Blackjack

State and action spaces

The Vec<u32> state is [player_sum, dealer_showing, usable_ace] in MultiDiscrete([32,11,2]). Actions are 0 = stick and 1 = hit. Cards are drawn uniformly from the infinite-deck table [A,2,...,9,10,J,Q,K], where all face cards count as 10.

Dynamics and reward

A usable ace contributes 11 when doing so keeps the hand at or below 21. On hit, draw \(c\sim\text{Deck}\), append it, and return reward \(-1\) if the player busts or \(0\) otherwise. On stick, the dealer draws until its sum is at least 17, then

\[ r=\operatorname{sign}(\operatorname{score}_{player}-\operatorname{score}_{dealer}). \]

With sab, a player natural against a non-natural dealer is an outright \(+1\). Otherwise, when natural is enabled, a natural that already wins pays \(+1.5\).

Episode end

The episode terminates when a hit busts the player or immediately after stick. It never truncates.

Configuration

Info is (). Reference: Gymnasium Blackjack.