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PENNIES, Monday, May 14, 2001

I believe the solution given is incorrect.  For the HHT case, O has already won the game after the 2nd flip with HH.  Thus, X will never win with HHT because the game has already concluded.

Phatib
Thursday, March 04, 2004

Yes I agree.

So what is the correct solution?

Manish Joshi
Friday, March 12, 2004

Flipping isn't finished once someone wins.  It just gives that person one win.  The game continues...

Michael Pryor
Fog Creek Software
Friday, March 12, 2004

O needs HH, X needs HT.

The win combinations of both start with "H". Both have the same chance to get a H. So one of them may throw:

O or X: ...TTTH

If this is O, he needs a H to win, if this is X, he needs a T. Again, both are equally likely. Both players have a fifty percent chance to win next round. No advantage for anyone YET. Now assume that a player DOESN'T win this time. For O and X, this looks differently:

O: ...TTTHT
X: ...TTTHH

X has a fifty percent chance to win the next round, but O can't win next round, because first he needs another H. This situation is equally likely for both players, and now X has a clear advantage.

Vigor
Monday, April 05, 2004

I agree with Vigor's explanation. It's the solution I came up with as well. The whole explanation using the 3 turn game confused me and I am still not sure if it is correct.

Manish Joshi
Thursday, April 08, 2004

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