
#1
Jul2408, 06:04 PM

P: 2,828

Hi,
It is often frustrating when tossing a coin if there is just one tossing and it's over. Let's say, Nicolas and George toss a coin and are after two given configurations, each his own. Nicolas likes the configuration HeadTailTail. George chooses HeadTailHead. Whenever they argue, they play the game : they toss a coin, and the first to get his configuration wins. Is this a fair game ? 



#2
Jul2408, 06:07 PM

P: 342

why not?




#3
Jul2408, 06:12 PM

P: 640

So long as it always starts from zero, I don't see why it would be any different than a single flip. Before either can possibly win, a HeadTail pattern must occur. Then from that point, its a 50%.
Unless the wording is wrong somehow... 



#4
Jul2408, 06:16 PM

P: 2,828

Tossing a coin... 3 times ?This puzzle is really one of the best I have ever seen. It's simple, and nobody gets it right. 



#6
Jul2408, 06:58 PM

Mentor
P: 2,917

Hmmm, not sure if this is right...and it's hard to say with words.
Spoiler
George, with the HTH configuration.
It first appears that the winner is simply decided by the last toss, since they both chose HT as the first two flips in their configurations. But since the first toss of the each configuration is an H, that H could be George's winning flip, since his last flip is H. Like I said, it's hard to say with words. English is my second language...an I don't have a first one . 



#7
Jul2408, 07:00 PM

Mentor
P: 2,917

OK, so nevermind the last post...it didn't seem quite right anyway.
So what is the correct wording? 



#8
Jul2408, 07:09 PM

P: 2,828





#9
Jul2408, 07:45 PM

P: 655

How about they just keep flipping until their pattern shows up 3 times (or something of that nature).




#10
Jul2408, 08:19 PM

Emeritus
Sci Advisor
PF Gold
P: 10,424

Any string of flips of length three (HHH, TTT, HTH, THT, THH, HTT, TTH, HHT) is equally probable, so the game is certainly fair. It just takes more time to play.
 Warren 



#11
Jul2408, 08:25 PM

P: 655

Right, but if you wanted 3 repititions of hth, then you could win in 7 flips with hththth, whereas its going to take 9 flips for htt (htthtthtt).




#12
Jul2408, 08:37 PM

Emeritus
Sci Advisor
PF Gold
P: 10,424

 Warren 



#13
Jul2408, 10:20 PM

P: 2,828

Contrary to intuition (at least mine), the average number of tosses until HTH is 10, whereas the average number of tosses until HTT is 8. Still, HTH wins as often as HTT. The distributions of tosses until the configuration is reached are not the same. 



#14
Jul2508, 10:25 AM

P: 24

I did what you recomended and simulated this (in excel). Over 10,000 trials, both win evenly and both win in an average of 5 tosses.




#15
Jul2508, 10:29 AM

P: 2,828





#16
Jul2508, 10:50 AM

P: 24

Actually I did not use a macro I just used the options available in the sheet I just set up a series of tosses extracted the critical info from the seires, copied the series and info 100 times to the right (100 trials), and then copied that 100 times down (10,000) trials. At the very end I took totals and averages, averages then I can recalculate the sheet just by hitting F9. I tried to put a standard deviation to it but i dont think that is the correct way to do it. however averages are averages and pretty hard to screw up. I dont know how you wrote your program, if you were calculating odds or just running a random trials. random trials the result is prety clear and repeatable




#17
Jul2508, 11:26 AM

P: 2,828

Just to make it clear : I have the number 8 and 10 from a researcher in statistics applied to genetics at Oxford. They are what made me interested in this in the first place. I found them by myself by writing simluation programs, but I do not believe they are questionable.




#18
Jul2508, 01:03 PM

P: 24

Here is 1/10 of the data I used. Unfortunately due to the brute force nature of the solution it was too large to keep in excel format and also in its entirety.
Description Odd Columns  Tosses generated with =int(rnd()*2) Even Columns  winner of series Third to last row shows winner in odd colums and the toss he won on in the even column The second to last row shows the toss that he won on if HTH won The last row shows the toss he won on if HTT won On the far right the last two rows show the following table HTH, qty won, average toss won on HTT, qty won, average toss won on I know this isn't the easiest format to work with but you can import it into most spreadsheet software. If anyone can point out my error I would like to know my mistake so I don't repeat it in the future. 


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