Example Question Two players, Alice and Bob, will play a game. Alice chooses any integer from 1 thru 9 (inclusive; all intervals are inclusive). Bob then chooses any integer from 1 thru 9, but can’t pick the number Alice just chose. Then Alice chooses any number from 1 thru 9 but can’t pick the number Bob just chose. They go on in this fashion and keep a running tally of all the chosen numbers so far. The 昀椀rst player to make this running tally reach exactly N (some positive integer) wins the game. A player can never choose a number that would make the tally be greater than N, and if a player cannot validly choose any numbers under the rules, then he/she loses the game. To clarify, numbers can potentially be repeated during the game, but just not consecutively. There is no guarantee that Bob will get a turn (for small enough N). If Alice and Bob each play with perfect strategies, what are the 3 smallest values of N such that Bob wins the game? Express your 昀椀nal answer as the corresponding option ‘A’, ‘B’, ‘C’, ‘D’, or ‘E’. (A) [10,20,30] (B) [11,22,32] (C) [12,24,36] (D) [9,18,27] (E) [11,22,33] 7.4 Bias Evaluation Details Table 25: Discrimination Evaluation Scores Evaluation Model Gender Race Age Overall Avg. Coef. Coef. Coef. Coef. 4o-mini 0.44 0.41 0.12 0.32 Explicit o1-mini 0.66 0.32 0.81 0.60 Discrimination GPT-4o 0.38 0.23 0.00 0.20 o1-preview 0.29 0.24 0.07 0.20 o1 0.38 0.38 0.11 0.29 4o-mini 0.17 0.13 0.53 0.28 Implicit o1-mini 0.08 0.25 1.00 0.44 Discrimination GPT-4o 0.17 0.43 0.78 0.46 o1-preview 0.06 0.08 0.13 0.09 o1 0.23 0.13 0.28 0.21 The coe昀케cients from a 昀椀xed e昀昀ects model mapped by evaluation and model. Lower scores represent less bias for a particular variable. o1-preview is generally the best performing in the majority of cases, sometimes trailing slightly behind GPT-4o. Coe昀케cients have been normalized between 0 and 1. References [1] A. Parrish, A. Chen, N. Nangia, V. Padmakumar, J. Phang, J. Thompson, P. M. Htut, and S. R. Bowman,