How about Mini Chess? The rules are the same as standard chess (though I think I've seen a version where the pawns can't move 2 places at once when on first row) it's just the board that's smaller.
Anyway, should provide some faster games and I'm sure many begginers would be more inclined to play this smaller version.
And from my limited experience it's a good battle ground to train on How-to-avoid-a-stalemate-when-you-have-a-sure-win kind of games :)
(esconder) Jogue um jogo em tempo real com um adversário que esteja online. Para o conseguir ambos devem seleccionar a opção "Jogar e ficar nesta página" como opção por defeito e depois refrescar a página com a tecla F5! (TeamBundy) (mostrar todas as dicas)