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
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In the Jan 4' 2007 ( Appendix 18 ) update by The Wizard of Odds he says to Stand on 16 vs 10 with 3 or more cards. Since everybody's BS chart shows a Hit on 16 vs 10 and the 3 or more cards 16 is a more common occurance than the 2 cards 16, is this a change now for the BS charts.
My other question is on the European BJ. On his Dec 13, 2006 European BJ update he says to Surrender 14 to 17 vs 10. This is a radical departure from the usual Surrender of 15 & 16 vs 10 in the American BJ and not just a matter of not doubling or splitting against the 10 & Ace.
Does anybody knows what the correct BS is for European BJ and in particular what is the correct hit/stand play against tha Ace since there is no surrender against the Ace.
My other question is on the European BJ. On his Dec 13, 2006 European BJ update he says to Surrender 14 to 17 vs 10. This is a radical departure from the usual Surrender of 15 & 16 vs 10 in the American BJ and not just a matter of not doubling or splitting against the 10 & Ace.
Does anybody knows what the correct BS is for European BJ and in particular what is the correct hit/stand play against tha Ace since there is no surrender against the Ace.