Blackjack 21+3 Combinations

Blackjack 21 3 Combinations Worksheets

After a recent thread about the 21+3 side bet, I received a few PMs asking for more info on the sidebet. I did some extensive work on excel, and believe I have found an easy method to determine when the side bet has become +EV. Utilizing the COMBIN function, as well as determining the number of possible outcomes when a card of a certain suit is removed, I have arrived at the following findings.
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

Blackjack 21 3 Combinations Words

If you made the 21+3 wager and these three cards form a winning combination, you have won a generous 9 to 1 payout relative to the 21+3 bet. The blackjack hands are then played out as usual. Winning Three Card Hands.
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)=5356 for the 2-deck game. Probability of obtaining a natural blackjack is P = 8/663 = 1.20663% in the case of a 1-deck game and P = 16/1339 = 1.19492% in the case of a 2-deck game.

How To Play Blackjack 21 3

Blackjack 21+3 Odds

The blackjack is very realistic. Most people who complain about the blackjack have never been to a casino. Let me explain, in most casinos a blackjack game is dealt with 8 decks of cards, there are sixteen “10s” in each of those decks, that means 128 out of 416 cards will be a 10. This means NEARLY 1/3 cards will be a 10. '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. Weigh the odds and place your bets - it's 21 or bust! Count on a fun online game of Blackjack. Play for free online!