Blackjack 21+3 Combinations
- Blackjack 21 3 Combinations Worksheets
- Blackjack 21 3 Combinations Cheat
- Blackjack 21+3 Odds
- Blackjack 21 3 Combinations List
This is for the variation of 21+3 that pays 9 to 1 for Straight Flushes, Straights, Flushes, and Trips. A flush is the most common winning hand in the 3CP side bet.
In a full 6 deck shoe, there are 303,264 three-card flush combinations. There are 5,013,320 total 3 card combinations. Off the top, the chance of receiving a flush (your 2 up cards plus the dealer’s) is 6.049165%. Multiply this by the 9 to 1 payout, and you can expect to lose about 45% of every unit wagered. The house edge, if not for straights and trips, which have 155,520 and 26,312 combinations possible respectively, would be 54.4%. With those factored in, this game features a house edge of only 3.2386%
Since flushes are the most common winner, we will concentrate on flushes for this strategy. There is a more precise way to track suits, however it would either require a four person team (one person to count each suit) or somebody very good at keeping four separate counts.
For my strategy, you will assign red cards a + value and black cards a – value (or vice versa if you prefer). Hearts and Diamonds would be worth +1, Clubs and Spades worth -1. You will keep a running count just like with hi-low, starting at 0 since this is a balanced count. You will then keep a running count, and convert to a true count by dividing by remaining decks. When the true count reaches +20 or -20, the side bet becomes +EV (1.056048387).
I realize this seems unlikely; however this is the easiest way to count for this side bet.
I would like to hear your thoughs, questions, and comments on this post. Thanks!
I would like to thank the wizard of odds for the following data that helped me in my research.
http://wizardofodds.com/blackjack/appendix8.html#21+3
http://wizardofodds.com/threecardpoker
See full list on wizardofodds.com. «21+3 Blackjack» is an original version of online blackjack with side bets where poker combinations formed of three first cards are paid by side bets. This Blackjack game features an additional bet '21 + 3'. Not compulsory, it is however interesting if you are looking to win a max in one hit! It will take into account your two cards and the one returned from the croupier to make a combination. 'We find that the dealer's first two cards can produce the counts from 2 to 21 in 1,326 ways.' Indeed, Combinations C (52, 2) = 1,326 two-card blackjack hands (combinations of 52 cards taken 2 at a time). That is the only thing. Half-way mathematically correct! The truly correct method applies the mathematics of combinatorics alright.
Blackjack 21 3 Combinations Worksheets
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
Blackjack 21 3 Combinations Cheat
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.
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.
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.
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.
Blackjack 21+3 Odds
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.
Blackjack 21 3 Combinations List
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.