Coin Flip

Mikhail Gorbachev · 08-23-2009, 11:04 PM

Quote:

On Monday, you flip a coin all day. You start flipping it until you see the pattern Head, Tail, Head. You record the number of flips required to reach this pattern, and start flipping again (and counting up from 1 again) until you see that pattern again, you record the second number, and start again. At the end of the day you average all of the numbers you’ve recorded.
On Tuesday you do the EXACT same thing except you flip until you see the pattern Head, Tail, Tail.

Will Monday’s number be higher than Tuesday’s, equal to Tuesday’s, or lower than Tuesday’s?

[Mindcipher: Coin Flip]

If you think you have the answer, note this ambiguity not resolved in the original problem which caused me to get it wrong:
Spoiler Below

When you get a pattern, you start from scratch looking for the next one. HTHTH doesn't count as two instances of HTH.

***CaptHayfever*** · 08-23-2009, 11:19 PM

Spoiler Below

Truthfully: There is no certain answer until you actually do it.
Mathematically: Tuesday's number will be higher, since the raw odds of flipping Tails are greater.
Statistically: They'll be equal, since the difference in the odds is negligible.

And remember, "I'm-a Luigi, number one!"

Jailbreaker · 08-24-2009, 01:40 PM

Quote:

On Monday, you flip a coin all day. You start flipping it until you see the pattern Head, Tail, Head. You record the number of flips required to reach this pattern, and start flipping again (and counting up from 1 again) until you see that pattern again, you record the second number, and start again. At the end of the day you average all of the numbers you’ve recorded.
On Tuesday you do the EXACT same thing except you flip until you see the pattern Head, Tail, Tail.

Will Monday’s number be higher than Tuesday’s, equal to Tuesday’s, or lower than Tuesday’s?

Equal. There's a fifty-fifty chance, each time you flip, of NOT messing up the pattern. This applies to both heads and tails. There's no difference.

Spoiler Below

Oh, I looked at the answer... That's incerdible! I've never said "Ahhhhh!" before in my life!
It wasn't even "Ah-ha!" It was "Ahhhhh!" With 5 h's!

**Deku Trii** · 08-24-2009, 05:58 PM

Spoiler Below

I would think Monday's number would be higher than Tuesdays, because on Tuesday, if you miss the pattern by flipping Head on what would be your third flip, it's already the first in a new Head, Tail, Tail pattern.

I REALLY HATE POKEMON! · 08-25-2009, 05:03 PM

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I'd have to say the days outcome will be equal. Even though the order is jumbled, there's still a 50% chance every time you flip a coin for it to be either heads or tails.

08-23-2009, 11:19 PM	#2
*CaptHayfever* Smash SuperMod Join Date: Jul 2002 Location: (n) - the place where I am Gender: Posts: 27,659 Thanks: 1,991 Thanked 2,486 Times in 1,513 Posts	Spoiler Below Truthfully: There is no certain answer until you actually do it. Mathematically: Tuesday's number will be higher, since the raw odds of flipping Tails are greater. Statistically: They'll be equal, since the difference in the odds is negligible. And remember, "I'm-a Luigi, number one!" Last edited by CaptHayfever; 08-24-2009 at 07:48 PM.

08-24-2009, 05:58 PM	#4
Deku Trii PP&R Mod Current Events Mod Join Date: Jun 2000 Location: Texas Gender: Posts: 9,031 Thanks: 521 Thanked 1,099 Times in 583 Posts	Spoiler Below I would think Monday's number would be higher than Tuesdays, because on Tuesday, if you miss the pattern by flipping Head on what would be your third flip, it's already the first in a new Head, Tail, Tail pattern.

08-25-2009, 05:03 PM	#5
I REALLY HATE POKEMON! Goku lives on the Sun Join Date: Jun 2000 Location: California, U.S.A Gender: Posts: 12,717 Thanks: 1,334 Thanked 275 Times in 234 Posts Blog Entries: 1	Spoiler Below I'd have to say the days outcome will be equal. Even though the order is jumbled, there's still a 50% chance every time you flip a coin for it to be either heads or tails.