Reprinted with permission from Quanta Magazine's Abstractions blog. In the 1950s, four mathematically minded U.S. Army soldiers used primitive electronic calculators to work out the optimal strategy for playing blackjack. Their results, later published in the Journal of the American Statistical Association, detailed the best decision a player could make for every situation encountered in the game. Yet that strategy--which would evolve into what gamblers call "the book"--did not guarantee a player would win. Blackjack, along with solitaire, checkers, or any number of other games, has a ceiling on the percentage of games in which players can expect to triumph, even if they play the absolute best that the game can be played.