Jack has challenged you to play a card game with him. The idea of the game is that a player gets a random card and after seeing it it's placed back in the deck. The player may get as many cards as he/she wants and the sum of the values of these cards represents the points this player got. However if the player gets an ace he/she gets zero points as total and the other player may try. How should one play this game (how many cards should be picked) for maximum chance of winning against Jack?
Face cards can be interpreted so that king is 13 points, queen is 12 points and jack is 11 points.
jack and I should play a set of games towards a predefined
amount of points, say 500. Each game will start by a player
who was second in the previous game, first game beginner
being decided by tossing a coin.