Jane Street Quantitative Research Intern Technical Phone Screen

45 minutes, two questions, no resume testing. The first question was relatively simple, a classic question that involved playing dice with a casino. Since my impression wasn't very strong, I won't pos

45 minutes, two questions, no resume testing. The first question was relatively simple, a classic question that involved playing dice with a casino. Since my impression wasn't very strong, I won't post it to avoid misleading anyone. Question 2: (The following content requires a score higher than 188. You can already view it.) Let's say A and B both roll a 21-sided die labeled from -10 to 10 on every side. A gets to roll first. The game works as follows: A rolls the die first and gets a value. He may accept or reject it. If he accepts, the game is over, and B pays the value on the die to A. On the other hand, if A rejects, the game shifts to B. B then plays the game exactly as A did. He rolls the die again and sees whether he accepts or rejects. Again, if B accepts, the game is over. If B rejects, the game passes to A again. This continues. So, what are the most optimal strategies for players in this game? (Initially, I didn't have a clear idea and just calculated an expected payoff if both players set the threshold to 0.) Under guidance, I initially learned to lower A's threshold, but I didn't realize that A and B's thresholds would be the same, so the calculations became quite complicated. After realizing this, I lowered both parties' thresholds. Although I didn't finish the calculations, the basic idea was conveyed. Jane Street's results came out quickly; two days later, I was informed of the second interview. Additional content (2025-10-12 11:16 +08:00): Please give me some points!! I'm diligently saving them up 😭