Coin Flipping Poll

[Oldandeasilyconfused]

statistically, there isn't a difference.

Yes.


The chance on every toss is 50/50. With a large sample the results will be even. There are no real patterns.

That comes from Business Statistics, which I did in 1972. I might have misremembered.

[Violet]

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Since both begin with TH, we'll assume we already have that and we're about to flip the coin for the xth amount of time.

If we want THH, we flip the coin. If it is heads we have THH and we're done. But, if it tails we have the beginning tails in the our sequence of THH, which means we need to flip two consecutive heads.

If we want THT, we flip the coin. If it is tails we got our match, but if it is heads we have to start over and need to flip 3 more coins to try to get THT.

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Oh... well now I feel like a moron...

But then: I always feel like that!

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The question wasn't "which sequence done once takes fewer" (that would be 50/50).

It is "which is statistically more common should this continue?"

I have now learned to recognize the difference... : o I have learned something this otherwise blissfully ignorant day >_<

[Tiberius]

Well, 14 of you voted. 11 got it wrong, and only 2 got it right (with 1 person not wanting to guess).

The answer is actually that Tails, Heads, Heads comes up with fewer tosses on average. The reasoning is quite easy, but first you need to understand what the question is asking. The question wasn't "Which result requires fewer tosses if you only have 3 tosses" as some people seem to have thought. In that case, the 11 would be correct. If you have only 3 tosses, then all combinations of the 3 tosses (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT) are equally likely of coming up, so THH and THT both have an equal chance (1/8th) of coming up.

However, the question was asking on average, which pattern took the fewest tosses to appear. That means, that if you toss three coins and get HTH, you haven't got either pattern yet and must continue flipping. The same goes for the other 5 patterns that don't equal either THH or THT.

Since we are moving from left to right, we should be able to deduce that both patterns start with TH. This is the common factor between them, and it turns out to be very important. To answer the question, it is necessary to see what happens when each pattern is struck with failure.

If we assume that the first and second coins flipped were T and H respectively, then both patterns have 2/3 completion. Something statistically significant happens on the next flip though:

If the third flip is a H, then the THH pattern has been found, and we have to flip at least 3 more times to get a THT pattern.
If the third flip is a T, then the THT pattern has been found, and we have to flip at least 2 more times to get a THH pattern.

The THH pattern has a better chance of coming up because it doesn't overlap itself. A failure for the THT pattern means you have to start all over again, whilst a failure for the THH pattern means you already have the first T and so only need two more flips.

In order to show this in an objective way, I wrote a piece of code: http://pastebin.com/cjkeMnhg

It plays the game 10,000 times (to get a nice sample size), each time flipping 3 coins to start, and then continually flipping until both patterns are found. The average for each pattern is averaged and displayed as the result:

THH found after an average of 8.0015 (~8) flips.
THT found after an average of 10.0362 (~10) flips.

It doesn't stop there though. You can try it with other patterns, and it doesn't matter how big your patterns get, a T followed by a string of H will always come up with fewer tosses on average than the same length alternating pattern:

THHH found after an average of 16.035 (~16) flips.
THTH found after an average of 20.0729 (~20) flips.

THHHH found after an average of 31.6734 (~32) flips.
THTHT found after an average of 41.9732 (~42) flips.

THHHHH found after an average of 62.9272 (~63) flips.
THTHTH found after an average of 82.5089 (~83) flips.

THHHHHH found after an average of 129.6385 (~130) flips.
THTHTHT found after an average of 169.5909 (~170) flips.

Statistics is fun! Points go to Paul the Human for the correct answer, and double points go to Zhalentine for posting a solution

Better luck next time everyone else!

[Paul the Human]

WoO!

*collects his winnings*

Which way is the Blackjack table?

[fr0d0]

1 minus point to Adrian for swearing in the post title. Gilligan will be along shortly to issue you with your 'threat'.

[Violet]

1 minus point to Adrian for swearing in the post title. Gilligan will be along shortly to issue you with your 'threat'.

Fuck fuck fuckity fuck.

Can I be threatened too now?