New Posts For Thread: Maths Questionhttps://community.betfair.com/exchange_games/go/thread/view/94066/23855382/maths-questionHow do I calculate the probability or 16 consecutive heads occurring when continuously tossing a coin? Is it as simple as 2 to the power of 16, that would mean that if I tossed a coin 65,536 times I could expect to see a run of 16 heads once?ThanksBoth Winning and Losing runs can be calculated in terms of reasonable probability.In this case (Heads and Tails odds = 2 over 65535 flips) the result is:Winning runs could be: 16Losing runs could be: 16I made a calculator ages ago for working this ouhttps://community.betfair.com/exchange_games/go/thread/view/94066/23855382/maths-question?post_id=429866262#429866262Both Winning and Losing runs can be calculated in terms of reasonable probability.In this case (Heads and Tails odds = 2 over 65535 flips) the result is:Winning runs could be: 16Losing runs could be: 16I made a calculator ages ago for working this ouFri, 23 Apr 2010 10:14:56 -0500Yeah, Ive got it and its answered another question, I think. As I see it, the reason for this is because the coin is being continually flipped. If it was only flipped 16 times then every sequence has the same chance of occurring because there wouldhttps://community.betfair.com/exchange_games/go/thread/view/94066/23855382/maths-question?post_id=429866258#429866258Yeah, Ive got it and its answered another question, I think. As I see it, the reason for this is because the coin is being continually flipped. If it was only flipped 16 times then every sequence has the same chance of occurring because there wouldThu, 22 Apr 2010 19:43:10 -0500It's subtle but there is a difference between different sequences when looking at sub-sequences. It's counter-intuitive (and makes my head hurt too) but I think it's true. I'll try to do some examples to convince myself of that fact.E.g. if we toss ahttps://community.betfair.com/exchange_games/go/thread/view/94066/23855382/maths-question?post_id=429866254#429866254It's subtle but there is a difference between different sequences when looking at sub-sequences. It's counter-intuitive (and makes my head hurt too) but I think it's true. I'll try to do some examples to convince myself of that fact.E.g. if we toss aThu, 22 Apr 2010 18:11:21 -0500Thanks for replying, I looked at that page and now my brain hurts. It raised another question though, I used the run of heads just to make it easier. I was under the impression that 16 heads have the same expectation as any other sequence. So, in ohttps://community.betfair.com/exchange_games/go/thread/view/94066/23855382/maths-question?post_id=429866250#429866250Thanks for replying, I looked at that page and now my brain hurts. It raised another question though, I used the run of heads just to make it easier. I was under the impression that 16 heads have the same expectation as any other sequence. So, in oWed, 21 Apr 2010 17:29:20 -0500http://mathworld.wolfram.com/Run.htmlThat page has the mathematical details. Unless I've miscalculated, the expected number of runs length 16 or greater is 0.5Also, the "longest expected run" of heads in 65536 flips is 15.This is from formulae 14 andhttps://community.betfair.com/exchange_games/go/thread/view/94066/23855382/maths-question?post_id=429866246#429866246http://mathworld.wolfram.com/Run.htmlThat page has the mathematical details. Unless I've miscalculated, the expected number of runs length 16 or greater is 0.5Also, the "longest expected run" of heads in 65536 flips is 15.This is from formulae 14 andWed, 21 Apr 2010 16:37:00 -0500Yes to the first part, no to the second.https://community.betfair.com/exchange_games/go/thread/view/94066/23855382/maths-question?post_id=429866242#429866242Yes to the first part, no to the second.Wed, 21 Apr 2010 16:22:55 -0500Yep.https://community.betfair.com/exchange_games/go/thread/view/94066/23855382/maths-question?post_id=429866238#429866238Yep.Mon, 19 Apr 2010 09:31:21 -0500How do I calculate the probability or 16 consecutive heads occurring when continuously tossing a coin? Is it as simple as 2 to the power of 16, that would mean that if I tossed a coin 65,536 times I could expect to see a run of 16 heads once?Thankshttps://community.betfair.com/exchange_games/go/thread/view/94066/23855382/maths-question?post_id=429866234#429866234How do I calculate the probability or 16 consecutive heads occurring when continuously tossing a coin? Is it as simple as 2 to the power of 16, that would mean that if I tossed a coin 65,536 times I could expect to see a run of 16 heads once?ThanksMon, 19 Apr 2010 04:09:20 -0500