Duplicator has no available move, so she loses. Nguyen notes that in this particular game, Duplicator could have won if Spoiler had not made the best possible move in the first round. For example, if Spoiler had instead selected the fourth digit, there would be sequences of moves that would give Duplicator the victory. To analyze the game, Nguyen assumed that each player always makes the best possible move. Then, examining the key characteristics of all possible sequences, she found that a given sequence belongs to one of 78 distinct families, or equivalence classes.
Duplicator can always win if the both sequences in a given game belong to the same class.
It turns out, for example, that two equivalent sequences must have the same first digit and the same last digit. If the first digits of the two sequences are different, Spoiler wins the game. Future research could extend this analysis to Ehrenfeucht games having more than two rounds or more than two sequences. Nguyen's work is one manifestation of her longstanding love for rigorous and creative mathematical proofs. Because of her fascination with the idea of gathering economic data through statistical sampling and modeling human behavior through mathematical economics, she studied game theory and statistics at the Harvard Summer School.