Putting our spin on the dreidl

It doesn't take a great genius to realize that the dreidl probably did not originate, per the myth, with Jewish children in Hasmonean times trying to disguise the fact that they were learning Torah. But where does it actually come from? I'd previously never really thought about it, but learned today that it was in fact a popular game in Europe, and especially Germany, in the 16th century -- particularly around Christmas time (aha!). As this site explains, the word 'dreidl' itself is derived from the German word drehen, which means to spin (the explanation I had today, which I don't have to hand , connected it to another German word as well -- will try and update this tomorrow).
So far, so unsurprising. I was intrigued to discover, however, that not only is the game itself Germanic in origin, but that the letters on the dreidl come directly from the German as well:

The letters on the faces of the gambling toy, which were mnemonic for the rules of the game, varied in each nation. The letters on the English spinning top were: T for Take, H for Half, P for Put, N for None. In the German game, the letters were: N for Nichts (nothing), G for Ganz (all), H for Halb (half), S for Stell (put). The Hebrew letters on the dreidel seem to have come directly from the German gambling toy: Nun for Nichts (nothing), Gimel for Ganz (all), Hay for Halb (half), Shin for Stell (put). In an effort to link the game to the celebration of Hanukkah, the Hebrew letters nun, gimel, hay and shin were said to stand for the phrase Nes Gadol Haya Sham, which means "a great miracle happened there."

Also interesting because I had always assumed that 'nun-gimmel-hay-pay' was the real thing and that our diaspora 'nun-gimmel-hay-shin' was the poor cousin....