Being hot vs being due

[RydenStoompala]

You left out "3. Kill Yourself. You're flipping coins for even money all day so your life is over."

[ThinkQuick]

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Tails. It doesn't really matter, but the slight chance of it being favored towards tails would make me lean towards it.

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Agreed. There is a nonzero chance that the results are due to the coin being biased to land tails. Let that work with you.

note that this has nothing to do with runnning hot or being due..

[AlanBostick]

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I'm still amazed that people are actually are sticking with heads more than switching to tails. The chances that this coin is perfectly fair is growing smaller and smaller and it is much more likely that the coin is biased toward tails.

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Go read the problem as posed again:

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Suppose you and your friend are flipping a quarter for $10 a pop for a day. You win on heads. He wins for tails.

Somewhere in the middle, you find yourself down $160 and tails has landed 7 of the last 8 times and your friend offers you to switch to tails.

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You're tossing coins all day. Let's say you started at 9:00 AM, toss once each minute, and are continuing until 5:00 PM.


"Somewhere in the middle," i.e. around 1:00 or 2:00 PM, i.e. after three hundred tosses or so, you're stuck $160 -- that is, tails have come up 16 more times than heads has, and that the last seven tosses have been tails.

After three hundred tosses, you expect heads to have come up 150 +/- 8.7 times. Being behind by 16 tosses at midday is a two-sigma event. But note that you had just tossed tails seven times in a row. Just before that run, you had only been behind by nine tosses -- just slightly more than a one-sigma event. And a run of seven tails in a row is not terribly unlikely, with odds of just 127:1 against.

The OP doesn't specify how often the coin is tossed. If you tossed every second, rather than every minute, by 1:00 PM you would have tossed the coin 14,400 times, and would expect to see heads 7,200 +/- 60 times. Being sixteen tosses behind is well within expected results and you would also expect to have seen a number of long runs of tails and long runs of heads, and there would be no reason to even begin to suspect that the coin is biased.

[MTBlue]

If this a unbiased random event, then your odds on future tosses are not affected by switching to tails. (Tails=Heads)

If this is a biased event i.e. Tails>Heads or Heads>Tails then switching to tails is the right choice. The chances are greater at this point that the coin is biased toward Tails instead of heads. It is possible that the event is biased toward heads just more unlikely.

There are two scenarios biased and unbiased. Biased P(T)>.5 > P(T)<.5. Unbiased P(T)=.5. Compared to heads where the Biased P(H)<.5 > P(H)>.5. Unbiased P(H)=.5

Unbiased scenarion the switch is inconsequential to the results. In the biased example the switch makes sense.

[ThinkQuick]

I appreciate your analysis demonstrating that there may be no difference between the game coin and a fair coin.

And it isn't even the run of tails which would have me switch, although this event does allow for the possibility that something recently happened to the coin.

Here is what I am saying,

We must assume there is some (albeit small) chance of the coin being weighted
There are 3 possibilities:

a) the coin is weighted towards tails
b) the coin is fair
c) the coin is weighted towards heads

You are offered a one time opportunity to switch mid-day

If the coin is weighted to tails and you switch to tails, you gain expectation
If the coin is fair and you switch, nothing changes
if the coin is weighted to heads and you switch to tails, you lose


You are down 16 flips after 14k flips. We cannot prove that the coin is weighted but this insignificant but nonzero tails-favoring demonstrates that if it is weighted, it is more likely weighted to tails. If you were down 1 flip after 14k flips then the odds of a being true would still be greater than the odds of c being true. Therefore switch.

I can see no argument for staying. By the law of large numbers (law of averages), if the coin is fair you will still be down about 16 flips at the end of the day. But if it isn't fair... take advantage of that small possibility by switching.

[AKQJ10]

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the correct answer (if it's possible that the coin is not fair) is switch to tails, because you have slightly more evidence that the coin is biased toward tails than toward heads.

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True, unless you suspect your friend of selectively unbalancing the coin. Then you'd be foolish to switch, because he offered you the switch, which must mean he's confident he can switch it back.

Other than subtleties of cheating at coin-flipping, this topic is a waste of disk space.

[NLSoldier]

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In this particular scenario, my first instinct is definitely to stick with what's due for whatever reason. That doesn't go across the board though, again, for whatever reason. Sometimes momentum outweighs being due. Not often, but sometimes.

GoT

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[NLSoldier]

GOT and HomieHomie,

obviously these guys arent asian and will never understand.

gamb000000l,
nl

What the hell is "momentum" in coin tossing. Please. I'm asian by the way, and I still know that on a fair coin, staying or switching still gives you the same odds :P

[uncleshady]

This question is why that "history board" is up next to most Bacarrat tables in Vegas.