Assume two players play against each other, and assume the initial number the game start with is 1. Each turn a player can add 1 or add 2 or multiply by 2.
Goal: The winner is the player who reaches the number T (and above).
Is there a global winning strategy for a random number T?
When trying to solve private examples the strategy seems to change each time, for example when T=100 or T=103.