General Betting
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Consider the two patterns Head-Tail-Head (HTH) and Head-Tail-Tail (HTT). Which of the following is true:
A) The average number of tosses until HTH is larger than the average number of tosses until HTT
B) The average number of tosses until HTH is the same as the average number of tosses until HTT
C) The average number of tosses until HTH is smaller than the average number of tosses until HTT
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*ok i've been told so many times that coin tossing is 50/50 and what i've researched tells me its not quite true and if you start to be interested in sequences of tosses its even more obvious, for me at least, im not a math wiz but some here obviously have those type of skills, so do you agree or even knew about this??
here are two interesting links:
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-unfair-proposition
http://www.youtube.com/watch?v=kLmzxmRcUTo (TED conference - Peter Donnelly: How juries are fooled by statistics)
[;)]
A) The average number of tosses until HTH is larger than the average number of tosses until HTT
B) The average number of tosses until HTH is the same as the average number of tosses until HTT
C) The average number of tosses until HTH is smaller than the average number of tosses until HTT
.....................
*ok i've been told so many times that coin tossing is 50/50 and what i've researched tells me its not quite true and if you start to be interested in sequences of tosses its even more obvious, for me at least, im not a math wiz but some here obviously have those type of skills, so do you agree or even knew about this??
here are two interesting links:
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-unfair-proposition
http://www.youtube.com/watch?v=kLmzxmRcUTo (TED conference - Peter Donnelly: How juries are fooled by statistics)
[;)]
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Replies: 59
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Googled this, interesting, cheers.
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*As always a lot of the "Trick" is in making sure the wording is exactly right. (Which it is)
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**In fact I'm not keen on the wording the more I look at it as you can correctly get the wrong answer or the right one depending on how you interpret it.
I would add the words "Starting from scratch" to each of the three scenarios. |
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A but that doesn't change the probability of a head or tail, it's just the way the problem is set out with an overlapping sequence.
The article is an illustration that you can bias a toss |
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http://en.wikipedia.org/wiki/Penney%27s_game
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2 different ideas really. The physics of tossing a small engraved disc and the probability of sequences of 3, that consist of the same 2 things at random
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Of course 50/50 is not quite true because there is a very little chance of a coin dropping and staying on its edge :p
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ok A) is the correct answer
why? because HTH overlaps itself and what that means is that you can have this sequence appear with less coin tosses HTHTH = you can have five tosses to achieve two sequences now you cant ever do that with HTT HTTHTT = you need six tosses to achieve two sequences |
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A. The average number of tosses until HTH is larger than the average number of tosses until HTT
because HTH overlaps itself and what that means is that you can have this (HTH) sequence appear with less coin tosses have you got it back to front? |
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LOL coming to think of it, YES!!
 where you read "tosses" you should read "occurrences" thanks breandauk1 |
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A. The average number of tosses until HTH is larger than the average number of tosses until HTT
because HTH overlaps itself and what that means is that you can have this (HTH) sequence appear with less coin tosses have you got it back to front? Not according to the Youtube clip. HTH on average takes 10 spins, HTT takes 8 spins |
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no, he himself got confused and said HTT 8 spins but in the end corrected to HTH (6:32), also in the powerpoint presentation you can see it clearly HTT 10th toss (4:17)
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Tossing a coin is a complete waste of time .. Two guys could sit down for the next 10 years 7x7 365 days .. and there would not be 40 points in it it is evens , it could be evens .. have you guys got 20 years to waste .. try the horses
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you can see it clearly HTT 10th toss (4:17)
Think that is for that particular sequence HHTHHTHHTT not on average |
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Two guys could sit down for the next 10 years 7x7 365 days .. and there would not be 40 points in it
Not true zipper. The more throws there are the bigger the expected gap between the two. |
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Feck ,who told you that ?
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The theory of probability becomes of enhanced value to gamblers when it is used with the law of large numbers. The law of large numbers states that:
“If the probability of a given outcome to an event is P and the event is repeated N times, then the larger N becomes, so the likelihood increases that the closer, in proportion, will be the occurrence of the given outcome to N*P.” For example:- If the probability of throwing a double-6 with two dice is 1/36, then the more times we throw the dice, the closer, in proportion, will be the number of double-6s thrown to of the total number of throws. This is, of course, what in everyday language is known as the law of averages. The overlooking of the vital words 'in proportion' in the above definition leads to much misunderstanding among gamblers. The 'gambler's fallacy' lies in the idea that “In the long run” chances will even out. Thus if a coin has been spun 100 times, and has landed 60 times head uppermost and 40 times tails, many gamblers will state that tails are now due for a run to get even. There are fancy names for this belief. The theory is called the maturity of chances, and the expected run of tails is known as a 'corrective', which will bring the total of tails eventually equal to the total of heads. The belief is that the 'law' of averages really is a law which states that in the longest of long runs the totals of both heads and tails will eventually become equal. In fact, the opposite is really the case. As the number of tosses gets larger, the probability is that the percentage of heads or tails thrown gets nearer to 50%, but that the difference between the actual number of heads or tails thrown and the number representing 50% gets larger. Let us return to our example of 60 heads and 40 tails in 100 spins, and imagine that the next 100 spins result in 56 heads and 44 tails. The 'corrective' has set in, as the percentage of heads has now dropped from 60 per cent to 58 per cent. But there are now 32 more heads than tails, where there were only 20 before. The 'law of averages' follower who backed tails is 12 more tosses to the bad. If the third hundred tosses result in 50 heads and 50 tails, the 'corrective' is still proceeding, as there are now 166 heads in 300 tosses, down to 55-33 per cent, but the tails backer is still 32 tosses behind. Put another way, we would not be too surprised if after 100 tosses there were 60 per cent heads. We would be astonished if after a million tosses there were still 60 per cent heads, as we would expect the deviation from 50 per cent to be much smaller. Similarly, after 100 tosses, we are not too surprised that the difference between heads and tails is 20. After a million tosses we would be very surprised to find that the difference was not very much larger than 20. A chance event is uninfluenced by the events which have gone before. If a true die has not shown 6 for 30 throws, the probability of a 6 is still 1/6 on the 31st throw. One wonders if this simple idea offends some human instinct, because it is not difficult to find gambling experts who will agree with all the above remarks, and will express them themselves in books and articles, only to advocate elsewhere the principle of 'stepping in when a corrective is due'. It is interesting that despite significant statistical evidence and proof of all of the above people will go to extreme lengths to fulfill there belief in the fact that a corrective is due. The number 53 in an Italian lottery had failed to appear for some time and this lead to an obsession with the public to bet ever larger amounts on the number. People staked so much on this corrective that the failure of the number 53 to occur for two years was blamed for several deaths and bankruptcies. It seems that a large number of human minds are just simply unable to cope with the often seemingly contradictory laws of probability. If only they had listened to their maths teacher. The full story is publish here. An understanding of the law of the large numbers leads to a realisation that what appear to be fantastic improbabilities are not remarkable at all but, merely to be expected. |
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Lusitano ,
just read that the number of tosses the more it is evens zip told you that .. and zip did not go to school |
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Lusitano .. see my post 16.05
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You obviously didn't read Lustiano's post zipper.
In fact, the opposite is really the case. As the number of tosses gets larger, the probability is that the percentage of heads or tails thrown gets nearer to 50%, but that the difference between the actual number of heads or tails thrown and the number representing 50% gets larger. |
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Feck, dont take this wrong I know the odds inside out .. if Lusitano 71 .. has a different view .. well good luck to her /him its all about opinions .. and my opinion is as good as anyones . and i put my money were my mouth is .. unlike some thats why iam know as zipper
Zip It Zipper thats the wife . dont you just love em .. she reads this now and again Sue if you read this .....I Love You |
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zipper, you really must let me know who your scriptwriter is.
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jesus wept. there is none so blind as he who will not see.
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In fact, the opposite is really the case. As the number of tosses gets larger, the probability is that the percentage of heads or tails thrown gets nearer to 50%, but that the difference between the actual number of heads or tails thrown and the number representing 50% gets larger.
It seems to me there must be some point when the gap gets smaller, for instance 60/40 followed by 45/55.. |
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Indeed Kenilworth. Who is to say that in the next 100 tosses of the coin, it does not even out to 40/60 and you are much closer to 50/50 again?
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Zipper: Two guys could sit down for the next 10 years 7x7 365 days .. and there would not be 40 points in it.
Feck N. Eejit Not true zipper. The more throws there are the bigger the expected gap between the two Zipper is correct, as a percentage (and that's what matters here) the gap will close with the more throws there are, but obviously the gap will usually be larger as a number simply because of the amount of throws is larger as a number. The best of 10 throws could result in 2 heads and 8 tails, a difference of 6 or 300%, but you won't throw 1000 times and get a difference anywhere near that large even though the difference as a number may well be 60 not 6, which means the gap has closed. |
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I don't buy in to the HTH / HTT theory either, it's just a play, the chance of either is 7/1, there is no adavantage to calling HTH over HTT.
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There's no theory to buy into, it's correct. The wording is what makes it look odd though.
If you and I start of flipping coins I'll call HTT and I'll hit my HTT first more often than you hit your HTH. If we then start again, I have an edge. This is because there are two ways for HTx to pan out HTH and HTT, obviously. So, we both get to HTx after two tosses and lose You've flipped: HTT and I've flipped HTH so we keep flipping as nobody has won However, I'm already 1/3rd of a way to winning while you're restarting The reason it "works" is that if we have a constant stream of flips, then They'll come up the same amount. If the string "HTHTH" comes up in a string then HTH has come up twice. By the rules of the game we're playing though, when you get HTH you win, and we start again, so the "TH" fourth and fifth flips never get you that extra victory. |
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the chance of either is 7/1
At the start of the game, this is correct for the first three flips. If we both flip a heads, now we're both 3/1 to hit in the next two. If we now both flip a tails we're both evens to hit next go. Of those evens shots. If we both hit = draw If you hit and I miss = you win If I hit and you miss = I win If we both miss = keep flipping. HOWEVER We keep flipping with me starting on a H and you flipping on a T, so I'm 3/1 to hit in my next two spins, but you're back to no chance in two spins and 7/1 in the next three. |
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If we don't flip independently, we're 50-50 and that's my problem with the wording.
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*I haven't watched the video, which may be helping
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Ok i'll make it more obvious then, lets say i was betting in multiple events with two outcomes and i choose a pattern (either HTH/HTT), how many bets do i need to get a good run:
HTH = 3 tosses/ 1 pattern HTHTH = 5 tosses/ 2 patterns HTHYHTH = 7 tosses/ 3 patterns HTHTHTHTH = 9 tosses/ 4 patterns HTHTHTHTHTH = 11 tosses/ 5 patterns HTHTHTHTHTHTH = 13 tosses/ 6 patterns and so on.... HTT = 3 tosses/ 1 pattern HTTHTT = 6 tosses/ 2 patterns HTTHTTHTT = 9 tosses/ 3 patterns HTTHTTHTTHTT = 12 tosses/ 4 patterns HTTHTTHTTHTTHTT = 15 tosses/ 5 patterns HTTHTTHTTHTTHTTHTT = 18 tosses/ 6 patterns and so on... Conclusion: for me to achieve the same good run of 6 consecutive HTH with HTT i would need to make 5 more bets The likelihood of HTH appearing in a random string is more often than HTT, which has statistically significance. |
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My tuppence flip: Assuming the coin is balanced, and a fair test, surely B, equal?
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I still don't buy in to it, because you're using the previous now dead spin to claim a win.
In your example above of HTH = 13 tosses/6 patterns, I see 13 tosses = 2 patterns of HTH and 2 of THT, THT always following HTH. How can you use a dead spin HTH in the real world to your advantage? |
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I don't buy into it for the simple reason no coin toss has any previous knowledge of any previous coins toss, the absolute fundamental thing about probability that some don't understand, and from that viewpoint, each sequence begins anew with each toss, and therefore each sequence has a likely probability, AS LONG AS every event in the sequence has a likely probability.
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Lori : If you and I start of flipping coins I'll call HTT and I'll hit my HTT first more often than you hit your HTH. If we then start again, I have an edge.
Lori, I wouldn't normally nit pick, but you did say in another thread when I cussed off a nit picker for picking you up that it was the right thing to do :) |
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Lusitano71
LOL coming to think of it, YES!! where you read "tosses" you should read "occurrences" thanks breandauk1 Whilst in nit picking mode, what's the difference between tosses and occurences? I would have thought answer C best fits your theory, as Brendan suggested? |
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you guys are thinking in terms of the base pattern (3 letters) and im thinking of a pattern that keeps appearing on a never ending string of random H's and T's, simples
why should the last H be the ending and not the start of the next pattern??? |
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Because the last H is a done deal, it's expired, you can't use it again in the real gambling world. Or if you can, how?
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