I think that 10^60 is a gross underestimation of the size of the game tree of Scrabble. If we account for exchanging tiles and passes, then each player has 128 or 2^7 options of what to do a turn without even playing a tile on the board. We can alternate doing this for 5 turns each time until one player plays a tile (2 on the first move of the game) and then repeat. Because there are 100 tiles in the bag, there will be ~98 or so repetitions of this and we'll end up with ~490 or so moves. Each moves has a 2^7 (assuming all tiles are different, which is not the case, but for our purposes let's assume this). (2^7)^490 = 2^3430 ~= 10^1000 (which is considerably larger than 10^60). yes, we are making the assumption that the tiles on the racks are unique to come up with the 2^7 number, but notice that we haven't even taken into consideration the geometry of the board at all.
I believe that Scrabble has a game tree complexity significantly greater than 10^60. --- In [email protected], Graham Toal <gt...@...> wrote: > > The *exact* number is impossible to calculate; it would have to be > enumerated - and it's so large that that isn't possible either! > > However an estimate would be around 10^60. > > Russell Honeybun is the expert in this area and should be able to give > you a derivation of the above estimate. If he's not on this list, try > wordgame-programmers which is where I saw him last. > > > Graham > > > On Thu, Feb 26, 2009 at 7:14 AM, allstrugglewithin <pookp...@...> wrote: > > I just search wikipedia and it seems like 'Go' has the most total > > number of possible games that can be played. > > > > But wikipedia doesn't say anything about Scrabble, so if someone knows > > the exact number, please tell me. >
