Random Market vs Set Expectancy

I think people are confused, and so I will make my attempt to clarify a few misnomers..

And I shall start with my favorite instrument, the roulette wheel.

In a perfect environment, the spin of the roulette wheel is "random".

BUT, the game of roulette is set with a certain expectancy.

Win% = 1 out of 38
Pay% = 1 to 36

Final expectancy = -5.26%

Now most think the casino's try to cheat, in fact, they work really hard to make the spins as random as possible; they level the wheel, change the balls etc.. all in an attempt to make it "random".

Given X to be spins
Given Sigma(E) to be a summation of expectancy in the real world


We derive for roulette that:

As X -> Infinity, Sigma(E) will asymptotically approach -5.26%.

So even if the markets are "random" as some claim, it probably is not the point that people should be focused on. Is the bias positive or negative against the player, and thus begging the question, is expectancy positive or negative for the system you are using at hand?

If your system is negative, no amount of non-randomness or randomness is going to help you.

If your system is positive, then you want the market to be as random as possible.

If you have no clue; because you are on FF, I'm sure you will still chime in with "I don't know any math but I still disagree".

Everybody keeps focusing on the equivalent of predicting what number will come up next on the roulette wheel. That shouldn't be the focus. If I was the house, like I said before, I'd work really hard to make sure the roulette was completely random, as any bias will more than likely work against me and not for me.

Do you have a system, that given ideal conditions, has a positive expectancy? If not, then debating the randomness of the market is a moot point.

Hi Albert,

As usual, I'm going to argue with you.

Your math is impeccable, as always. If you get a 36 to 1 payout, once in 38 spins, expectancy is hard-wired, given enough spins.

The thing that gives traders confusion is the sample size - number of spins. In a casino, you can approach infinity a lot quicker than in trading since you're spinning maybe once per minute (1440 spins per day). (Actually, you don't approach infinity any faster, but you know what I'm saying.)

In trading a system, say you get 2 or 3 trades per day. It takes a year or two to run what the wheel does in a day, so it may take many years to determine a truly accurate expectancy.
"Ideal" conditions? Maybe in the "mathematical", but not in the real world....

What worked very well for me in Dec / Jan has not worked for a couple months now. The market changed, and the difference cannot be backtested, manually or mechanically. Expectancy can only be determined over the coming months / years.

This is frustrating, causes hopelessness, and would make it seem to some that the markets are totally random.

I will go ahead and assume you are not a programmer; because having 2 trades a day might take a few years to get a good sample size, but if you were a programmer, then the possibility of 100 trades a day, is quite possible.

As far as the real world, I trade in the same market as you, and have no problems with randomness, and so it ain't the math nor the market..

Great post, at the risk of sounding like a broken record I will paraphrase you, what you are saying is that you need a mathematical edge, or else no amount of randomness/non-randomness, MM & psychology is going to save you.

The difficulty is in defining a mathematical edge, which MM will play a huge role in. In the OP it would represent entirely the Payout and also have a role in the win%. What makes up the majority of the win% is what needs to be understood. IMO.

Expectancy =
(Win% * Payrate when I win) - (Loss% * payrate when I lose)

There are 3 types of positive expectancy systems:

1) high win rate, even or low payrate

2) low win rate, high payrate

3) a combo of high win rate, and high payrate


Type 1) This type will allow for good growth and random entries as entry distribution will be relatively even. This is the type of system that is needed if you cannot take every signal, and in fact trade randomly with no set time or schedule. Systems like this have no disadvantage in lower timeframes. This type of system however has much slower growth rate and will depend on high frequency. Trade volume will be high on these.

Type 2) This type is like what the turtle traders do, 28:1 or so payrates, but lower than 50% winrates. The problem with this type of system is that because you don't know when the "big" winner is going to be; you have to take EVERY signal.. also because winrate is generally lower than 50% for this type of system, morale is generally low.. Telling a woman "my winrate is 28%" will not get her in bed..nor will she be likely to marry you. Trade volume however is quite low, and moving to longer timeframes is quite easy.

Type 3) This system has all the advantages and disadvantages of the previous two.


I was a big fan of type 2 until I realized I can't really sit in front of the computer and take every signal. Fortunately though, type 2 lends itself to automation quite easily.

Wouldn't type 1 be the best for automation because of the random entry aspect?

As I read it:
Type 1 would be a scalping system.
Type 2 is the turtles long time frame breakouts or other long term systems

What would a type 3 system be? Is that like asking for the holy grail?

the best system is having high winning rate and at the same time high payrate

1) high win rate, even or low payrate

2) low win rate, high payrate

3) a combo of high win rate, and high payrate

type #1 and #2 = gambling, you might have 3 - 4 good months, but your account might got wiped out in just another 3 - 4 days
so go live only if you have found your type #3

It depends.. The problem is generally type 1 racks up the trading.. And so you have NO CHOICE but to depend on programs.

Type 2 has few signals, which you can take manually. That lends itself for automation... in terms of signal generation and manual trading, which I have now come to believe to be superior.

#3 is the way it "should be". High win rate and high pay rate, and then of course you couple that with high frequency and now you are richer than Buffett..


The Holy Grail is a system that is right > 75% of the time, the payrate is > 4:1, and it only requires 2 minutes a day.. Oh wait, I've got 2 systems that do that!! hahahaa