completing them". Sports wagering is legal in only a few US locales that typically also allow other forms of gambling—Las Vegas for instance. Gambling laws, which are predominantly written at the State level, continue to evolve in the US. The degree to which 'chance', 'randomness' or 'luck' factors into the determination of legality varies significantly between the states and around the world. A distinguishing difference between unique bid auctions and traditional lotteries, games of chance, and sporting events (gambling) is the absence of an external randomizing device. All cards games, lotteries, raffles and mechanical games typically found in casinos utilize an exogenous device to introduce chance into the game. In card games it is the deck of cards. Lotteries use randomly selected numbers while raffles rely on randomly selected tickets or markers to select the winner. Table games in casinos use dice. In sporting events, the participants in the competition (football players for instance) represent the element of chance since their behavior is outside the control of those wagering on the outcome. In a unique bid auction, there is no external device that introduces chance or randomness. The outcome of the auction, while not controlled exclusively by one player, is controlled exclusively by the collective group of players wagering on the outcome. And only those participating in the game can wager on the outcome. Receiving a reward of some kind The unique bid auction model's attractiveness is the possibility of obtaining an item at significantly lower cost than the retail price. Mathematical analysis The theory of unique bid auctions has been the subject of mathematical investigation. In a 2007 paper Bruss, Louchard and Ward proposed a technique for calculating game-theoretic probabilistic optimal strategies for unique bid auctions, given a small set of extra assumptions about the nature of the auction. Another paper by Raviv and Virag in the same year made theoretical predictions and compared their results to the results of real-world unique bid auctions. Another paper by Rapoport et al. compared theoretical results to the results of experimental auctions. Further work by Bruss et al. and a number of other researchers including Gallice, and Rapoport and Otsubo has continued to develop the theory on this subject. In a 2012 study Pigolotti et al. conducted a thorough study of the unique bid auction in the grand canonical ensemble, finding a theoretical expression for the Nash equilibrium distribution and showing that