish viewpoint.

Bernoulli was never interested in the exact point of focus for the high or the low of any distribution curve. The point was to scale your entry at or very near the top or bottom of a move....start small and build your trade position because the odds will be in your favour. Keep your total risk in monetary terms fixed and open very small positions initially and scale the trade with the stop being quickly adjustable without increasing your risk liability even when scaling a trade this must never increase.

I am not trying to build a case for adding to a loss making trade in the hope that your revised average break even will be achieved as that is folly but we can scale winning trades very rapidly.

Obviously live trades will be posted as per usual along with the relevant distributive curves as a reference pointer.

— Edited by Robert Ryan

*fxtime is a pseudonym
12 October
fxtime fxtime
It may be pertinent here to suggest that each and every day it is imvho prudent to place an order day only for a reversal in market sentiment. When we see European markets make their usual morning high and low we get a sense of direction for the morning eg FTSE100 cash index open range broke to the downside and has not tested the upper side at all so perhaps a day only order on the break of that high may well be prudent? Likewise the DAX etc etc as change in sentiment and trend are often strong moves and as we approach FOMC we may well have greater volume to make a greater move.
12 October
Qi2 Qi2
Great article fxtime, always a learning experience, I really enjoy reading your writings!
12 October
fxtime fxtime
Many thanks mate.
I have also done a ''stop trade'' management article but don't know if that is coming out soon as it is relevant to the cable movements.
12 October
Michael O'Neill Michael O'Neill
I spending my retirement money on lottery tickets with a sum total of 177or higher. Wish me luck. :)
12 October
fxtime fxtime
LOL....unfortunately the National Lottery realised the flaw approx 1 yr ago and changed the numbers from 1 - 49 to I believe 1 - 60 to substantially reduce the ability of syndicates. I guess it is the roulette table for you and I in our retirement :-)
12 October
Michael O'Neill Michael O'Neill
It was another very entertaining an informative article, fxtime.
12 October
Market Predator Market Predator
@fxtime: hello Sir, I agree with concept mentioned above, BUT "Keep your total risk in monetary terms fixed and open very small positions initially and........" here at Saxo it's NOT possible to open very small positions, because they apply (e.g. Fx Market) poison called> commision threshold fee structure. So effective management is not possible!
"A simple three-day trading range and a central pivot point" sounds interesting for me.
12 October
fxtime fxtime
Saxo is not my primary platform. I use it heavilly but certainly not for options trading or large scale order placement. CFD scalping is where I utilise Saxo. Also SIPP dealing can be done via this platform too. Their charting is clear, concise and basic...sure it has all the classic modes of charting but my trades are often off excel and programming as for the 3day scenario there is already an article I posted on that but what i describe above is an overlay which you need additional criteria which I will post later for you.
Original link below;
https://www.tradingfloor.com/posts/mechanical-swing-trading-full-facts-and-real-figures-6968989
Remember all the trade ideas can be overlaid with another to improve the trade structure but you also need a filter system to erase weak signals too...and that I will post.
13 October
Karen Holander Karen Holander
very informative
13 October
Nearthecasino Nearthecasino
Hello fxtime, you are certainly very strong for the forex, but less for the roulette...There are 36 numbers (and not 64...) on the roulette plus one zeo on the european roulette and two zeros on the american one. Have a very day.
13 October
fxtime fxtime
The daft thing is....I know only too well the numbers on a roulette table etc as I used to work in casinos during holiday periods so heaven knows why I wrote about 64 LOL...thanks for the correction but thankfully the principle point in the article remains the same. Many thanks :-)
13 October
C.A.L. gr C.A.L. gr
As always: Informative and useful. Many thanks!
13 October
fxtime fxtime
Your welcome :-)
13 October
C.A.L. gr C.A.L. gr
Also: The comment above about the (expensive) fee structure of SAXO correct. Most trades must have a certain volume otherwise you may end up trying to cover the entry-exit fees. With "small" positions is not unusual that the security has to move 2% -or even more- before brake even.
13 October
fxtime fxtime
Very true. Liquidity of the market is the key point imho....is the trade viable inclusive of all costs. I trade what is regarded as large contracts and seek economies of scale to ensure cost reduction per se. Saxo aren't the most expensive provider but they are dependable and fills are done timely as you expect. A good rapport with your acct manager is paramount as costs per basis pt can be negotiated. At the end of the day you run your trade account like any business...income and expense measures are paramount. The fee structure is just one of those things you build into your trade model and costing parenthesis...I would never seek 2% movement to reach b/e as too far imho.
13 October
fxtime fxtime
Perhaps I should write an article on cost basis reduction techniques as there seems to be strong opinion on this topic?
13 October
Market Predator Market Predator
@fxtime: concerning cost reduction >> permission granted, Sir :)
13 October
fxtime fxtime
LOL..thx...I am drafting the article at present at home :-)
13 October
Market Predator Market Predator
@fxtime: highly appreciate, Sir!
13 October
Qi2 Qi2
Hey fxtime, I would love to see such an article, you're my professor, just sayin -)
13 October
fxtime fxtime
I think you are ahead of me mate :-)
Your programming resources exceed what i can do myself.
18 October
fxtime fxtime
@Market Predator...the cost reduction article intertwines with requested stop control scenarios and there is just too much to comment on within a single weekly article so I will start at a basic foundation point and write a few articles to build from there over the next few weeks. Hope this is OK with you?
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