21+3 Side Bet Strategy

SWFL Blackjack

Well-Known Member
#1
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
 

matt21

Well-Known Member
#2
SWFL, I am very interested in these findings. Did you make any assessment on the percentage of times that the side bet would have +EV?

Matt21
 

matt21

Well-Known Member
#3
SWFL I have found your post that shows the TC frequency distributions on another site - all good.

I think one of the downfall's with exploiting this side bet is the low maximum bet that would regularly be encountered. In most of the places I have seen a limit of some $100 on the side-bet, this being where the table was 25-5000. This would restrict the potential return for trying to exploit this bonus bet? Though the key issue would be the need to have as many as four or more people just to track the various combinations!

What do you think?
 

SWFL Blackjack

Well-Known Member
#4
matt21 said:
SWFL, I am very interested in these findings. Did you make any assessment on the percentage of times that the side bet would have +EV?

Matt21
I'm not exactly sure, but I think it is pretty rare that the deck will be that rich in either red or black cards. I will perform additional math to check this. I think if you used this method in simultaneously with counting, it could be profitable and good cover since counters rarely play side bets.
 

SWFL Blackjack

Well-Known Member
#5
matt21 said:
SWFL I have found your post that shows the TC frequency distributions on another site - all good.

I think one of the downfall's with exploiting this side bet is the low maximum bet that would regularly be encountered. In most of the places I have seen a limit of some $100 on the side-bet, this being where the table was 25-5000. This would restrict the potential return for trying to exploit this bonus bet? Though the key issue would be the need to have as many as four or more people just to track the various combinations!

What do you think?
Yes, the low table max for this particular side bet makes it rather difficult to make it worth exploiting, especially if you need a team of four or five people to do it. Out of curiosity, what was the website that you found the TC frequency distributions on?
 
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