It's a lot better than that surely?
Six four times in a row is (1/6)^4 = 0.0008 ish.
If he's got three boxes (win, lose, draw), one of which is a correct prediction and he chooses a box at random he's got a probability of 1/3 of being right. The probability of him being right three out of three times is (1/3)^3 = 0.037 which is a hell of a lot higher.
fake edit: It looks like he's only got two boxes, so (1/2)^3 = 0.125 if we're ignoring draws, which are pretty good odds.
Since he's a German octopus in Germany I'm assuming he's only predicting games for the Germans. If he was predicting all of them you'd expect him to be correct for more than one out of thirty-two teams.