SWFL Blackjack
Well-Known Member
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
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