Blackjack 21+3 Combinations

We first present the probabilities attached to card dealing and initial predictions. In making this calculus, circumstantial information such as fraudulent dealing is not taken into account (as in all situations corresponding to card games). All probabilities are calculated for cases using one or two decks of cards. Let us look at the probabilities for a favorable initial hand (the first two cards dealt) to be achieved. The total number of possible combinations for each of the two cards is C(52, 2) = 1326, for the 1-deck game and C(104, 2)=5356for the 2-deck game.

1. Blackjack 21+3 Combinations Cards
2. Blackjack 21 3 Combinations Worksheets
3. Blackjack 21+3 Combinations Chart
4. Blackjack 21+3 Odds
5. Blackjack 21 3 Combinations Words
6. Blackjack 21+3 Combinations List

Version 1 Version 1 of 21+3 I noticed at the Las Vegas Hilton in April, 2001. The side bet pays based on the player's first two cards and the dealer's up card. If the three cards equal a flush, straight, straight flush, or three of a kind the side bet pays 9 to 1. 21+3 Blackjack is a very popular side bets blackjack variation, invented and patented by Derek J. The game is a combination of blackjack and three card poker, where your first 2 cards and the dealer’s face up card are used to combine a three card hand. 21+3 blackjack rules. The popular 21+3 blackjack side bet is based on the first two cards dealt to the player and the dealer’s face card. You win if the combination of these cards is either: Suited trips (e.g. Three Queen of Diamonds) – 100:1; Straight flush (e.g. Jack, Queen, and King of Diamonds) – 40:1.

Probability of obtaining a natural blackjack isP= 8/663 = 1.20663% in the case of a 1-deck game andP = 16/1339 = 1.19492%in the case of a 2-deck game.

Probability of obtaining a blackjack from the first two cards isP= 32/663 = 4.82654%in the case of a 1-deck game andP = 64/1339= 4.77968%in the case of a 2-deck game.

Similarly, we can calculate the following probabilities:

Probability of obtaining 20 points from the first two cards isP = 68/663 = 10.25641% in the case of a 1-deck game andP= 140/1339 = 10.45556%in the case of a 2-deck game.

Blackjack 21+3 Combinations Cards

Probability of obtaining 19 points from the first two cards isP = 40/663 = 6.03318%in the case of a 1-deck game andP = 80/1339 = 5.97460%in the case of a 2-deck game.

Probability of obtaining 18 points from the first two cards isP= 43/663 = 6.48567%in the case of a 1-deck game andP= 87/1339 = 6.4973% in the case of a 2-deck game.

Probability of getting 17 points from the first two cards isP= 16/221 = 7.23981%in the case of a 1-deck game andP= 96/1339 = 7.16952%in the case of a 2-deck game.

A good initial hand (which you can stay with) could be a blackjack or a hand of 20, 19 or 18 points. The probability of obtaining such a hand is calculated by totaling the corresponding probabilities calculated above: P = 32/663 + 68/663 + 40/663 + 43/663 = 183/663, in the case of a 1-deck game and P = 64/1339 + 140/1339 + 80/1339 + 87/1339 = 371/1339, in the case of a 2-deck game.

Probability of obtaining a good initial hand isP= 183/663 = 27.60180%in the case of a 1-deck game andP= 371/1339 = 27.70724%in the case of a 2-deck game.

The probabilities of events predicted during the game are calculated on the basis of the played cards (the cards showing) from a certain moment. This requires counting certain favorable cards showing for the dealer and for the other players, as well as in your own hand. Any blackjack strategy is based on counting the cards played. Unlike a baccarat game, where a maximum of three cards are played for each player, at blackjack many cards could be played at a certain moment, especially when many players are at the table. Thus, both following and memorizing certain cards require some ability and prior training on the player’s part. Card counting techniques cannot however be applied in online blackjack.

The formula of probability for obtaining a certain favorable value is similar to that for baccarat and depends on the number of decks of cards used. If we denote by x a favorable value, by nx the number of cards showing with the value x (from your hand, the hands of the other players and the face up card in the dealer’s hand) and by nv the total number of cards showing, then the probability of the next card from the deck (the one you receive if you ask for an additional card) having the value x is:

This formula holds for the case of a 1-deck game. In the case of a 2-deck game, the probability is:

Blackjack 21 3 Combinations Worksheets

Generally speaking, if playing with m decks, the probability of obtaining a card with the value x is:

Example of application of the formula: Assume play with one deck, you are the only player at table, you hold Q, 2, 4, A (total value 17) and the face up card of the dealer is a 4. Let us calculate the probability of achieving 21 points (receiving a 4).

We havenx = 2, nv = 5, so:

.

For the probability of achieving 20 points (receiving a 3), we havenx = 0, nv = 5, so:

.

Blackjack 21+3 Combinations Chart

For the probability of achieving 19 points (receiving a 2), we havenx = 1, nv = 5, so:

.

If we want to calculate the probability of achieving 19, 20 or 21 points, all we must do is total the three probabilities just calculated. We obtainP = 9/47 = 19.14893%.

Unlike in baccarat, where fewer cards are played, the number of players is constant (two), and the number of gaming situations is very limited, in blackjack, the number of possible playing configurations is in the thousands and, as a practical matter, cannot be entirely covered by tables of values.

Overview of 21+3 Blackjack

The 21+3 side bet is optional, and its size does not need to be the same as the main bet. In order to play the side-bet, you need to participate in the main hand.

Placing a bet in the 21+3 square is all you need to do to participate. As soon as the deal is made, and before any player takes any actions the 2 player cards and the dealer’s up-card (or only card in European Blackjack) are compared to the pay table.

There are several variations of 21+3 payouts, the most simple pays from a ‘flush +pair’ and up, with 9-to-1 payouts in each case. When pairs are also included, this is hit more often, so the prizes are lowered to reflect this. There are 3-to-1 for all hands (pair, flush, straight, trips and straight flush) or there are staggered pay tables.

When the prizes are staggered, a straight flush or better can win significant money. Here is an example:

• Flush – Pays 5:1
• Straight – Pays 10:1
• Straight Flush – Pays 35:1
• Three of a Kind – Pays 33:1
• Suited 3 of a Kind – 100:1

Keep in mind that depending on the pay table, the house edge can get as high as 13% for this side bet. You can find examples of games (depending on the number of decks in use) where this is around 2.78% instead.

Blackjack 21+3 Odds

Strategy for 21+3 Blackjack

It goes without saying that knowing the correct basic strategy of the base game is a prerequisite here. Without this you are just handing money to the house.

Blackjack 21 3 Combinations Words

Your main ‘strategy’ decision over the long run with the 21+3 side-bet is whether to play or not. The house edge is bigger than in most base games. If you know this, then you get to decide whether the added interest and entertainment (and chance of a windfall win) are worth it to you. If the extra engagement from the 21+3 bet works for you – then you can simply add a little to your bankroll to cover this.

Blackjack 21+3 Combinations List

Card counters can beat this game by memorizing the suits as they are dealt. It is possible on some deals to find one suit over-represented as the shoe gets smaller – turning the edge positive for players. The expected hourly rate for this is very low compared to other forms of counting. Online the deck is shuffled after each hand, making card counting impossible.

Pros and Cons of 21+3 Blackjack

Adding a poker style hand to blackjack makes for an interesting variation – though I do wonder whether ‘purists’ in either discipline would approve! Depending on which of the pay tables you use there is the chance of a 9-to-1 or even bigger windfall. That elusive suited 3-of-a-kind (paying 100-to-1) would certainly be memorable.

Whether you participate depends on your attitude towards side-bets in general. Some players like these bets, and are happy to pay the extra house-edge for the chance of the occasional big win. Others scorn these bets as long-term losers.