[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.