3 Card Poker: Rules of the Popular Three - Card Casino Game

Here are the general rules for a simple three - card game:

I. Preparation

1、Deck: Use a standard deck of 52 playing cards. For each round of the game, only 3 cards are selected from the deck.

II. Gameplay

1、Dealing

- The dealer randomly picks 3 cards from the deck and lays them face - down on the table.

2、Betting (Optional in some versions)

- Players may place bets on the outcome of the game before the cards are shown. Bets can be in the form of money (in gambling - based versions, which might not be legal in all areas) or points (in a more casual, non - gambling version).

3、Revealing and Scoring

- Then, the dealer reveals the 3 cards.

- Different card combinations have different values:

Straight Flush

- If the three cards are of the same suit and in consecutive order (for example, 3 of hearts, 4 of hearts, 5 of hearts), it is the highest - ranking combination. In this case, the probability of getting a straight flush is relatively low. There are only 40 possible straight flushes in a standard 52 - card deck (10 possible straights in each of the 4 suits). When a player gets a straight flush, they usually receive a very high payout in a gambling - based game or a large number of points in a non - gambling version.

Three of a Kind

- All three cards have the same rank (such as three kings). The odds of getting three of a kind are also not very high. There are 52 ways to get the first card, 3 ways to get the second card of the same rank, and 2 ways to get the third card of that rank. So, there are a total of 52 * 3 * 2 / 6 = 52 different three - of - a - kind combinations (we divide by 6 to account for the different orders in which the cards can be picked).

Straight

- The cards are in consecutive order but not of the same suit (for instance, 3 of spades, 4 of clubs, 5 of diamonds). There are more possible straights compared to straight flushes. To calculate the number of possible straights, we consider that there are 10 possible starting ranks for a straight (A - 2 - 3 up to 10 - J - Q). For each starting rank, there are 4 choices for the first card (one in each suit), 4 choices for the second card (again, one in each suit), and 4 choices for the third card. So, there are 10 * 4 * 4 * 4 = 640 possible straights. However, some of these are also straight flushes, so the actual number of unique straights is a bit less.

Flush

- All three cards are of the same suit but not in consecutive order (like 2 of hearts, 5 of hearts, 9 of hearts). The number of ways to get a flush can be calculated as follows. There are 4 suits. For each suit, we need to choose 3 cards out of 13. This can be done using the combination formula C(n, r)=n! / (r!(n - r)!), where n = 13 (number of cards in a suit) and r = 3 (number of cards we are choosing). So, for each suit, there are C(13, 3)=13! / (3!(13 - 3)!) = 286 ways. Since there are 4 suits, there are a total of 4 * 286 = 1144 possible flushes.

Pair

- Two of the three cards have the same rank (for example, two 7s and a different card). To calculate the number of pairs, we first choose the rank for the pair. There are 13 ranks, so there are 13 ways to choose the rank of the pair. For the chosen rank, there are C(4, 2)=6 ways to choose 2 cards out of 4 of that rank. Then, for the third card, there are 48 remaining cards to choose from (52 - 4 of the pair - rank). So, the total number of pairs is 13 * 6 * 48 = 3744.

High Card

- If none of the above combinations are present, the value of the game is determined by the highest - ranking card among the three. For example, if the cards are 2 of clubs, 5 of spades, and 8 of diamonds, the 8 of diamonds is the high card.

In a gambling - based three - card game, winning players receive payouts according to the odds associated with the combination they bet on. In a non - gambling version, players can simply compare their hands for fun or to earn points in a multi - round game.

It should be noted that in many regions, gambling - related three - card games are illegal outside of regulated casino environments. Additionally, in a non - gambling version, this game can be a great way to pass the time at social gatherings or family events. It can also be used as an educational tool to teach probability concepts to students. For example, by calculating the probabilities of different hands, students can gain a better understanding of combinatorics and chance. Moreover, in some cases, this game can be modified to include special rules or bonuses. For instance, if a player gets a "royal" straight flush (10 - J - Q of the same suit), they could receive an extra bonus in either the gambling or non - gambling version. Another modification could be to introduce a "wild card" concept, where a certain card (for example, a joker if added to the deck) can be used to substitute for any other card to form a better hand. However, these modifications should be clearly defined before starting the game to avoid confusion.