Highest winning odds: Blackjack.

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How to Play Blackjack
Although scenes of 21 are common in various movies, it is a game that is only popular in casinos and not widely played. Let's first introduce how to play 21.

This game is divided into a banker and two players. Usually, the banker simultaneously deals with 5 to 7 players who are fighting on a semi-circular table. The equipment used is multiple decks of poker cards with the jokers removed. The players' goal is to have a higher total point value of cards than the banker without exceeding 21 points (going "bust"). Face cards are worth 10 points, and Aces can be counted as either 11 points or 1 point.

In the first round, both the player and the banker receive two initial cards, with one card face up and one card face down. In each subsequent round, players can choose to:

1. Hit: Take one more card.
2. Stand: End the turn without taking another card.
3. Double: Double the bet and take one more card (if allowed).
4. Split: If the player's initial two cards are of the same rank, they can be split into two separate hands. The player places an additional bet equal to the original bet, and two more cards are dealt, effectively playing two separate games.
5. Surrender: Forfeit the round, losing half of the bet, and start the next round.

The three matrices provided above cover almost all possible scenarios that can occur during the game. The top row of the horizontal axis represents the banker's initial card's point value (T stands for 10 points). The leftmost column of the first matrix represents the player's current hand point total, referred to as "Hard" (meaning that Aces are counted as 1 point, if present). The leftmost columns of the other two matrices represent the two initial cards held by the player.

The remaining elements in the matrices indicate the best possible move for the player in each situation. H denotes Hit, S denotes Stand, P denotes Split, D denotes Double (if allowed), and Ds denotes Double (if allowed, otherwise Stand).

By carefully analyzing these matrices, many strategies for taking additional cards can be understood with some thought. There are also some interesting points, such as when the player has a total of 12 points, and the dealer's initial card is 2 or 3, the best move is to Hit, but when the dealer's initial card is higher, the player should Stand.

The reason for this is based on probability. Let's take a look at the probability of the player winning when they Stand with a 12-point hand. If the dealer starts drawing cards and stops when their total is 17 or higher, then the player can only win if the dealer busts.

For example, when the dealer's initial card is 2, the probability that they will bust is calculated. The dealer's hand can start from H2, and it is straightforward to calculate the probability of reaching H3 (getting an Ace) and then busting:

F(H3) = 1/13 × F(H2) = 0.07692

Similar calculations can be performed for H4 to H21, taking into account the possibility of treating an Ace as 11 points. When the dealer's hand total is H5, there is a different situation because an Ace can be counted as 11 points without busting. In this case, Aces are counted as 11 points, so the probability of the dealer busting is not straightforward to calculate. The most straightforward way to calculate it is to consider all possible dealer hand totals and the likelihood of busting in each case.

For example, when the dealer's hand total is H5, the dealer can bust in several ways. They can start with H2 and draw a 3 or an Ace. If they start with H3 and draw a 2 or an Ace, they can also bust. And so on, until they start with H5 and draw an Ace. The probabilities of these different scenarios must be added up to calculate the overall probability of the dealer busting. This can be a complex calculation, and the result will depend on the rules used in the specific version of the game.

Overall, the game of 21 involves a combination of strategy and probability. Players must make decisions based on the information available to them and the likely outcomes of different actions. While the basic rules of the game are straightforward, mastering the optimal strategy for every possible situation can be a challenging and rewarding endeavor.

Samiksha

"I have always been interested in blackjack."

Kahn332

"Because of this article, I have gained a better understanding of blackjack."