Telling everyone else you're going to pick 1 and then picking 1 feels like kind of an optimal strategy to the last round of game 2. You're essentially in a situation where the only way you can lose is if another player actively chooses to pick 1 thereby giving up their chance at the cash solely to make sure you don't win, and we know people are selfish. They either think you're bluffing and wont pick 1 and know that everyone else also believes this and are likely to pick 1 therefore won't pick 1, or that you aren't bluffing and pick something other than 1 hoping that someone will pick 1 and negate you making their number a better choice. You get less but seem more likely to win.