new_bot_game starts a game against the bot at the chosen level and ends the
search for an opponent. BotPlayer works out the bot's moves on its own thread
pool and plays them on the game loop after the previous move's animation and a
thinking time. Bot games keep their settings across restarts.
Negamax with alpha-beta on Position scores every move; the strength sets the
depth, the softmax temperature and the chance of a random move. The levels
are ranges of strengths drawn per game. A calibration tournament checks that
each level beats the one below.
