The Welsh tafl game Tawlbyund or tawl bwrdd is thought by many scholars to have obtained its name meaning "throwing board" specifically because it most often was played with dice. Linguistically this makes sense but evidence is otherwise scarce. The game was definitely played on an 11x11 grid and a diceless version is described at http://www.gamecabinet.com/history/Hnef.html. The dice if used would as noted above either have determined if a player got to take a turn or how far he could move a piece.