You want something that is perceived to be fair in order to minimize the chances of someone deciding he'd rather get nothing than 2 points. If I were in the cl

You want something that is perceived to be fair in order to minimize the chances of someone deciding he'd rather get nothing than 2 points. If I were in the class I'd propose a weighted lottery where everyone had a chance to be one of the sixes but those with worse grades had a somewhat better chance. While there might be disgruntlement over the weight, I'd guess it'd be less severe than if someone that an entire fairness factor was being ignored. An interesting questions would be what to do if someone issued an ultimatum to the group "give me one of the sixes or I will ruin it for everyone". I'd think in that case every move ends with no one getting any points.