# Is Oh Tetris Oh! always a draw?

Alice and Bob were playing Oh-Tetris-Oh!, when they decided that every game must be a draw (played intelligently).

Can you prove this?

(Oh yes, the rules: A $$10\times10$$ grid, you can pick any Tetris piece you like from an infinite pool, into any position fully on the grid with no overlapping. The first player to make a horizontal line wins.)

• Are they only playing to get a draw? If so, then Alice plays only on the left and Bob plays only on the right. It will always end Up in a draw. – Alain Remillard Jan 30 at 3:37
• Do the players have different colours? And if yes, do you need to make a line in your own color? Or is it just enough to make a line without any empty spaces in it, no matter who put which piece? – mihomir Jan 30 at 10:18
• @mihomir; Orignally, it was the second one. But having your own colour makes sense, and also I suppose easier to prove it's always a draw. – JMP Jan 30 at 10:26