Targeting 21+3 side bets

Last night i decided to try my luck at the 21+3 side bet blackjack. Over a period of about 8 hours i - went down 300, and then proceeded to win 600 by betting the table minimum and putting $5 on the side bet every turn no matter what. I was successful this time to say the least. lots of flushs, had three 9s twice, and a striaght flush at one point as well. overall the side bets are not worth it when the table minimum is 25 and above, but when i catch a 15 and below table i love betting them. they come out more than the wins sometimes which is sad.

Edit - and i will also say that most of the time, i lost, so i dont think about it as a mindless side bet, i see it as im not playing blackjack, but 3 card poker, and when it came to blackjack i lost a lot of the hands, but the attempt at the side bet was actually profitable and more successful than attempting to win at blackjack. its funny because when a good hand does come, im not even worried about it - blackjack ... crap no flush or straight..., and on the flip side, when a bad hand does come, it didnt matter again as the 3 card hands came out more often then ... who cares i was betting 15 and had 10 on the main bet and 5 on the side so when it came to doubling or splitting it was nothing

I'm seeing the same thing your seeing. I'm up about 3000 in less than 10 hours. I'm in Indiana how about you?

guys... GUYS... the 21+3 side bet is a sucker bet. Nice that you had a lucky run, perfectly in keeping with normal variance. but do quit while you are ahead.

What's the 3-card pay table?

Quote: Gialmere

What's the 3-card pay table?

If you're asking in general, I've only seen 9-9-9-9 for sfl/3oak/str/flu.

3 of a kind suited 270-1.
Straight flush 180-1.
3 of a kind unsuited 90-1.

At what point in a plus minus system does the game turn beatable?

I'm seeing it at plus or minus 6 seems to be the point to bet the side bet.

Quote: heatmap

Last night i decided to try my luck at the 21+3 side bet blackjack. Over a period of about 8 hours i - went down 300, and then proceeded to win 600 by betting the table minimum and putting $5 on the side bet every turn no matter what. I was successful this time to say the least. lots of flushs, had three 9s twice, and a striaght flush at one point as well. overall the side bets are not worth it when the table minimum is 25 and above, but when i catch a 15 and below table i love betting them. they come out more than the wins sometimes which is sad.

Edit - and i will also say that most of the time, i lost, so i dont think about it as a mindless side bet, i see it as im not playing blackjack, but 3 card poker, and when it came to blackjack i lost a lot of the hands, but the attempt at the side bet was actually profitable and more successful than attempting to win at blackjack. its funny because when a good hand does come, im not even worried about it - blackjack ... crap no flush or straight..., and on the flip side, when a bad hand does come, it didnt matter again as the 3 card hands came out more often then ... who cares i was betting 15 and had 10 on the main bet and 5 on the side so when it came to doubling or splitting it was nothing

To sum this up, you played a side bet that has a negative 3.24% house edge that cannot be overcome in the long run , and you happened to get lucky.

Shuffle-up mid-shoe. What?
Beating the 21 + 3 Blackjack Side Bet: Some Really Cool Graphs https://www.888casino.com/blog/side-bets/beating-the-21-3-blackjack-side-bet-some-really-cool-graphs

There's 21+3 Extreme in my area.
Perfect Play against the 21+3 Extreme Blackjack Side Bet https://www.888casino.com/blog/side-bets/perfect-play-against-the-213-extreme-blackjack-side-bet

In particular the house edge for 21+3 is 3.24%, whereas the house edge for 21+3E is 13.39%.

There's also Match The Dealer BJ that has higher payouts & a higher house advantage than Match The Dealer in Spanish 21 in my area.
The following table shows Wizard's analysis in eight-deck blackjack when an unsuited match pays 3 to 1 and a suited match pays 14 to 1. - Blackjack ~3.67% HA
https://wizardofodds.com/games/blackjack/side-bets/match-the-dealer/

The following table shows Wizard's analysis in eight-deck blackjack when an unsuited match pays 3 to 1 and a suited match pays 12 to 1. - Spanish 21 ~3.0% HA
https://wizardofodds.com/games/blackjack/side-bets/match-the-dealer/

Thank you for the courtesy of a reply. None of the reference articles uses the correct pay table of:

3 of a kind suited paying 270-1.
Straight Flush paying 180-1.
3 of a kind unsuited 90-1.

Using these pay tables with a count of plus or minus 6 and higher is the casino advantage lower?

Quote: goodh2o1

Thank you for the courtesy of a reply. None of the reference articles uses the correct pay table of:

3 of a kind suited paying 270-1.
Straight Flush paying 180-1.
3 of a kind unsuited 90-1.

Using these pay tables with a count of plus or minus 6 and higher is the casino advantage lower?

I don't know the answer, but i'll throw back two questions:
What count are you using and why would a high count improve your chances with these side bets.
I mean, we all know how a shoe rich in tens can make an insurance bet advantageous, but surely something as simple as richness of tens does not easily correlate to an increased likelihood of a flush or three of a kind. Using a normal high low count is a pretty blunt tool, probably the wrong tool, to attack 21+3 side bet.

But at least it's something less researched than regular hi-lo counting. It just means you have more research to do from less sources.

Quote: OnceDear

I don't know the answer, but i'll throw back two questions:
What count are you using and why would a high count improve your chances with these side bets.
I mean, we all know how a shoe rich in tens can make an insurance bet advantageous, but surely something as simple as richness of tens does not easily correlate to an increased likelihood of a flush or three of a kind. Using a normal high low count is a pretty blunt tool, probably the wrong tool, to attack 21+3 side bet.

But at least it's something less researched than regular hi-lo counting. It just means you have more research to do from less sources.

1. I think that a shoe that is rich in the ranks 3-6 has:

- a higher probability of 3-card straight flushes that a fresh shoe ( All of those ranks are able to participate in three different straights, i.e., a 4 can participate in a 543, 432, and 32A straight.)
- In general, the odds of making some straight flushes will be elevated, namely those of these sequences : 654, 543, 765, 432. Other straight flushes will have reduced probabilities but the net effect will likely be to have more straight flushes.

2. HOWEVER, the probability of making a 3oaK -whether unsuited or suited - will go down with penetration, on average, because there are fewer and fewer cards remaining in the deck. And much of the return on this sidebet paytable comes from making 3oaKs. So, I do suspect that this paytable offers even fewer cases (less frequent instances) in which the player will have a +EV situation with computer perfect play. Indeed, the frequency of having a +EV sidebet with this paytable may be well below 1%.

Thanks for the courtesy of a reply and feedback.

I'm using simple plus minus from "Playing Blackjack as a Business". Really you can't see where having counts of 19-20-21-20 at the table would not result in better chances of three of a kind or straights, some of those straights are straight flushes.

The Trulix version of this game in Missouri pays, unsuited three of a kind at 33 to 1 on the plus 3 and the top three pays 90 to 1.

Just as there are more chances for straights and flushes with a lot of high cards in the deck. The same has to be there when there are lots of small cards left in the deck. The chances of straights has to go up. The Count good or bad is an indicator to bet on the side bet.

The AP that I see is to just play Blackjack the best you can and bet the plus 3 and top 3 when it is most favorable. What I'm seeing in my case is that once the count gets to plus or minus 6 I'm seeing more pairs. Of the pairs I caught the other day, 4 of the 5 pairs dealt to my hand occurred when the count was plus 6 or more. I had a bet on 4 of the 5 occasions. There were two players and the other player caught three of a kind suited paying 1350 for a 5 dollar bet and then caught a three of a kind unsuited for 450 for a 5 dollar bet. Both of those occasions the count was plus 6 or more. The other player was betting every hand. However the winning hands were dealt with the count being plus 6 in these cases.

I had at least 4 chances for straight flushes and 5 chances for three of a kind.

Most responses I get aren't using the higher payouts figure when they are responding.

I'm probably only betting this about 30% of the time.

Quote: goodh2o1

Thanks for the courtesy of a reply and feedback.

I'm using simple plus minus from "Playing Blackjack as a Business". Really you can't see where having counts of 19-20-21-20 at the table would not result in better chances of three of a kind or straights, some of those straights are straight flushes.

The Trulix version of this game in Missouri pays, unsuited three of a kind at 33 to 1 on the plus 3 and the top three pays 90 to 1.

Just as there are more chances for straights and flushes with a lot of high cards in the deck. The same has to be there when there are lots of small cards left in the deck. The chances of straights has to go up. The Count good or bad is an indicator to bet on the side bet.

The AP that I see is to just play Blackjack the best you can and bet the plus 3 and top 3 when it is most favorable. What I'm seeing in my case is that once the count gets to plus or minus 6 I'm seeing more pairs. Of the pairs I caught the other day, 4 of the 5 pairs dealt to my hand occurred when the count was plus 6 or more. I had a bet on 4 of the 5 occasions. There were two players and the other player caught three of a kind suited paying 1350 for a 5 dollar bet and then caught a three of a kind unsuited for 450 for a 5 dollar bet. Both of those occasions the count was plus 6 or more. The other player was betting every hand. However the winning hands were dealt with the count being plus 6 in these cases.

I had at least 4 chances for straight flushes and 5 chances for three of a kind.

Most responses I get aren't using the higher payouts figure when they are responding.

I'm probably only betting this about 30% of the time.

Here's another Wizard of Vegas thread about the Top 3 bet that uses your pay table (270/180/90): https://wizardofvegas.com/forum/gambling/blackjack/29932-blackjack-side-bet-21-3-top-3/#post619154

How many decks are in the shoe? For a 6-deck shoe, I get a house edge of 11.073%.

For a 6-deck shoe, I think a hi-lo true count of 11 would be the index (edit: also, -11.) But that's ignoring the 21+3 side bet that is required to be made with the Top 3 bet.

Quote: goodh2o1

Thank you for the courtesy of a reply. None of the reference articles uses the correct pay table of:

3 of a kind suited paying 270-1.
Straight Flush paying 180-1.
3 of a kind unsuited 90-1.

Using these pay tables with a count of plus or minus 6 and higher is the casino advantage lower?

This is because this is not the 21+3 bet. It is an additional.bet sometimes offered, usually in conjunction with the 21+3 bet, but it is called Top3. It's determined using the same 3 cards as 21+3, but it stands alone.

The HE on this bet is approximately 9%, as published in the UK.

http://www.ukcasinotablegames.info/blackjacktop3.html

Quote: goodh2o1

I'm probably only betting this about 30% of the time.

I never play these side bets, so forgive my ignorance, but..... To be eligible to play these side bets, you have to be sitting and playing the main game. Also, isn't the side bet wager size limited depending on your main bet? So, 100% of the time, your bankroll is being mostly used on a game that will tend to deplete it. If the count is +6, you are laughing, but on average it's not. Plus you would play into a -6 count just for the opportunity to exploit the side bet?
Doesn't sound like a lucrative opportunity to me.

Quote: beachbumbabs

The HE on this bet is approximately 9%, as published in the UK.

http://www.ukcasinotablegames.info/blackjacktop3.html

OUCH!!!!!

But with volatility that would make a few lucky folk think they have the Holy Grail.

Quote: OnceDear

OUCH!!!!!

But with volatility that would make a few lucky folk think they have the Holy Grail.

I've played it a few times. Very fun, and I'm ahead on it lifetime. But that's still a very high HE. I think some.casinos are afraid.of it. The places I played, the limits were $1-10 only.

The bets required are table minimum on blackjack and 5 dollar minimum 100 max on plus 3 and 1 to 25 on top 3.

If there are more chances to hit a straight with a high count because more big cards are "Cllumped" together the exact same situation exists for high negative counts.

Maybe it needs to be tweaked to say only betting it as the plus ten level or negative ten level. If there is clumping available then this bet is more vulnerable.

What I find amazing is all the poo pooing and nobody even knows the correct pay offs before trashing it.

Hell I know its a bad bet, I want to know how it changes with the count going high negative or positive, then apply the correct pay table.

Good luck to all, may you win all your splits and double downs.

Quote: goodh2o1

If there are more chances to hit a straight with a high count because more big cards are "Cllumped" together the exact same situation exists for high negative counts.

Here are two specific cases:

1) Cards remaining: 172 Running Count = -16

12 cards (3 each of each suit): 2, 7-A
16 cards (4 each of each suit): 3,4,5,6
Calculated House Edge: -0.1275

2) Cards remaining: 172 Running Count = +16

12 cards (3 each of each suit): 2-9, A
16 cards (4 each of each suit): T,J,Q,K
Calculated House Edge: -0.1197

So, you can see that being rich in cards 3-6 is better than being rich in Tens-King. This is because the Kings can only participate in making 2 straights (AKQ, and KQJ).
******************************************************
Here is how House Edge varies with the number of (full) decks in the shoe:

8 decks: -0.0900
6 decks: -0.1107
4 decks: -0.1504
3 decks: -0.1876
2 decks: -0.2545
*******************************************
Given a 6-deck shoe, if the first 24 cards out of the shoe are the 24 Aces, then the remainder of the shoe is favorable to the dealer with EV= +0.00174.

Given a 6-deck shoe, if the first 48 cards out of the shoe are the 24 Aces and 24 Deuces, then the remainder of the shoe is favorable to the dealer with EV= +0.1847.

Quote: goodh2o1

If there are more chances to hit a straight with a high count because more big cards are "Cllumped" together the exact same situation exists for high negative counts.

Maybe it needs to be tweaked to say only betting it as the plus ten level or negative ten level. If there is clumping available then this bet is more vulnerable.

What I find amazing is all the poo pooing and nobody even knows the correct pay offs before trashing it.

Hell I know its a bad bet, I want to know how it changes with the count going high negative or positive, then apply the correct pay table.

Good luck to all, may you win all your splits and double downs.

There's a lot of crosstalk going on here.

Quote: goodh2o1

3 of a kind suited 270-1.
Straight flush 180-1.
3 of a kind unsuited 90-1.

At what point in a plus minus system does the game turn beatable?

I'm seeing it at plus or minus 6 seems to be the point to bet the side bet.

21+3 is NOT the bet you're trying to evaluate. It's called TOP3. All they share is the felt.

Straights and flushes LOSE on this bet, as do pairs.

3oak, including suited, for 6 deck = 26312
SF for 6 deck = 10368

All possible hands = 5013320

36950/5013320 = .007370 hit rate, or 1 in 136 hands.

You will NEVER get to 136 hands in a 6 deck shoe before it's shuffled, let alone the rare TC +/-6 or better. (IDK how often that heavy of clumping occurs). There are only 306 cards in the deck. 136 hands would take 544 cards head to head if NONE was hit.


I'm guessing, if you tried this a couple hours every week for the next 10 years, you would NEVER win this bet on a favorable (your parameter) count shoe. Maybe lightning would strike and you'd win once, but in the mean time, you'd be waiting for the one shoe a month to get you to the clumping, and then betting against a 9% HE for maybe 1 or 2 hands before the shuffle.

Waste of time even running the numbers. Have fun with the bet, don't bother chasing the confluence.

I took 52 random cards from a 6-deck shoe and found the Top 3 bet's EV. This is like the last hand in a game with the cut card one deck from the bottom.

I repeated this for a total of 10,000 trials and computed the frequency of each hi-lo count and the fraction of the time that the Top 3 bet was positive at each count.

Below are my results:

Hi-lo	Number	Number EV>0	Fraction EV>0
-21	1	1	1.00
-20	4	3	0.75
-19	2	2	1.00
-18	10	10	1.00
-17	4	3	0.75
-16	10	8	0.80
-15	23	17	0.74
-14	29	9	0.31
-13	57	32	0.56
-12	80	39	0.49
-11	123	60	0.49
-10	164	63	0.38
-9	190	59	0.31
-8	264	76	0.29
-7	308	77	0.25
-6	426	93	0.22
-5	464	98	0.21
-4	567	108	0.19
-3	630	101	0.16
-2	665	103	0.15
-1	700	110	0.16
0	653	85	0.13
1	699	110	0.16
2	609	97	0.16
3	583	112	0.19
4	529	93	0.18
5	448	77	0.17
6	420	91	0.22
7	331	86	0.26
8	307	84	0.27
9	211	70	0.33
10	138	44	0.32
11	114	41	0.36
12	77	40	0.52
13	50	27	0.54
14	45	24	0.53
15	31	25	0.81
16	9	8	0.89
17	11	8	0.73
18	7	7	1.00
19	4	4	1.00
20	2	2	1.00
21	1	1	1.00
	10000	2208

That's pretty interesting, ChesterDog! Thanks for doing it.

So, just so I understand how to evaluate it. This is evaluating a single hand (opportunity) after reaching a particular status. Which implies that, on the ends of the bell curve, with a threshold of +/-6, there would also have been earlier opportunities within that shoe.

In this particular case, the shoe was +EV 22% of the time. But, with these results, almost 50% of those fall between +5 and -5 TC, so you would not be betting them, leaving 11% of shoes where you would be +EV.

There is an overlap of shoes that are +/-6 or better, but they are -EV for this bet. That is partially accounted for by only looking at the success rate on those that are +EV, but a rough estimate of your numbers shows that a little more than 50% of the shoes you bet using that threshold will actually be -EV, and you won't know + from - depending only on TC.

So, using that count, it's a coin flip whether you have an advantage when you do place your bet. And you will miss roughly 50% of +EV T3 opportunities, another coin flip, because you're not betting it in the middle of the bell curve.

To me, that indicates you won't have any overall advantage using a base count, at least the one that determines TC. However, what was the program counting to determine +/- T3 EV? Perhaps a side count could be determined that accurately does show opportunities? Maybe you can shave significantly into that 1 in 136 win rate if you know that.

Also, while the 21+3 is a standalone from T3, they are largely correlated, and (always in my experience) offered together. With those paying 9-9-9-9, if the same side count indicated +EV opportunities on both, there could be a more frequent bet point on 21+3 that could help you survive sitting there until the T3 turns positive, or you can be playing both and enjoying double +EV with similar indicators.

All just thinking out loud.

I don't understand the graph your referring to. That's why I'm asking for help, it sounds like it is a little better bet if the count is real high or real low, is that it essentially?

Quote: goodh2o1

I don't understand the graph your referring to. That's why I'm asking for help, it sounds like it is a little better bet if the count is real high or real low, is that it essentially?

Yes, when the hi-lo count is very high or very low, the Top 3 bet is +EV.


With 52 cards remaining in the 6-deck shoe, the absolute value of the count has to be 12 or more for the bet to be advantageous. Unfortunately, the probability of the count's being more than 11 or less than -11 with 52 cards remaining is only 4.62%. And for more than 52 cards remaining, the probability of true counts like that are much less.


By the way, in the table of results of only 10,000 shoes for 1 deck remaining, you can see the count is good 457 times which is close to the theoretical number of 4.62%.

Well that is what I'm seeing. When the count is plus 6 and higher is about the cut off of where I'm seeing more pairs and two to a straight flush hands. Just something I noticed and have been betting. I think I need to more any betting up to the plus 9 or higher range.

The occasion that made me think of this was on a six deck game and the deck went +20 for about 4 rounds with three people. I upped my bet to 10 dollars and the count started down and a straight flush was hit. The count was unusually high for two shoes and during a one hour period there were 5 straight flushes hit with one unsuited three of a kind. There were at least 15 other three to a straight flushes dealt to the table of 3 to 4 people.

Obviously it is a bad bet overall. I'm just looking for the point at which I can get a bet down that I'm not at the 11% disadvantage.

The TriLux game in Missouri offers even better odds on the Plus 3 portion of the game. It pays 33-1 on the unsuited three of kind on the small side and 90 on the big side. In Indiana it only pays 25-1 and most only pay 9-1 on the small side.

Thanks for the info ChesterDog

Do you know which las Vegas Casino we have the Top3 side bet?

Quote: OnceDear

guys... GUYS... the 21+3 side bet is a sucker bet. Nice that you had a lucky run, perfectly in keeping with normal variance. but do quit while you are ahead.

Do you know which las Vegas Casino we have the Top3 side bet?