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Probability Paradox!?!

  • #41
  • Jan 16, 2012 7:16am Jan 16, 2012 7:16am
Quoting nubcake
fuck the math.... if you have an even payout game then add one extra element that favors one side then that is an edge and where the money goes.
Got it in one nubs
  • #42
  • Jan 16, 2012 7:46am Jan 16, 2012 7:46am
Quoting hanover
unweighted randomly generated charts (i.e. where there is always exactly 50% probability of an uptick, and 50% downtick)
...
Finally (and getting off-topic, sorry), threads like this one disturb me. Not that there's anything wrong with the material that's being presented --- it goes without saying that any edge is eroded to the extent that the trader is unable to implement it --- but the heavy...
Why not make a technical study of random charts, with psych and 10Kh on the side to keep things level?
I've been looking forever for a free online random chart generator that requires no programming/Excel skills -- You just go to the site and start drawing (or applying indicators etc.) Then, one can show if it's possible or not to have an edge on random charts, or at least get some good practice in.
  • #43
  • Jan 16, 2012 7:58am Jan 16, 2012 7:58am
Quoting Reactor
You haven't done the maths correctly. If it was only 36 slots (1/36 = 2.78% probability of winning) the probability is still 97% that you will lose. Having an extra slot does not increase the casino's edge by 2.7% either (1/37 = 2.70% probability of winning, not 2.78%-2.70% = 0.08%). Let's be clear here, it's the 97% that is the real reason for the casino's advantage, not the 3%. There is no gimmick with the 0, it's just obvious maths.

Don't worry, your behaviour reminds me when they first introduced the National Lottery in the UK. Everyone thought...
You are confusing a straight bet of 50/50 (ie re or black) with betting on a single number.

A bet on either red/black gives the casino a 2.7% edge.
  • #44
  • Jan 16, 2012 8:02am Jan 16, 2012 8:02am
Quoting ha-pattern
Why not make a technical study of random charts, with psych and 10Kh on the side to keep things level?
I've been looking forever for a free online random chart generator that requires no programming/Excel skills -- You just go to the site and start drawing (or applying indicators etc.) Then, one can show if it's possible or not to have an edge on random charts, or at least get some good practice in.
and what good will that do for anyone? you can't even find an edge with all the bullshit you do with REAL charts. random chart generators are easy to write, yet prove little. what a typical waste of time.
Congratulations ScalaFX for coming out of the closet!
  • #45
  • Jan 16, 2012 8:52am Jan 16, 2012 8:52am
Quoting nubcake
and what good will that do for anyone? you can't even find an edge with all the bullshit you do with REAL charts. random chart generators are easy to write, yet prove little. what a typical waste of time.
I didn't say anything about an edge.
While the concept is valid and often useful, my overall approach involves edge as described here. From there, whatever I do technicals with is a list, sometimes a very short one, that I practice with to hone the use of as well as the psychology and mm of. That's not really the usual idea of an edge.
  • #46
  • Jan 16, 2012 8:59am Jan 16, 2012 8:59am
Quoting Scotty B
Alright, nothing in the living room is broken. By weighting the random data we can achieve a "net-flow" much like in the real market. One simple principle that undercuts the random market idea is the fact that it's a normal market procedure to split large orders into little chunks over a day or whatever time frame is required. This gives us a baseline confidence in pervasive/persistent moves in price (trends). Again the mechanism is net flow, and it may be random in the sense that the world is random and the net flow happens to be negative the...
I could not have sumed up the reason for years of bitching and screaming any better
  • #47
  • Jan 16, 2012 9:06am Jan 16, 2012 9:06am
Quoting ha-pattern
I didn't say anything about an edge.
of course you didn't....

Quoting ha-pattern
Then, one can show if it's possible or not to have an edge on random charts, or at least get some good practice in.
i must have imagined it.

Quote
While the concept is valid and often useful, my overall approach involves edge as described here. From there, whatever I do technicals with is a list, sometimes a very short one, that I practice with to hone the use of as well as the psychology and mm of. That's not really the usual idea of an edge.

i swear you just throw words together.
Congratulations ScalaFX for coming out of the closet!
  • #48
  • Edited 9:46am Jan 16, 2012 9:12am | Edited 9:46am
Quoting nubcake
{Did so!}.
True.
What clarification I can offer:

You often read members writing that this or that will "give" them an edge, when, unless there are exact rules that one follows to create that edge, the word 'edge' in such a context becomes meaningless.
And I've found that when one combines those so-called edges into a list, you depend heavily on your own ability to make decisions.
So here I am, practicing away like most others drawing on PA in demo, and I realize that I have to get an edge for every trade and chart area from using a collection of items from a drawing-methods list. Sometimes I do this, other times I fall back to a standard of, say, trend angles and lines. NEITHER ONE GIVES ME A LONG-TERM EDGE. So I look to psychology and, as much as I can, combine it with the chart. Perhaps it's my decision-making, perhaps something deeper that I bring to such.

I do sense an edge in psychology, only I haven't arrived at it yet -- At least, I want it on paper for if I get there.
  • #49
  • Jan 16, 2012 10:57am Jan 16, 2012 10:57am
What about this for an idea of 'edge':

You have a simple coin flip betting experiment. In theory there is a 50% chance of getting heads and a 50% chance of getting tails. If you guess correctly you win $10. If you guess wrong you lose $11 (consider the extra $1 as transaction costs). What will happen over time? You will lose your money.

Now, what if we factor in the concept of series' of flips as has been mentoned in the thread instead of taking each flip as a single event. What if we say the probability of getting heads on the next flip decreses each time a consecutive head appears. So the probibility of getting 3 heads in a row is less than 2 times. 4 times has less probability again. 5 even less. 50 times very unlikely.

How can we use this idea to create an edge in our trading?

We trade a simple random entry system with a fixed SL and fixed TP. We use the smallest lot size available on our account for each trade UNTIL we have 5 losses in a row. Once we have 5 losing trades in a row we take the next trade with our normal lot size, which must be greater than the sum of 5 losing trades at the smallest lot size. If trade number 6 is a win - great. If not, we repeat the whole process.

The idea being after 5 losing trades the probability of a winner being around the corner is higher than after one losing trade. More times than not, the 6th trade should be a winner. And so over time we make money.

So does it work or not? It will be interesting to see some replies to this.
  • #50
  • Jan 16, 2012 12:23pm Jan 16, 2012 12:23pm
Quoting Roofx
What about this for an idea of 'edge':

You have a simple coin flip betting experiment. In theory there is a 50% chance of getting heads and a 50% chance of getting tails. If you guess correctly you win $10. If you guess wrong you lose $11 (consider the extra $1 as transaction costs). What will happen over time? You will lose your money.

Now, what if we factor in the concept of series' of flips as has been mentoned in the thread instead of taking each flip as a single event. What if we say the probability of getting heads on the next flip...
Roulette players tried the same thing. You can't cheat the maths. The likelihood of getting tails is always 50%, no matter what happened before. If we got a million tails before, then the likelihood is still 50% that the next time it will be tails again.
Ask a maths professor if you don't believe it.
  • #51
  • Jan 16, 2012 2:45pm Jan 16, 2012 2:45pm
Quoting Reactor
You haven't done the maths correctly. If it was only 36 slots (1/36 = 2.78% probability of winning) the probability is still 97% that you will lose. Having an extra slot does not increase the casino's edge by 2.7% either (1/37 = 2.70% probability of winning, not 2.78%-2.70% = 0.08%). Let's be clear here, it's the 97% that is the real reason for the casino's advantage, not the 3%. There is no gimmick with the 0, it's just obvious maths.

Don't worry, your behaviour reminds me when they first introduced the National Lottery in the UK. Everyone thought...
Reactor,

You're right about the lottery, but Agro's comments about roulette in post #35 are correct. With one 0 on the wheel, the house odds are always 2.7% against the player, regardless of whether he bets on red/black, a whole row, a whole column, 4 numbers in a square, a single number, etc etc.

Here's what you're missing: Odds are calculated from expectancy, not probability. If a player bets on a single number, he will be correct 1 time in 37, and wrong 36 times. Hence you're correct about the probability being 1 in 37, or 3%. But let's assume he bets $1 each time. Over 37 spins, he will (on average) have 36 losses of $1, and 1 win of $35, due to the 35:1 payoff on single number. Hence his net position is (1 x $35) - (36 x $1) = -$1. Divide this by 37 and you have an expectancy of -0.027, or 2.7% per spin.

Now do the math for betting on red or black. Over 37 spins, the player will have 18 wins with a 1:1 payoff, and 19 losses. Hence his expectancy is (18 x $1) - (19 x $1) = -$1. Divide this by 37 and you have 2.7% again.

As a final example, let's do the math for betting on a whole column of 12 numbers. The payoff is 2:1. The player will win 12 times @ $2 and lose 25 times @ $1, in 37 spins. Hence expectancy = (12 x $2) - (25 x $1) = -$1. Once again we find ourselves dividing -1 by 37, for 2.7%.

Just for fun, suppose the casino paid out 50:1 on a single number bet. Then the expectancy would be (1 x $50) - (36 x $1) = +$14. Divide by 37 and we get about 37.8%. This is positive, hence the expectancy is now heavily in favor of the player. He still wins only 3% of the time, but he will gain $14, on average, every 37 spins. That is why gamblers calculate expectancy, rather than probability.

I suppose you could say that this loosely equates to win rate and RR. If my average RR is high enough (say 2:1), then I can end up ahead despite winning less than 50% of my trades. As a hypothetical example, suppose I set a 1 pip SL and a 500 pip TP. Now my win rate will be tiny, but every time I win, the payoff is 500 to 1 (if we ignore the spread). Expectancy incorporates both the win rate, and the average net win size (RR).

David
  • #52
  • Jan 17, 2012 4:09pm Jan 17, 2012 4:09pm
Here's a thought.

When you discuss coin flips, the underlying premise is that the tosses themselves are perfectly independent. No matter how you want to extend that premise, the results should end up independent.

But why not take a source of real information (i.e. market instrument move) and then analyze the conditional likelihood of some event based upon that study.

For instance, 5 moves up in an instrument might result in a conditional likelihood of a move down that is not 50/50. Or one event conditioned on another might not be 50/50. These are the kinds of studies that might be of interest to pursue.

Toby Crabel did a lot of these type of studies years ago. Long before this board was even around.
  • #53
  • Jan 17, 2012 4:36pm Jan 17, 2012 4:36pm
Quoting jamjamjam
Here's a thought.

When you discuss coin flips, the underlying premise is that the tosses themselves are perfectly independent. No matter how you want to extend that premise, the results should end up independent.

But why not take a source of real information (i.e. market instrument move) and then analyze the conditional likelihood of some event based upon that study.

For instance, 5 moves up in an instrument might result in a conditional likelihood of a move down that is not 50/50. Or one event conditioned on another might not be 50/50. These...

There was a bot that did this coded by SH little while ago, look for moves based on a criteria such as x number of consecutive bars closing in the same direction, place your trade accordingly on an inside bar that gets formed after that.

It didn't do too bad.
  • #54
  • Jan 17, 2012 4:42pm Jan 17, 2012 4:42pm
Quoting Custos
Roulette players tried the same thing. You can't cheat the maths. The likelihood of getting tails is always 50%, no matter what happened before. If we got a million tails before, then the likelihood is still 50% that the next time it will be tails again.
Ask a maths professor if you don't believe it.
I can attest to this, I took $1k to $10k in a few hours playing roullette based on my premise that a series of outcomes gives less likelyhood of it contining to happen in the future. It seemed to work, i was also doing a semi-martingale to increase my expectancy. However as I tipped $10k I was playing online I ran into a nasty streak of losing trades (either expected based on math) or the fact that I was playing online and may have been put on "manual" mode. I saw something like 10 blacks in a row where I was betting red. I saw it multiple times and only when I traded. Was kinda weird but I can't really prove that it was bs.

To try to prove to myself that it wasn't a fluke I did it again taking it to $5k with another IP. Dunno but maybe I'm just lucky

Seems like whatever strategy I used(that had an edge in my mind based on the premise in this thread) worked initially but failed to work after a while. Probably averaging in on my statistical disadvantage.
  • #55
  • Jan 17, 2012 6:05pm Jan 17, 2012 6:05pm
Quoting Custos
Roulette players tried the same thing. You can't cheat the maths. The likelihood of getting tails is always 50%, no matter what happened before. If we got a million tails before, then the likelihood is still 50% that the next time it will be tails again.
Ask a maths professor if you don't believe it.
This is the problem with thinking too abstractly. If you were to toss a physical coin with 1 million tails in a row, I would gladly wager that the same physical coin would turn up tails in the next toss.

We shouldn't get too bogged down in any theory to lose sight of common sense.
  • #56
  • Jan 17, 2012 6:34pm Jan 17, 2012 6:34pm
Quoting Reactor
The '0' is not the house's edge and a myth. The ball can only land in one slot, so that is 1 in 36 (using UK roulette), which means a probability of you winning is only 3%.

Worded differently, you have a 97% chance of losing, which means the house has a 97% chance of winning. Saying the house has an edge gives the impression they only have a small advantage, when in reality they have a certainty.

In regards to the OP's opening post, it's coincidence that you get two in a row as the probability remains at 50/50 each time. Do enough coin flips...
That's hilarious. Let me guess: you're not a mathematician.
  • #57
  • Jan 17, 2012 6:47pm Jan 17, 2012 6:47pm
@OP: The best way that I've found to explain this apparent "paradox" is to look at it this way:

The probability of a streak can only be calculated before the streak begins. Once the streak is in full swing, the outcomes of all previous tosses are already known and cannot be used to calculate probability (since the outcome is known with 100% probability). Each future toss itself is still 50-50.

For example if I've tossed 5 straight tails, the probability of that was about 3% before I started, but since I have already done it, its probability is now 100% (because we already know it happened), and the probability of any subsequent tosses is just 50-50, until they happen and we know the outcome.

Hope that helps.
  • #58
  • Jan 18, 2012 12:12am Jan 18, 2012 12:12am
Quoting jamjamjam
This is the problem with thinking too abstractly. If you were to toss a physical coin with 1 million tails in a row, I would gladly wager that the same physical coin would turn up tails in the next toss.

We shouldn't get too bogged down in any theory to lose sight of common sense.
If maths isn't the purest of common sense, then I don't know what is. Go to a maths professor and ask what's the likelihood of tails coming up after a million tails in a row. it is ALWAYS 50%, no matter what happened before.
  • #59
  • Jan 18, 2012 12:29am Jan 18, 2012 12:29am
Quoting Custos
If maths isn't the purest of common sense, then I don't know what is. Go to a maths professor and ask what's the likelihood of tails coming up after a million tails in a row. it is ALWAYS 50%, no matter what happened before.

You are missing the point. I suggest you find a physical coin that you can flip 1 million times (or far less) and get 1million tails to come up in a row. In the event that you do, based upon the evidence (and not abstract belief), you are far more likely to get another tail than a head.

It's not the maths that is the issue, it's your interpretation of it.
At some point you need to correct your model to reflect reality
(from a mathematical perspective, you'd be updating your prior belief--
look into Bayesian statistics if it helps any).
  • #60
  • Jan 18, 2012 12:33am Jan 18, 2012 12:33am
Quoting jamjamjam
You are missing the point. I suggest you find a physical coin that you can flip 1 million times (or far less) and get 1million tails to come up in a row. In the event that you do, you are far more likely to get another tail than a head.

It's not the maths that is the issue, it's your interpretation of it.
At some point you need to correct your model to reflect reality
(from a mathematical perspective, you'd be updating your prior belief).
If it works as you suggest, then why don't you go to the casino and only bet on red after ten blacks in a row. I assure you, in the long-term you would still lose. Past events, in this case, are not linked to future events.
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