You're playing a number guessing game with 100 people

You have to pick a number between 1 and 50 000, then the average number will be taken. You get 10 minutes to discuss the strategy with other players, you are not allowed to communicate when guessing.

The win conditions are:
- Your number is 2x lower or 3x higher than the average
- Nobody else has picked the same number
- The number has to be within 1-50 000 range as mentioned previously, any other number will be invalid

If you win, you get as much money (in american dollars) as the number you've choosen. If you lose, you get nothing.

What number do you pick? Would you try to gaslight other players to increase your odds? That is if you can persuade them in the first place.