Something else to add: this was all assuming a night 1 setting. The 14 in the inequality comes from a new player randomly jailing one of the 14 other players. That 14 will be set to the number of players remaining in the game minus 1. Additionally as the game goes on, gamma decreases as the utility you get from a kidnapper thinking your scum is much less if he's already used his execute - both of these factors make remaining silent in jail on nights 2+ THAT much more difficult to justify.