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Probability Paradox!?!

  • #1
  • First Post: Jan 14, 2012 9:11pm Jan 14, 2012 9:11pm
I have a question regarding probabilities that has always confused me


it seems to me to be a paradox but please feel free to correct me


so lets take a coinflip.. it has been said that going opposite the previous outcome doesnt mean shit... so it lands heads and going tails will not net me a better probability?

but when you factor in the probabilities of streaks it does not make sense

for example if I flip a coin 10 times.. the probability of it landing heads 2 times in a row is 85.93%... so thus betting on tails would offer better probabilities when viewing it as a streak... but if I view it as a single outcome then sure its still a 50/50.. since there is two sides of the coin...

to me its an interesting paradox.. let it land heads 3 times out of the 10 flips and I'll bet on tails.. theres only a 25ish% chance of it landing heads again..


Hmmm...
  • #2
  • Jan 14, 2012 9:18pm Jan 14, 2012 9:18pm
individual flip says you have 50% probability as an individual event

but the paradox gets even more paradoxical

the more you flip the more probability of you being wrong, but if you take into account the rule of large numbers over 10,000 flips you will get roughly 50/50.
AVT INVENIAM VIAM AVT FACIAM
  • #3
  • Jan 14, 2012 9:38pm Jan 14, 2012 9:38pm
there's no paradox;

every time the coin leaves your hand,

it has 50/50 chances.


With that being said, it is the different sequences of heads and tails that carries with it the proposed probabilities.

it is the SEQUENCE that has a 85.93% chance of occurring, not the actual flip.
  • #4
  • Jan 14, 2012 9:44pm Jan 14, 2012 9:44pm
Quoting fluiDynamic
there's no paradox;

every time the coin leaves your hand,

it has 50/50 chances.


With that being said, it is the different sequences of heads and tails that carries with it the proposed probabilities.

it is the SEQUENCE that has a 85.93% chance of occurring, not the actual flip.
thus the point being betting on tails after 3 heads is a high probability based on sequence yet not higher probability based on 50/50
  • #5
  • Jan 14, 2012 10:13pm Jan 14, 2012 10:13pm
Quoting newyear498
thus the point being betting on tails after 3 heads is a high probability based on sequence yet not higher probability based on 50/50
No it is not. I think it would be easier for you to understand this if you ran a simulation: make random coin toss series in excel/scripting language and try your "betting strategy". You'll see that it fails. All betting strategies would also fail. You can't predict a random series.

Let's try a more intuitive example: betting on "red" after a "black" streak on roulette. It's the same thing as the coin. For simplicity assume that it's a strictly red/black roulette (no zero/green). It's the same thing.

Now the real roulette. For you visiting a casino, seeing a 8 times red streak would seem like a miracle, and you'll be very tempted to bet against it. But dealers tell how each and every night at some table there is a 8 times same color streak. And once a month there is even a 14 times same color streak. Imagine how much money the house makes on that day from all the fools betting against it (starting from when it was just an 8 streak).
  • #6
  • Jan 14, 2012 11:04pm Jan 14, 2012 11:04pm
Quoting newyear498
thus the point being betting on tails after 3 heads is a high probability based on sequence yet not higher probability based on 50/50
the probability is more to reveal an overall in/equality in possible outcomes over time. you don't know how long the sequence needs to be for the outcomes to even each other out, so individual flips are still one way or another.

if you knew the timeline of when the sequence would balance THEN you would know the probabilities of subsequent tosses over time. that is to say, if you knew that within 10 coin flips you would have 5 heads and 5 tails, and after 9 flips you had 5 heads and 4 tails.... well, then you bet the house on the next flip being a tail. but nobody knows how long it will take for everything to balance.

probabilities are a compass, not a gps.

now, think about this... what is more likely, that a coin will evenly toss back and forth heads and tails over and over, or that you will get streaks? how often do you see an even streak of heads then tails? so, what's better, to bet on the next flip being the 'other side' to even out the probabilities or to bet on the same side as is currently flipped to bet on the sequence going even further out of what probabilities suggest?
Congratulations ScalaFX for coming out of the closet!
  • #7
  • Jan 14, 2012 11:30pm Jan 14, 2012 11:30pm
Quoting newyear498
I have a question regarding probabilities that has always confused me


it seems to me to be a paradox but please feel free to correct me


so lets take a coinflip.. it has been said that going opposite the previous outcome doesnt mean shit... so it lands heads and going tails will not net me a better probability?

but when you factor in the probabilities of streaks it does not make sense

for example if I flip a coin 10 times.. the probability of it landing heads 2 times in a row is 85.93%... so thus betting on tails would offer better...
Explained here.
  • #8
  • Jan 15, 2012 12:22am Jan 15, 2012 12:22am
Each coin toss is an independent event. What you flipped 2 minutes ago, 2 weeks ago or 2 years ago has no bearing on the current flip so the probability is always 50/50 for each flip.
  • #9
  • Jan 15, 2012 2:21am Jan 15, 2012 2:21am
Best "selection" method for betting 50/50 (or close as possible) is to bet on the second previous outcome

This way you will always be "correct" and betting on those long streaks while others are betting against it, hoping for it to end, bit like FX traders picking the bottom while trend traders are going with it

It takes a lot for me to IGNORE you, but you can try.
  • #10
  • Jan 15, 2012 2:58am Jan 15, 2012 2:58am
Quoting Erebus
Best "selection" method for betting 50/50 (or close as possible) is to bet on the second previous outcome

This way you will always be "correct" and betting on those long streaks while others are betting against it, hoping for it to end, bit like FX traders picking the bottom while trend traders are going with it

No 'selection method' will improve the odds. It is a 50/50 chance on a coin flip no matter what. No but's about it. If you are talking about a casino game (such as roulette) then the house have a built in edge (the 0). It is a mugs game and you will always lose in the long run.
  • #11
  • Jan 15, 2012 3:26am Jan 15, 2012 3:26am
Perhaps this experiment to help by throwing dice.
Law of Large Numbers
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  • #12
  • Jan 15, 2012 3:41am Jan 15, 2012 3:41am
Quoting Agro
No 'selection method' will improve the odds. It is a 50/50 chance on a coin flip no matter what. No but's about it. If you are talking about a casino game (such as roulette) then the house have a built in edge (the 0). It is a mugs game and you will always lose in the long run.
Exactly.

But there are still gullible folk who believe that they have 'selection' or staking (MM) systems that can somehow shift the odds into their favor.
  • #13
  • Jan 15, 2012 7:39am Jan 15, 2012 7:39am
Thanks everyone I understand better now...
  • #14
  • Jan 15, 2012 12:02pm Jan 15, 2012 12:02pm
Is it correct to say that to get a 50% chance over, say, 200 tosses, you HAVE to either stick with heads or tails all the time?
  • #15
  • Jan 15, 2012 12:11pm Jan 15, 2012 12:11pm
Quoting pipexplorer1
Is it correct to say that to get a 50% chance over, say, 200 tosses, you HAVE to either stick with heads or tails all the time?
i'm confident that this is not actually a question.
Congratulations ScalaFX for coming out of the closet!
  • #16
  • Edited 1:14pm Jan 15, 2012 1:02pm | Edited 1:14pm
Quoting newyear498
I have a question regarding probabilities that has always confused me


it seems to me to be a paradox but please feel free to correct me


so lets take a coinflip.. it has been said that going opposite the previous outcome doesnt mean shit... so it lands heads and going tails will not net me a better probability?

but when you factor in the probabilities of streaks it does not make sense

for example if I flip a coin 10 times.. the probability of it landing heads 2 times in a row is 85.93%... so thus betting on tails would offer better...
No you should not view the problem with flipping a coin 10 times because I believe you are actually looking at the probability of having a tail after 2 times of head in a row.

Say they are 2 series of events, the probability of having 2 heads in next 2 flips is 0.5 x 0.5 = 25%, and the probability of having 2 heads in a row but followed by a tail is 0.5 x 0.5 x 0.5 = 12.5%.

So what is the probability of having tail, given that you had 2 heads in last 2 flips? It is 12.5% / 25% = 50%. The answer is same with 50% if you view each flips as an independent event.

This is a typical conditional probability problem. There is no paradox.
  • #17
  • Jan 15, 2012 1:08pm Jan 15, 2012 1:08pm
Quoting nubcake
i'm confident that this is not actually a question.
You are wrong. It is a question. What I meant was if you change your choice in between, does your probability of success decrease or deviate from a 50 percent probability. Maybe you just don't have the understanding to answer the question
  • #18
  • Jan 15, 2012 1:10pm Jan 15, 2012 1:10pm
Quoting pipexplorer1
You are wrong. It is a question. What I meant was if you change your choice in between, does your probability of success decrease or deviate from a 50 percent probability. Maybe you just don't have the understanding to answer the question
maybe you just didn't formulate an understandable question. as for the answer, i think by now you should have come to the conclusion that a coin flip is 50/50.
Congratulations ScalaFX for coming out of the closet!
  • #19
  • Jan 15, 2012 1:14pm Jan 15, 2012 1:14pm
Quoting nubcake
maybe you just didn't formulate an understandable question. as for the answer, i think by now you should have come to the conclusion that a coin flip is 50/50.
It was very understandable, maybe for you it wasn't. Looks like you still havnt got it.
  • #20
  • Jan 15, 2012 2:23pm Jan 15, 2012 2:23pm
Quoting pipexplorer1
It was very understandable, maybe for you it wasn't. Looks like you still havnt got it.
Ok, if this is a genuine question, the answer is that it doesn't matter. Your chance of success will always be 50%. Sticking with heads, sticking with tails, switching every round, switching every other round - it's all the same.
The nail that sticks out gets hammered back in
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