That White seems to have an overwhelming advantage in "Mancala" could be that the "no moves" rule was set backwards. Indeed, I always heard that when one player had no stones left in his side of the board, HE captured all of the opponent's pieces. In other word, it is of the player's responsibility to ensure that the opponent can always move.

I wikied Mancala, and although it is a wide game family, the rules played here seem to be the rules of "Oware" (http://en.wikipedia.org/wiki/Oware) . Here is the part of the rules that deal about having no moves :

<quote>
The proscription against capturing all an opponent's seeds is related to a more general idea, that one ought to make a move that allows the opponent to continue playing. If an opponent's houses are all empty, the current player must make a move that gives the opponent seeds. If no such move is possible, the current player captures all seeds in his/her own territory, ending the game.
</quote>

Not the most enlightening way to write it, but I think it means that the remaining seeds are due to the player who finds himself without a move.