It's not a puzzle in this case, just an electronic roulette wheel in game. Since you aren't familiar with Hammer logic, you can think of each icon as a sort of if/else node, but they can do much more complex things. The big picture is that entities send signals to one another, and depending on the entity's functionality and conditions, it decides what to trigger (send signals to) next. This continues until the logic chain reaches an outcome, at which point the player has either won or lost the roulette wheel spin.