Interview Question for Trader at Jane Street Capital:

I choose 7 because if you pick say 6, the closest digit with lower value than 7 (meaning greater range of winning numbers), I get from [7,12], but you only get from [2,6]. And if I choose 7 and you choose say 8, the closest digit with higher value than 8, I get from [2,7], but you only get from [8,12]. Therefore, if I pick 7 I always have a greater chance of being closer to the correct number.

the EV of rolling a dice is 3.5, so if you roll a dice twice the number with a greater chance is 7