We consider binary private contributions to public good projects that succeed when the number of contributors exceeds a threshold. We show that for standard distributions of contribution costs, valuable threshold public good projects are more likely to succeed when they require more contributors. Raising the success threshold reduces free-riding incentives, and this strategic effect dominates the direct effect. Common intuition that easier projects are more likely to succeed only holds for cost distributions with right tails fatter than Cauchy. Our results suggest government grants can reduce the likelihood that valuable threshold public good projects succeed.