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Gaming-What Are The Odds Of...

Discussion in 'Non-Vegas Chat' started by DOUBLE B, Jan 4, 2013.

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  1. DOUBLE B

    DOUBLE B Tourist

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    To flip a coin for head/tails the odds are 50-50 for it to be either heads or tails-correct?

    What are the odds of the flip turning up either heads or tails 2 times in a row?--- 3 times in a row?--- 4 times in a row?....5 times in a row? and on and on and on. Is there a formula used to calculate the odds on multiple back to back to back hits on the same heads/tails?

    Thanks in advance for any info-help?
     
  2. nostresshere

    nostresshere Mr. Anti Debit Card

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    Lots of theories out there. I typed "odds of coin flip" into google and was amazed at the discussions. After reading about 3 of them, I need to go get a drink.

    I will tell you that with out any other factors such as the coin being weighted one way or the other, the chance of EVERY SINGLE flip is 50/50. No matter how many times in a row it was heads, the chance of the next one being heads is still 50%. ALWAYS.
     
  3. thecarve

    thecarve Misanthrope

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    Odds of winning multiple bets in a row = (X)^N

    X = odds of success on a single trial
    N = number of trials

    If you want to know what the odds of hitting four tails in a row:

    We know that the odds of hitting tails once are 50/50, or ½ so…

    (1/2)^4
    = 1/16
    = .0625
    = 6.25% chance of landing on tails four times in a row
     
  4. Jersey_Bill

    Jersey_Bill High-Roller

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    Ok, let me reach back to my basic statistics and challenge someone to correct me....

    I seem to recall that the odds of sequential coin flips are conditional probabilities - or a series of probabilities in a row you need to achieve to reach the end result of 3 or 4 or 5 flips in a row. Thus, the odds are multiplicative.

    One flip would be 50/50 odds or a 0.50 (50%) probability.
    Two heads in a row would be (0.50)x(0.50) or 0.25 (25%) probability.
    Three heads in a row would be (0.50)x(0.50)x(0.50) or 0.125 (12.5%) probability.
    Four heads in a row would be (0.50)x(0.50)x(0.50)x(0.50) or 0.0625 (6.25%)
    Five heads in a row would be (0.50)x(0.50)x(0.50)x(0.50)x(0.50) or 0.03125 (3.125%)

    and so forth...

    Many people here know more about stats than I do so please correct as needed...

    JZB
     
  5. NandJfrmNJ

    NandJfrmNJ High-Roller

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    Nostresshere is correct. The laws of probability state that each flip in independent of every other flip and the probability is that each flip has a 50-50 chance of coming up either heads or tails. That being said, you could flip 10 times and get 10 heads. The larger the sample, the closer you will come to the expected 50-50 ratio.
     
  6. tacallian

    tacallian Low-Roller

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    Saying what are the odds of a coin flip and providing a condition such as heads 5 times in a row is a prediction. Jersey Bill is correct and as an event on it's own of course the odds of it happening are far less than 50%. Each coin flip while an individual 50/50 chance if applied to a specific circumstance reduces the overall chance of that event occuring by an additional 50%.

    Barring imperfections in the coin of course.

    In much the same way you can calculate the chance of 17 coming up twice in a row on a roulette wheel. It doesn't mean that the 17 has more or less chance of coming up the second time as it's an independant trial, but the odds of the event on the whole can determined. (A specific number coming up is a 2.7% chance (on a double 0 wheel), twice in a row is around 0.073%)

    Unfortunately for many people the mind see's a streak and generally convinces itself the streak will break because it knows the odds of a long streak are low.
     
  7. Auggie

    Auggie Dovahkiin

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    As said, the math looks like:

    (x/y)^z

    where:
    x = the number of positive outcomes
    y = the total number of possible outcomes
    z = the number of occurrences in a row

    So "whats the chance of a coin coming up heads 10 times in a row?" is: (1/2)^10

    Which equals: 0.0009765625
    Or could be expressed as: .09765625%
    Or written as: 1 in 1024

    To apply this to something like roulette, like if you were playing a 00 wheel and you were placing bets that covered 20 numbers and wanted to know the odds that your numbers would come up 3 times in a row...
    (20/38)^3 = .14579
    Or thats: 14.579%
    Or could be written as: 1 in 6.86


    But there are a few notes:

    If you wait for the first event to happen and then want to know the likelihood of it happening a certain number of times in a row, then for the above formula you would use z-1 as the exponent.

    An example of this is: if you are flipping a coin and it goes tails, tails, tails, heads...

    And now you want to know "now that I have hit heads, whats are the odds I will see 10 heads in a row?" the math becomes:
    (1/2)^(10-1)

    Thats because the first event has already happened so its a 100% chance of happening.


    And this all applies to events that have not yet happened. So using the example above: if you are flipping a coin and want to know the odds that it will be heads the next ten flips in a row, thats 1 in 1024...

    But if you have already flipped the coin 9 times and its been heads then that 10th flip the odds aren't 1 in 1024 that it will be heads, but only 1 in 2 since the first 9 occurrences have already happened - the math would be: (1/2)^(10-9) = 50% chance that the 10th flip will be heads if the first 9 were heads.
     
  8. Nevyn

    Nevyn VIP Whale

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    You're getting two different responses because there are two different questions.

    If your question is "I just flipped heads, what are the odds it will be heads if I flip it again" or even "I just flipped heads 10 times in a row, what are the odds it will be heads if I flip it again", then the answer is 50% (see nostresshere's response).

    If your question is "If I flip this coin X times in a row, what are the odds that each flip will be heads", then thecarve's answer is the one you need.



    In this case, your question sounds more like #2, so that is probably the answer you are looking for.
     
  9. Chuck2009x

    Chuck2009x VIP Whale

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    Before you make the first flip, the odds of the next one being heads is 50%, and it gets cut in half for each flip after that.

    So, BEFORE YOU FLIP THE FIRST TIME, the odds that
    the first one is heads = 50%
    the first two are heads = 25%
    the first three are heads = 12.5%
    the first four are heads = 6.25% etc etc

    But, AFTER EACH flip occurs, the odds of the next one being heads is always 50%.

    So if the first 100 flips come up heads, is tails due? Nope, it's still 50 - 50 on the next flip.

    Of course, at that point you gotta consider that maybe the coin is flawed. :drunk:
     
  10. nostresshere

    nostresshere Mr. Anti Debit Card

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    Yes, you are getting answers to two different questions. It is important to understand that. Too many people think the last result has some bearing on the next one.

    If you want the answer to what that next SINGLE event will be - it is 50/50.

    If you want the answer of chances of getting x number in a row - see the above math/statistics shared by a few others.
     
  11. Dave

    Dave Low-Roller

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    The amazing thing is that people will walk by a roulette wheel and see that 17 has come up a few times, or that red has come up a lot of times and then assume that one of those two are "hot" and they should therefore bet on one of them.
     
  12. nostresshere

    nostresshere Mr. Anti Debit Card

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    Statistically, we should ignore this. Personally, I would consider playing it. #hit happens.
     
  13. mikenhe

    mikenhe VIP Whale

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    having a double headed coin really screws those theories up.





    in other words - test your conditions first.....
     
  14. BeeeJay

    BeeeJay President of The Red Lobster Hostess Satisfaction

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    17s never hit on roulette wheels, but if they do it is certainly because some degen said "there is nothing sweeter than a repeater":evillaugh:beer::evillaugh

    1/38*1/38
     
  15. jerseyguy

    jerseyguy VIP Whale

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    Here's a question

    What are the odds of it being 50/50 heads/tails on 10 flips?
    On 100 flips?
    On 1000 flips?
    Are they all still 50/50 or is there less of a variable the more flips you make?
    Is there any way that you could calculate a variable based on the number of flips in the first place?
     
  16. kingcrim05

    kingcrim05 Tourist

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    Look into this: Binomial Distribution and Pascal's Triangle

    Flipping heads 5 times after flipping a fair coin 10 times will happen ~24.61% of the time, for example.


    2 flips 4 permutations 2/4 = .5
    4 flips 16 perms 6/16 = .375
    6 flips 64 perms 20/64 = .3125
    8 flips 256 70/256 = .2734
    10flips 1024 252/1024 = .2461

    What variable are you exactly trying to calculate, in your last question?
     
  17. MangoPort

    MangoPort Low-Roller

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    Now, if you really want to push the envelope here (I'm sure this isn't what the original question was asking though), suppose I flip a coin 1,000 times and it's heads each time, what is the chances it will be heads the 1,001th flip?

    You might be tempted to shout "50/50", but the truth is there's a good chance there's something wrong with the coin.

    Hypothesis testing is a way of measuring the NEW expected results based on past results deviating from expectations.

    1 million flips all turning up heads? You've got a double-headed coin.

    But what about 10 flips turning up heads? Yes, even that changes our expected probability of the next flip. This is of course only true in circumstances where unfairness is possible. A roulette wheel may actually have a bias or flaw in it, whereas if you lose 1 million hands in a row in baccarat your odds of losing the next one don't change at all unless you're being cheated... which you probably are :)
     
  18. jerseyguy

    jerseyguy VIP Whale

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    Thank you I respectfully withdraw the question

    I'm getting into a world I dont belong near to or in,to me perms are what women used to do to their hair.
     
  19. thedukeofdublin

    thedukeofdublin Low-Roller

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    Well all I can say is that this reminds me of losing 10 in a row 19-36 on the Roulette whilst doubling my bet to cover myself up to the table limit of course (Bellagio):grrr::grrr:

    That was a bad day................................convinced that i was the worlds unluckiest man I trodded off head in hands. i swear if I had of stood on dog sh1t that day there would have been a nail in it:rolleyes2:

    I try to console myself with some auto roulette in the MGM (literally 90 minutes later) and got 10 in row 19-36 :evillaugh:evillaugh (unfortunately not having the balls to double my bet:rolleyes2:)

    For once in my life I was speechless and thought to myself all day - "Whats the odds?"

    Anyone care to hazard a guess of the odds I beat that day?
     
  20. angelo

    angelo Tourist

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    1. 100% / 2 = 50%
    2. 50% / 2 = 25%
    3. 25% / 2 = 12.5%
    4. 12.5% / 2 = 6.25%
    5. 6.25% / 2 = 3.125%
    6. 3.125 / 2 = 1.5625%
    7. 1.5625% / 2 = 0.78125%

    and so on.
    :stir:
     
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