Advent calendar 2019
The final round of game show starts with £1,000,000. You and your opponent take it in turn to take any value between £1 and £900. At the end of the round, whoever takes the final pound gets to take the money they have collected home, while the other player leaves with nothing.
You get to take an amount first. How much money should you take to be certain that you will not go home with nothing?