Probability - or, when is it better to stay in bed?

[tomorton]

zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

I agree, but the markets are closed and there's precious little else to do.

 

[Barramundi]

Actually, I think I phrased this badly. I've heard of Gambler's Fallacy before but I'm not convinced it applies, the reason being I won't be betting on the result of the 8th consecutive event, I'm betting on 8 identical consecutive results of 8 different but consecutive events. Any one trade in the series has a 60% probability of being a win. But surely the entire series of 8 does not have a 60% probability of producing 8 wins?

At the start of the 8 size sample, the chance of having 8 consecutive winners based on a 60% chance of a win per event can be evaluated as 0.6^8 which equates to 1.67%.

However, if you've already had 7 winners, the chance of the 8th trade being a winner is not 1.67%. It remains at the chance of any of your signals succeeding - 60%.

Of course, if you've had 40 consecutive winners, you may begin to question whether the probability of your system is really 60%, or whether you may be in a period where your system is ideally suited to the market conditions. I'd say the converse is more typically the problem, where traders after a series of losses begin avoiding trades because they lose faith in the system, only to let a winning series slip them by.

Of course if you're on a massive winnning streak then why not go for it and start doubling up

 

[Masquerade]

I agree, but the markets are closed and there's precious little else to do.

Spend money, it's why we make it isn't it?

 

[tomorton]

At the start of the 8 size sample, the chance of having 8 consecutive winners based on a 60% chance of a win per event can be evaluated as 0.6^8 which equates to 1.67%.

However, if you've already had 7 winners, the chance of the 8th trade being a winner is not 1.67%. It remains at the chance of any of your signals succeeding - 60%.

Of course, if you've had 40 consecutive winners, you may begin to question whether the probability of your system is really 60%, or whether you may be in a period where your system is ideally suited to the market conditions. I'd say the converse is more typically the problem, where traders after a series of losses begin avoiding trades because they lose faith in the system, only to let a winning series slip them by.

Of course if you're on a massive winnning streak then why not go for it and start doubling up

That's well explained Barramundi, but I believe your calculation proves that after 7 wins in 7 days, it's best to stay in bed on Day 8. The probability of the 8th win of the series occurring on Day 8 remains as low as it was before the series started, way too low to justify taking the trade.

 

[Shanghai]

That's well explained Barramundi, but I believe your calculation proves that after 7 wins in 7 days, it's best to stay in bed on Day 8.

100% wrong. If you have achieved 7 wins in 7 days then it is time to go out and invest most of the winnings in beer and women on day 8.

 

[Barramundi]

That's well explained Barramundi, but I believe your calculation proves that after 7 wins in 7 days, it's best to stay in bed on Day 8. The probability of the 8th win of the series occurring on Day 8 remains as low as it was before the series started, way too low to justify taking the trade.

Don't be crazy, after 7 wins you're on a roll, go with it, treat it like a Texas Hold'em and go all in!!!

 

[BeginnerJoe]

Going all in is definitely more exciting. If you make it big with a single trade and then stop, you will never have to worry about 60% probability again, or how many heads or tails you will get after so and so many tosses. Never have to get up early again, either.

 

[new_trader]

I agree, but the markets are closed and there's precious little else to do.

There is your answer, it's days like this when it is better to stay in bed.

 

[kimo'sabby]

Let's suppose we have a strategy with a 60% win rate.


Wots the strat? Is it real or made up? No point in talkin' about fiction.

Speilberg: "Wot would happen to a small seaside town if a big mechanical rubber shark started attacking the locals?"

See wot i mean?

 

[greigmcl]

That's well explained Barramundi, but I believe your calculation proves that after 7 wins in 7 days, it's best to stay in bed on Day 8. The probability of the 8th win of the series occurring on Day 8 remains as low as it was before the series started, way too low to justify taking the trade.

To chip in my tuppenceworth, no it doesn't. The 1.67% chance of 8 in a row is based on a comletely random sample set. By saying that you have 7 winners under your belt you're talking about the sample sets which contain 7 winners and you're back to just assessing the probabilty of a win the next day, ie 60%.

The only other thing that muddies the waters is that trading instruments tend to trend. I don't have the maths to back it up, but that does suggest that it would skew the results in a way that you would expect to have longer winning streaks and longer losing streaks than you would have with something truly random.

 

[Martinghoul]

In your stylized setup, the results of your bets follow the Poisson process (or, rather, its special discrete case, the Bernoulli process). That means every new outcome is strictly independent of previous outcomes, if any. That would imply the probability of getting it right on every new bet is always 60%. The most common illustration given of this is the flipping a coin or rolling dice (unfair).

Where it actually gets a lot more interesting is when you start relaxing the various assumptions. E.g. what if you don't actually know how "unfair" the coin actually is? What if the "realized" probabilities differ from the assumed ones? What if the outcomes aren't independent as you originally assumed? There's all sorts of work in statistics that's been done on the subject.

 

[DashRiprock]

sorry martingoul but i think a binomial is more appropriate but in this simple case they are sort of the same but not acutally the same.

but I say binomial is better because 0.5 < p < 0.95. i also think binomial is more appropriate just from experience



but anyway yes the second bit is very interesting like autocorrelation in results and stuff like that

 

[Chartsy]

1+1=2

 

[tomorton]

Let's suppose we have a strategy with a 60% win rate.


Wots the strat? Is it real or made up? No point in talkin' about fiction.

Speilberg: "Wot would happen to a small seaside town if a big mechanical rubber shark started attacking the locals?"

See wot i mean?

Yes it's real, for real money, there's no point talking fiction.

 

[tomorton]

I read that Poisson was a nineteenth century university maths lecturer and mathematician but nothing about any expertise in trading his own money for his own livelihood. No doubt one of the foremost thinkers in his field, but traders have to be more pragmatic - we have to be profitable, not just right.

My proposal remains that it is irrational to risk a trade which would be the 8th consecutive win in a system with a 60% long-run win rate. The probability of 8 consecutive wins was tiny before the series started and it does not increase with each successive win. Of course, it couild be argued that if the win rate is 51% or better, it doesn't matter if the 8th trade or any individual trade is a win or not, long-term there will be a profit, but I am interested in avoiding trades with an excessive risk profile. Isn't that what we do?

 

[DashRiprock]

...

My proposal remains that it is irrational to risk a trade which would be the 8th consecutive win in a system with a 60% long-run win rate....

do u actually think this is true?

I rekon ur just doing this thread for LULZ

 

[Martinghoul]

sorry martingoul but i think a binomial is more appropriate but in this simple case they are sort of the same but not acutally the same.

but I say binomial is better because 0.5 < p < 0.95. i also think binomial is more appropriate just from experience



but anyway yes the second bit is very interesting like autocorrelation in results and stuff like that

Well, depends on what you're looking at... If you define your process in terms of the number of wins, then yes, it's a binomial distribution. Every individual trial is Bernoulli, though. At any rate, they are indeed intimately related.

 

[DashRiprock]

Well, depends on what you're looking at... If you define your process in terms of the number of wins, then yes, it's a binomial distribution. Every individual trial is Bernoulli, though. At any rate, they are indeed intimately related.

Bernoulli dist with 2 discrete results IS a binomial distribution.

a Bernoulli becomes a poisson when you do it in continuous time


(iirc)

 

[intradaybill]

Most of you are wrong. Martinghoul is as always asymptotically correct.

The market is nowhere near a coin toss. This is an abstract model you learn is school for the purpose of understanding probability.

In the market the game is not fair. Your actions provoke reactions. You may want to toss (trade) but there may not be enough shares available. You may win once and when you try again the counterparty is ready to take additional actions.

Gambler's fallacy does not apply to the market. Win rate is only measured after the fact. Everyone's problem here is that he assumed that saying "my win rate is 60%" makes sense. Your win rate is only measured when you quit trading for good and you look at the final numbers.

Martingale techniques make sense. When you make money reduce exposure. There is drawdown in the horizon because eventually the market is trying to take you winnings back. When you lose, take more risk, but only if you are sure you are doing the correct thing.

Do not toss any coins. Kids do that. You have grown up now.

 

[Martinghoul]

I read that Poisson was a nineteenth century university maths lecturer and mathematician but nothing about any expertise in trading his own money for his own livelihood. No doubt one of the foremost thinkers in his field, but traders have to be more pragmatic - we have to be profitable, not just right.

My proposal remains that it is irrational to risk a trade which would be the 8th consecutive win in a system with a 60% long-run win rate. The probability of 8 consecutive wins was tiny before the series started and it does not increase with each successive win. Of course, it couild be argued that if the win rate is 51% or better, it doesn't matter if the 8th trade or any individual trade is a win or not, long-term there will be a profit, but I am interested in avoiding trades with an excessive risk profile. Isn't that what we do?

Yes, but your question is meaningless without making assumptions a lot clearer. Do you assume that the outcome of every trade is indeed independent of previous outcomes? If not, then you have to make assumptions about the various conditional probabilities.

Point is that this is actually either an extremely simple or a rather complex question and it all depends on the exact assumptions you make, which are far from clear. For example, what if we allow the possibility that your 60% assumption is actually incorrect? So the answer, really, is, as usual, "it depends".