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Math Help: Probability

  • #21
  • Jul 11, 2011 10:44am Jul 11, 2011 10:44am
Quoting Adal
The problem is ill specified. It's like asking this: "If I increase the area of a circle with 20%, how much will this other segment length which is now 66 cm increase?" Well, that question doesn't make sense, you can't answer that question without knowing the relation between the segment and the circle area.

In the OP question, there are no mentions of stuff like if each run is independent of the previous ones (for example a binomial distribution). The computation which leads to 92% assumes independent trials. But we all know that financial...
This is likely the exact issue were having...

I don't know what binomial distribution is but I think I have an idea


but my trade has 6 outcomes.. they all have an equal chance of happening but 4 win and 2 lose

if there is a 50/50 that price could go up or down 100 pips it always holds true that 6 outcome have same probability of happening

however if there was a 70/30 and I was on the 70 side then the 4 winning positions have greater ability to happen and thus the 2 losing outcomes have a lower probability to happen


does this help?
  • #22
  • Jul 11, 2011 10:52am Jul 11, 2011 10:52am
Quoting nubcake
i don't understand this dark arts mathimagic you guys are doing.

if you start with a 50/50, then nothing can exceed 50%.

half the time you flat out lose. the other half of the time you win 66% of the time and the rest you again lose. 66% of the potentially winning 50% is 33%... out of 200 trades is 66 WINNING trades, and 134 losing trades.

without accounting for the R/R this potentially means little. but, my math differs to what has been presented here.

how can you get 90+% win rate when you already state half of the time you flat...
lol dark arts math ROFL

yeah like I said theres 6 scenarios that all share the same probability of happening if theres a 50/50 case of price going up or down 100 pips

it can go up or down and I still hold a similar chance of winning.. like I said I change the risk ratios (opening and closing positions) as it progresses it is sorta like a magic trick in some ways
  • #23
  • Jul 11, 2011 10:58am Jul 11, 2011 10:58am
Quoting newyear498
This is likely the exact issue were having...

I don't know what binomial distribution is but I think I have an idea


but my trade has 6 outcomes.. they all have an equal chance of happening but 4 win and 2 lose

if there is a 50/50 that price could go up or down 100 pips it always holds true that 6 outcome have same probability of happening

however if there was a 70/30 and I was on the 70 side then the 4 winning positions have greater ability to win and thus the 2 losing outcomes have a lower probability to happen


does this help?
Expected Value (EV) for case 50/50:
EV = 0.5 * 4 - 0.5 * 2 = 1

Expected Value (EV) for case 70/30:
EV = 0.7 * 4 - 0.7 * 2 = 1.4

So, for each trade you'd win 1 unit for the 50/50 probability, but 1.4 units for the 70/30 probability. This assumes that all the 6 trades are equal, in the sense that they all win/lose the same amount (1 unit). For example - 4 longs on EUR/USD and two shorts on EUR/USD at the same price. Obviously, transaction costs are not included (and the trade would be equivalent with a net trade of 2 units long on EUR/USD).

But I have a suspicion that in your case the trades are not equal - for example one of those 4 trades could win more than the others. If that's the case, the numbers above are not correct. And the equations don't take into account the fact that the probability distribution changes, and that individual probabilities are not independent. In financial markets, it's much more likely to have a string of loses than in a fair coin toss experiment. The equations above assume a fair coin toss experiment (Bernoulli trial).

In other words, they are fun to calculate, but you can't bet money on them.

Note: It's not clear from your example if equation 2 should be EV = 0.7 * 4 - 0.7 * 2 = 1.4 or EV = 0.7 * 4 - 0.3 * 2 = 2.2
  • #24
  • Jul 11, 2011 11:08am Jul 11, 2011 11:08am
Quoting Adal
Expected Value (EV) for case 50/50:
EV = 0.5 * 4 - 0.5 * 2 = 1

Expected Value (EV) for case 70/30:
EV = 0.7 * 4 - 0.7 * 2 = 1.4

So, for each trade you'd win 1 unit for the 50/50 probability, but 1.4 units for the 70/30 probability. This assumes that all the 6 trades are equal, in the sense that they all win/lose the same amount (1 unit). For example - 4 longs on EUR/USD and two shorts on EUR/USD at the same price. Obviously, transaction costs are not included (and the trade would be equivalent with a net trade of 2 units long on EUR/USD).

But...
Exactly on point about consecutive loses.. that's my greatest concern

I will share the 6 outcomes in units.. consider it dollars, lots, whatever but if you could kindly share your math I'd appreciate it

they all have the same probability of happening if there was 50% chance price moved in my favor

Scenario's

S1: +6
S2: +6
S3: +6
S4: -5
S5: -9
S6: 0


Thanks again appreciate your time! (I also guess I mis-spoke about 4 being winning..)
  • #25
  • Jul 11, 2011 12:05pm Jul 11, 2011 12:05pm
Quoting newyear498
Exactly on point about consecutive loses.. that's my greatest concern

I will share the 6 outcomes in units.. consider it dollars, lots, whatever but if you could kindly share your math I'd appreciate it

they all have the same probability of happening if there was 50% chance price moved in my favor

Scenario's

S1: +6
S2: +6
S3: +6
S4: -5
S5: -9
S6: 0


Thanks again appreciate your time! (I also guess I mis-spoke about 4 being winning..)
So now I just need to figure out odds of winning if price moves in favor 70% of the time ( this would increase probability of scenario 1,2,3, and 6 happening more often that 4&5
  • #26
  • Jul 11, 2011 12:24pm Jul 11, 2011 12:24pm
A simple probability question and a complexity in answers is increasing. That will surely increase mathematical and statistical knowledge of the thread starter and us.
  • #27
  • Jul 11, 2011 12:39pm Jul 11, 2011 12:39pm
Quoting newyear498
So now I just need to figure out odds of winning if price moves in favor 70% of the time ( this would increase probability of scenario 1,2,3, and 6 happening more often that 4&5
Those odds can't be computed with only the information listed here. At least by me, since I don't really understand what you mean. I mean, I do understand in principle, but you give too little information and the details matter.

What would happen with S4 and S5 if "prices moved in your favor" 70% of the time? Could S4 and S5 become positive? Will they have lower losses (lets say -3 instead of -5). Will they remain the same?

How do you define "winning"? As the expected value of the system? As the number of winning trades (4 out of 6)?

Do S1 through S6 have the same equal probability no matter what? If they do, then they will have the same even if prices move in your favor more. So then the question doesn't have sense - the probability stays the same, the 50% or 70% "in your favor" doesn't matter.

I suggest that it would be better for you to backtest the system. Or to do a Monte Carlo simulation of it with 50% and 70% chances. That would be much easier to understand than messing with probabilities. And it's quite hard to do a wrong Monte Carlo simulation. But it's much easier to get a probability equation wrong.
  • #28
  • Jul 11, 2011 1:08pm Jul 11, 2011 1:08pm
Quoting Adal
Those odds can't be computed with only the information listed here. At least by me, since I don't really understand what you mean. I mean, I do understand in principle, but you give too little information and the details matter.

What would happen with S4 and S5 if "prices moved in your favor" 70% of the time? Could S4 and S5 become positive? Will they have lower losses (lets say -3 instead of -5). Will they remain the same?

How do you define "winning"? As the expected value of the system? As the number of winning trades (4 out of 6)?

Do...
ok cool, I will probably write an EA for this to backtest scenarios.. but yes the returns remain constant.. the only thing that changes would be how often one scenario happens over the other.. or better put.. the chance of the profiting (and break even) scenario's increase/decrease in probability together,

exampe would be if my chances of price move in my favor increase then all the scenarios 1,2,3,6 all increase equally in probability of happening while 4 and 5 decrease equally of probability they will happen (again the returns remain constant)



but thank you for you insights.. as you know I am not that good with math so its not surprising I am overlooking sufficient data needed to run the numbers.. it took me long enough to calculate and verify all the numbers I wrote about already..

now I'm adjusting for the shift if I make more correct decisions (because my current rate is roughly a 70% correct guess) which means I have greater than 66% chance of profiting.. but I'm not sure the exact number.. 92% sounds right but its so high I'm suspicious

thanks for your help tho!
  • #29
  • Jul 11, 2011 1:57pm Jul 11, 2011 1:57pm
Quoting newyear498
ok cool, I will probably write an EA for this to backtest scenarios.. but yes the returns remain constant.. the only thing that changes would be how often one scenario happens over the other.. or better put.. the chance of the profiting (and break even) scenario's increase/decrease in probability together,

exampe would be if my chances of price move in my favor increase then all the scenarios 1,2,3,6 all increase equally in probability of happening while 4 and 5 decrease equally of probability they will happen (again the returns remain constant)



but...
What happens if prices move in your favor 100% of time?
S1 - 25% (100% / 4)
S2 - 25% (100% / 4)
S3 - 25% (100% / 4)
S4 - 0% (0% / 2)
S5 - 0% (0% / 2)
S6 - 25% (100% / 4)
expected value: 0.25 * 6 + 0.25 * 6 + 0.25 * 6 + 0 * (-5) + 0 * (-9) + 0.25 * 0 = 4.5 with 6 units = 0.75 profit per played unit

If yes, than for 70% moves in your favor you would have:
S1 - 17.5% (70% / 4)
S2 - 17.5% (70% / 4)
S3 - 17.5% (70% / 4)
S4 - 17.5% (30% / 2)
S5 - 17.5% (30% / 2)
S6 - 17.5% (70% / 4)
expected value: 0.175 * 6 + 0.175 * 6 + 0.175 * 6 + 0.175 * (-5) + 0.175 * (-9) + 0.175 * 0 = 0.7 with 6 units = 0.116 profit per played unit

For 50%:
S1 - 12.5% (50% / 4)
S2 - 12.5% (50% / 4)
S3 - 12.5% (50% / 4)
S4 - 25.0% (50% / 2)
S5 - 25.0% (50% / 2)
S6 - 12.5% (50% / 4)
expected value: 0.125 * 6 + 0.125 * 6 + 0.125 * 6 + 0.25 * (-5) + 0.25 * (-9) + 0.125 * 0 = -1.25 with 6 units = -0.208 profit per played unit

But you stated that for 50% chance you are profitable. So you probably mean something else. Yet this seems to be what you want:
Quote
exampe would be if my chances of price move in my favor increase then all the scenarios 1,2,3,6 all increase equally in probability of happening while 4 and 5 decrease equally of probability they will happen (again the returns remain constant)
As you can see, the probabilities of winning trades (S1,S2,S3 and S6) increase with higher in your favor odds in my computations. And of S4 and S5 decrease. Exactly as you seem to expect. But the 50% results don't match - in my computation it actually loses money.

You could try simulating on paper a few cases. There aren't that many. Then you just multiply each return with it's probability.

Exactly like I did here a few days ago:
http://dl.dropbox.com/u/190212/ff/prob_matrix.jpg

EDIT: Maybe you mean this for 50%:
S1 - 16.6% (100% / 6)
S2 - 16.6% (100% / 6)
S3 - 16.6% (100% / 6)
S4 - 16.6% (100% / 6)
S5 - 16.6% (100% / 6)
S6 - 16.6% (100% / 6)
expected value: 0.166 * 6 + 0.166 * 6 + 0.166 * 6 + 0.166 * (-5) + 0.166 * (-9) + 0.166 * 0 = 0.664 with 6 units = 0.11 profit per played unit

But then I don't know how to compute each probability for the 70% case.
  • #30
  • Jul 11, 2011 3:24pm Jul 11, 2011 3:24pm
Quoting Adal
What happens if prices move in your favor 100% of time?
S1 - 25% (100% / 4)
S2 - 25% (100% / 4)
S3 - 25% (100% / 4)
S4 - 0% (0% / 2)
S5 - 0% (0% / 2)
S6 - 25% (100% / 4)
expected value: 0.25 * 6 + 0.25 * 6 + 0.25 * 6 + 0 * (-5) + 0 * (-9) + 0.25 * 0 = 4.5 with 6 units = 0.75 profit per played unit

If yes, than for 70% moves in your favor you would have:
S1 - 17.5% (70% / 4)
S2 - 17.5% (70% / 4)
S3 - 17.5% (70% / 4)
S4 - 17.5% (30% / 2)
S5 - 17.5% (30% / 2)
S6 - 17.5% (70% / 4)
expected value: 0.175 * 6 + 0.175 * 6 + 0.175 * 6 +...
Something does not seem right... this could mean I am overlooking something


actually I think I figured it out... I was probably wrong.. maybe this is the true...

you wrote this..

For 50%:
S1 - 12.5% (50% / 4)
S2 - 12.5% (50% / 4)
S3 - 12.5% (50% / 4)
S4 - 25.0% (50% / 2)
S5 - 25.0% (50% / 2)
S6 - 12.5% (50% / 4)

but I think it is actually this...

For 50%:
S1 - 16.6% (50% / 3)
S2 - 16.6% (50% / 3)
S3 - 16.6% (50% / 3)
S4 - 16.6% (50% / 3)
S5 - 16.6% (50% / 3)
S6 - 16.6% (50% / 3)



in other words 1,2,3 are related and 4,5,6 are related

because scenario 6 results in a zero loss/ profit, that would fix this equation and make sense to my situation



thank you Adal for sharing this method.. simple and makes sense.. I'm pretty sure I figured out my problem now!!!
  • #31
  • Last Post: Jul 11, 2011 3:27pm Jul 11, 2011 3:27pm
Quoting newyear498
Something does not seem right... this could mean I am overlooking something


actually I think I figured it out... I was probably wrong.. maybe this is the true...

you wrote this..

For 50%:
S1 - 12.5% (50% / 4)
S2 - 12.5% (50% / 4)
S3 - 12.5% (50% / 4)
S4 - 25.0% (50% / 2)
S5 - 25.0% (50% / 2)
S6 - 12.5% (50% / 4)

but I think it is actually this...

For 50%:
S1 - 16.6% (50% / 3)
S2 - 16.6% (50% / 3)
S3 - 16.6% (50% / 3)
S4 - 16.6% (50% / 3)
S5 - 16.6% (50% / 3)
S6 - 16.6% (50% / 3)



in other words 1,2,3 are related...
70% of time would then be

For 70%:
S1 - 23.3% (70% / 3)
S2 - 23.3% (70% / 3)
S3 - 23.3% (70% / 3)
S4 - 10% (30% / 3)
S5 - 10% (30% / 3)
S6 - 10% (30% / 3)


i don't know the EV.. I'll look at that equation when I get a minute
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