In various types of multi-state card games, such as but not limited to blackjack and baccarat, a player competes against an opponent. For purposes of example, the player may be human and the opponent may be a dealer who plays on behalf of a “house” (e.g., a game provider such as a casino). These card games are typically played in hands, where each hand involves an initial number of cards being dealt from a deck to each participant. The cards that each participant holds during a hand may be referred to as the participant's hand, and cards may be added to or taken away from each participant's hand during the course of the hand.
The popularity of such card games is based in part on the strategy involved in playing the game, as well as the player being able to risk money or some other form of currency on the outcome of each hand. The possibility of gain and the risk of loss tend to make these games exciting and enjoyable. Nonetheless, for each type of multi-state card game, there are certain combinations of cards that result in a weak hand. When dealt such a hand, more often than not the player will lose to his or her opponent. Being dealt a weak hand reduces the player's level of excitement, as the player's optimal strategy may be to minimize losses rather than to maximize gains. The house that provides a card game usually expects a marginal profit for each hand played. Since exciting card games tend to encourage repeat play, the house profit is likely increased when the overall excitement level of a card game is enhanced.