The game has two players, the player (me) and the dealer. The player starts by rolling a 10-sided die. You roll the die as many times as you want adding all your rolls, your goal is to get as close to 21 as possible. If you go over 21 you lose automatically. Once you have rolled the die and decided to stop (and the sum is below 21), the dealer does the same process. If the dealer gets a sum less than or equal to 21 but larger than yours, you get nothing. Otherwise you win. What is the optimal strategy?
My probability is terrible and I have no idea how to tackle this. Any advice would be appreciated.
Two key points: The dealer knows your total and uses it strategically. A tie is considered a win.