I'm trying to isolate ST, i.e. ST = ...

PR = (1-((1-(1-(WR/100))^ST)^((TR*365*50)-(ST-1))))*100

Can anyone help me?

That monster looks to me like a financial formula, ST being the number of periods; yes?
As far as I can tell, cannot be solved directly for ST; numeric method required.

Anyhoooo: I suggest you simplify it as much as possible, a bit this way:
p=PR, w=WR/100, t=TR*365*50, s=ST

Originally Posted by joelray712
I'm trying to isolate ST, i.e. ST = ...

$$PR = \left(1-\left[ \left(1-\left[1-\left( \dfrac{WR}{100} \right) \right]^{ST} \right)^{TR\cdot 365\cdot 50-ST+1} \right] \right)*100$$

Can anyone help me?
I reformatted this to make it easier to read. There is no easy way to isolate $ST$. You are likely to wind up with the Lambert W function in the solution. Let's give single letters to every double-letter variable. $ST = x, WR = y, TR = z, PR = w$. Then you have:

$$w = \left(1-\left[ \left(1-\left[1-\left( \dfrac{y}{100} \right) \right]^{x} \right)^{18250z-x+1} \right] \right)*100$$

Perhaps a computer algebra system would be able to chew through this and solve for $x$, but there is no easy way to do that. The problem is that you have $x$ in two separate exponents.

Very astute of you; yes, it's a financial formula. PR = probability of x consecutive losing trades, WR = win-rate, TR = number of trades per day and ST = streak of consecutive losing trades.

Thank you SlipEternal for the cleaned-up formula and assessment of the unfeasibility of isolating ST. The problem of ST existing in two separate exponents was what was holding me up.

Originally Posted by joelray712
PR = (1-((1-(1-(WR/100))^ST)^((TR*365*50)-(ST-1))))*100
which is really:
PR/100 = 1-((1-(1-(WR/100))^ST)^((TR*365*50)-(ST-1)))
right?
PR = probability of x consecutive losing trades,
WR = win-rate,
TR = number of trades per day
ST = streak of consecutive losing trades.
Are these "reasonable" values:
PR = 25 (25% probability)
WR = 65 (win 65% of time)
TR = dunno...perhaps >0 and <100?
ST = calculated using above

Can you supply a clear actual example, and ST's calculated value?
I think can be solved not directly but from a very simple looper program.....

ALSO: can you explain "TR*365*50"....makes no sense to me as a power...

Ideally, the probability (PR) should be around 0.1%, since it is the probability of losing a certain number of trades in a row which would lead to a trading-account drawdown of a certain percentage (in my case 20%).

Win-rate (WR) at 65% is good.

Trades per day (TR) is usually around 0.5 or so, since the setups that I trade don't occur every day -- and also since there are only 5 trading days per week.

The streak (ST) is calculated using the amount of risk per trade to find the number of losing trades that would lead to a maximum account drawdown of 20%. Depending on the strategy, the streak number is usually around 10-15.

TR*365*50 is intended to return the total possible number of trades in 50 years.

Thank you kindly for all your help!

So, using WR = 65, TR = .5 and ST = 12, then PR = ~3.033

PR = (1-((1-(1-(65/100))^12)^((.5*365*50)-(12-1))))*100 = ~3.033

...which means PRobability = approx. 3.033

Relating that to your .1% then means 3.033/100 = .03% (approx.) : yes?

What seems STRANGE to me is : ^((TR*365*50)-(ST-1))))
WHY have -(ST - 1) in there: seems meaningless; here's why:

PR = (1-((1-(1-(65/100))^12)^((.5*365*50)-(12-1))))*100 = 3.030328833
remove the (ST - 1):
PR = (1-((1-(1-(65/100))^12)^((.5*365*50)))*100 = 3.030364876
....a difference of .000036043

Sooooo: remove the darn thing!!
Get my drift?

I hope SlipEternal checks this out...in case I goofed!!

Hi DenisB,

My apologies for my delayed response; I've been traveling around in Europe and the Middle East. Currently on a break in the Iceland airport.

I tested out your hypothesis about simply removing -(ST - 1), and it does seem to make only a minimal difference, insignificant for my purposes.

I'm still trying to isolate ST. I've got this far but am having a mental block.

PR = (1-((1-(1-(WR/100))^ST)^(TR*365*50))*100
PR/100 = 1-((1-(1-(WR/100))^ST)^(TR*365*50)
-(PR/100 - 1) = (1-(1-(WR/100))^ST)^(TR*365*50)
(TR*365*50) = ln(-(PR/100 - 1))/ln((1-(1-(WR/100))^ST))
(TR*365*50)*ln((1-(1-(WR/100))^ST) = ln(-(PR/100 - 1))

Do you know how to isolate ST?

Any help is much appreciated!