2 Teams Good, 8 Legs Better

Paul the Octopus has been causing quite a stir in the press, having correctly predicted the outcome of all of Germany's World Cup games. I've been doing a bit of thinking and I don't think it's as unlikely as it seems - in fact I believe the odds may be as low as 1/10.

Although in each group game the probability of him picking the winner is 1/3 (although Paul wasn't (as far as I know) given the opportunity to pick a draw, the possibility of there being a draw still remained), and each knockout game the probability is 2/1, that doesn't mean that the probability of Paul guessing all the games correctly so far is 1/3 x 1/3 x 1/3 x 1/2 x 1/2 x 1/2, because the possibility of Paul picking the winner of one game relies on him getting the previous guess correct. So, for example, if he had guessed the result of the 1st knockout game wrongly, he wouldn't have got the chance to guess the winner of the Quarter-Final. So the options of what he could have done are (what Paul actually did is in bold):

Guessed first game correctly
Guessed first game wrongly (Germany Lose)
Guessed first game wrongly (Germany Draw)
Guessed 2 correctly
Guessed first correctly, second wrongly (Germany Win)
Guessed first correctly, second wrongly (Germany Draw)
Guessed 3 correctly
Guessed 2 games correctly, third wrongly (Germany Lose)
Guessed 2 games correctly, third wrongly (Germany Draw)
Guessed 4 correctly
Guessed 3 correctly, fourth wrongly
Guessed 5 correctly
Guessed 4 correctly, fifth wrongly
Guessed 6 correctly
Guessed 5 correctly, sixth wrongly

So he has had 6 outcomes from a possible 15. At first, I thought that 6/15, or 2/5, were the odds, but if at any point Paul has got all his guesses right, he will guess the forthcoming game, so any previous outcome involving him getting them all right can be discarded. This leaves:

Guessed first game wrongly (Germany Lose)
Guessed first game wrongly (Germany Draw)
Guessed first correctly, second wrongly (Germany Win)
Guessed first correctly, second wrongly (Germany Draw)
Guessed 2 correctly, third wrongly (Germany Lose)
Guessed 2 correctly, third wrongly (Germany Draw)
Guessed 3 correctly, fourth wrongly
Guessed 4 correctly, fifth wrongly
Guessed 5 correctly, sixth wrongly
Guessed all six games correctly

Which gives us 1 in 10. Am I barking up the wrong tree here?