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#2
02-07-2007, 10:24 PM
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Re: Losing 6 Coinflips in a row?
[ QUOTE ]
WHAT is the frequency with which I should expect to lose 6 coinflips in a row? HOW ABOUT in a coinflip game with a loaded coin where I would win 48% of the coinflips? [/ QUOTE ] Try losing 165k in 85 flips at 4k/per. 
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#3
02-08-2007, 01:26 AM
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Re: Losing 6 Coinflips in a row?
it's just the probability of losing to the power of the number of losses
e.g. (0.5)^6
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#4
02-08-2007, 03:38 PM
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Re: Losing 6 Coinflips in a row?
Thanks. So at the outset of my coinflipping venture, my chances of losing 6 in a row are roughly 2%?
If I define "losing 6 in a row" as a LOSS and I define "NOT losing 6 in a row 10 times" as a WIN, what's my WIN:LOSS ratio going to be, on average? How would I go about calculating that? Help please!!! Thanks.
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#5
02-08-2007, 03:51 PM
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Re: Losing 6 Coinflips in a row?
[ QUOTE ]
Thanks. So at the outset of my coinflipping venture, my chances of losing 6 in a row are roughly 2%? If I define "losing 6 in a row" as a LOSS and I define "NOT losing 6 in a row 10 times" as a WIN, what's my WIN:LOSS ratio going to be, on average? How would I go about calculating that? Help please!!! Thanks. [/ QUOTE ]Since they are multiple events I'm not sure the answer to that would mean very much to you. Think of it this way: odds of losing 6 coinflips = .015625 = odds that a six coinflip or more loss streak begins on each coinflip. 1/.015625 = 64, so every 64 coinflips you should expect to begin one of these loss streaks (of 6 or more).
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#7
02-08-2007, 05:50 PM
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Re: Losing 6 Coinflips in a row?
[ QUOTE ]
Great, thanks.... How about LOSS:WIN? (where WIN is defined as being successful in not having a 6 flip losing streak TEN TIMES)? [/ QUOTE ] Chances of a loss are 1/64 so chances of 1 win are 63/64. Therefore, chances of a Big Win of 10 wins in a row are (63/64)^10 = 85.4% And you have about a 50-50 chance of a Super Big Win of 44 wins in a row. (63/64)^44 = 50% PairTheBoard
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#8
02-08-2007, 06:23 PM
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Re: Losing 6 Coinflips in a row?
No, sorry... perhaps I am not being clear. A "WIN" is not a single coinflip event. I'm defining it as 10 successful trials at NOT having a 6 flip losing streak....
In other words, I am asking what are the chances of "losing six coinflips in a row" VERSUS "failing to lose six coinflips in a row TEN TIMES"?
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#9
02-08-2007, 08:32 PM
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Re: Losing 6 Coinflips in a row?
[ QUOTE ]
No, sorry... perhaps I am not being clear. A "WIN" is not a single coinflip event. I'm defining it as 10 successful trials at NOT having a 6 flip losing streak.... In other words, I am asking what are the chances of "losing six coinflips in a row" VERSUS "failing to lose six coinflips in a row TEN TIMES"? [/ QUOTE ] Right. That's what I computed for you. I'm calling a "win" a single trial of not getting 6 bad flips in a row. What you're calling a "WIN" I'm calling a "Big Win" to make clear it's different from what I'm calling a "win". Your "WIN" and my "Big Win" mean 10 trials in a row where you don't get the Bad Run of 6 bad flips. Here's an example of a "WIN" or "Big Win" where tttttt is a loss. h tth th tttth h th ttttth h tth th As I computed above, chances of getting such a "WIN" are about 85%. I defined a "Super Big Win" as 44 such trials in a row. Chances of a Super Big Win are about 50%. PairTheBoard
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#10
02-09-2007, 12:30 AM
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Re: Losing 6 Coinflips in a row?
Yes, thanks... sorry I misunderstood you.
I appreciate it. So, when I sit down to play this hypothetical game until a Big Win or a 6 flip in a row Loss (whichever comes first), I can expect to have a Big Win 85% of the time. And therefore I can expect to have a 6 flip in a row Loss 15% of the time. (this is with a 50-50 coin... does this change much with a 48-52 coin or a 44-56 coin?)
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