CARD COUNTING IN CONTINUOUS TIME

• We consider the problem of finding an optimal betting strategy for a house-banked casino card game that is played for several coups before reshuffling. The sampling without replacement makes it possible to take advantage of the changes in the expected value as the deck is depleted, making large bets when the game is advantageous. Using such a strategy, which is easy to implement, is known as card counting. We consider the case of a large number of decks, making an approximation to continuous time possible. A limit law of the return process is found and the optimal card counting strategy is derived. This continuous-time strategy is shown to be a natural analog of the discrete-time strategy where the so-called effects of removal are replaced by the infinitesimal generator of the card process.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

Sampling without replacement

invariance principle

gambling theory

optimal control

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)