This does it by storing the current table in a variable and using .next()
to find the next table:
var current;
$('.next_round').click(function() {
if(typeof current == 'undefined' || current.next('table').length == 0){
current = $('.board table').first();
} else {
current = current.next('table');
}
$(current).find('td').each(function() {
$(this).css("background-color", setRandomColor);
});
});