Results from studies on risk taking behavior suggest that people tend to be risk seeking when making choices over lotteries that involve longshots: small probabilities of winning sizable payoffs. To investigate preferences over longshots systematically, we conduct an incentivized experiment using state lotteries in China, each involving a single prize and fixed winning odds. This enables our construction of single-prize lotteries involving winning odds between 10-5 and 10-1 and winning prizes ranging from RMB10 (about USD1.60) to RMB10,000,000 (about USD1.60 million) across different expected payoffs. For lotteries with expected payoffs of 1 and 10, subjects exhibit heterogeneous preferences for longshots: some prefer the smallest winning probability whereas others favor intermediate winning probabilities. As the expected payoff increases to 100, subjects become predominantly risk averse, even for the lowest winning probability of 10-5. Our findings pose challenges for utility models of decision making under risk.