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The “21 + 3” blackjack side bet is based on examining the player’s two cards and the dealer’s up-card. If the three cards form a flush, straight, three-of-a-kind or straight flush, the player wins. In the original version, the payout for each of these was 9-to-1. The one opportunity you do have to count cards online is with live dealer blackjack games, where are real dealer is using a real deck of cards via a video stream. However, this variant of the game.

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batman5318
i am new to the site so i will try not to sound stupid. this is about a side bet on a blackjack game. it is basically three card poker with the first two player cards and the dealer up card. winning hands are straight, flush, straight flush, and three of a kind. i was curious if anyone knows the house edge on this side bet with all of the payouts paying 9 to 1.
secondly this is where i might be wrong but couldn't you count suits and beat the house edge by increasing your bet when the chances for a flush are higher. the bet limits are $5-$100. i have never heard of anyone counting cards for a side bet but just curious. Thanks
AxiomOfChoice
IIRC this is covered at apheat.net (as is just about every other blackjack side bet). I think it was countable but not worth much.
1BB
I remember someone on another forum attempting to develop a count for 21+3. I think he gave up because the shoes never got rich enough in one suit. Does that make sense or am I leaving something out? Countable side bets do exist and they can be very lucrative.
The house edge on the 21+3 version that you describe is 3.24%. The Wizard of Odds site also has the scoop on side bets.
Many people, especially ignorant people, want to punish you for speaking the truth. - Mahatma Ghandi
teliot

IIRC this is covered at apheat.net (as is just about every other blackjack side bet). I think it was countable but not worth much.

It is worth a bit more than you might expect, but very hard to count. I've both developed a count for it and run a perfect play analysis. Any casino that worries about this one is overreacting.
http://apheat.net/2012/08/07/beating-the-213-blackjack-side-bet/
http://apheat.net/2013/06/21/beating-the-213-blackjack-side-bet-update-1/
AxiomOfChoice
I dunno. I consider those numbers to be 'not worth much'. 0.177 units per 100 hands? And you need to count the blackjack game as well, or you are going to be giving much more than that back. Keeping a 2nd count for an extra 0.177 units?
For an extreme example, suppose that the casino let you bet any amount on the side bet, regardless of your blackjack bet. So you play $5 blackjack with basic strategy (and lose, maybe 50c per hundred hands -- the low limit games with side bets tend to have terrible rules) and you slide out a black chip for the side bet when the suit count is favorable. You're going to make about $17 per hundred hands total, and I'm pretty sure that surveillance is going to take a second look at someone who bets this way. They would have to be completely asleep to not suspect something.
If you can afford to bet black chips, you are better off just going to the green or black chip blackjack game and counting that. You will make a lot more than $17 per 100 hands, draw less heat, and get comped better too.

Twenty One Plus Three Blackjack 2

teliot

I dunno. I consider those numbers to be 'not worth much'.

Please, don't misread what I wrote. I said that this bet is worth more than you might expect, not that it is an actual opportunity for advantage play. It isn't. I was just surprised at that 0.177 number, I expected it to be lower.
By the way, a perfect high-low blackjack counter who is Wonging a good six-deck game is only earning 0.337 per 100 hands. Not quite twice as much as 21+3. I have a hard time understanding why anyone would want to do ordinary card counting at blackjack.
http://apheat.net/2013/12/12/the-worlds-greatest-blackjack-card-counter/
AcesAndEights

I have a hard time understanding why anyone would want to do ordinary card counting at blackjack.


I sometimes wonder if I'm wasting my time with basic card counting, considering all of the other, more advanced AP techniques discussed here and elsewhere.
There are some factors to a basic count game that make it the 'lowest common denominator' of advantage plays. It's widely available. For the most part, any non-CSM BJ game that pays 3-2 on blackjack is at least playable. Your EV might not be great depending on the other rules and the penetration, but you can get past the break-even point on almost any BJ game anywhere. It doesn't require advanced scouting to find a bad dealer exposing cards, or a house that doesn't know the proper procedure (for example, the PGP exploit recently documented on your site). It doesn't require any advanced mathematical skills; all the work has been done for you ad nauseum for all the various rule variants and conditions. Dozens if not hundreds of books have been written.
And even with all of the books and publicity and general knowledge, it's not hard to get away with it, if you follow the 'hit-and-run' style advocated by Ian Andersen (a strategy that our own kewlj seems to use to totally acceptable reselts). And you will sometimes run into a casino staff that has their heads so far up their asses that you can stick around and play for a bit longer.
If I were a professional AP, I would definitely explore the other opportunities out there. But as a hobbyist, I don't have the time to scout for a hole card game. A lot of the beatable side bets (i.e. Lucky Ladies) are offered with poor paytables in my locality, making the profitable opportunities less frequent. Most of the carnival game exploits require a sloppy dealer and learning some kind of new strategy. I hole-card 3CP when I get the chance, but that cat has been out of the bag for a long time. One example of an 'intimidating' game is UTH..I have looked at the strategy guides for that game and I would have to set aside the time to learn the appropriate strategy plus the right deviations, and THEN find a game that is exploitable.One
Anyway, that's why people still do ordinary card counting :).
All that being said, I should really read more of apheat.net to broaden my 'portfolio' of skills. If I found a hole card BJ game, I wouldn't even know what to do with it (i.e. I don't have the proper strategy memorized). If I found a LL side bet with a decent pay table, I wouldn't know the trigger count with my specific counting system. In fact I was playing on a table with the 'Bust Bonus' bet today. At high counts, this is might be a +EV proposition? I haven't done the research to find out.
'So drink gamble eat f***, because one day you will be dust.' -ontariodealer
AxiomOfChoice

Please, don't misread what I wrote. I said that this bet is worth more than you might expect, not that it is an actual opportunity for advantage play. It isn't. I was just surprised at that 0.177 number, I expected it to be lower.
By the way, a perfect high-low blackjack counter who is Wonging a good six-deck game is only earning 0.337 per 100 hands. Not quite twice as much as 21+3. I have a hard time understanding why anyone would want to do ordinary card counting at blackjack.

' target='_blank'>http://apheat.net/2013/12/12/the-worlds-greatest-blackjack-card-counter/
I have to say, I find that you're overly-critical of blackjack card counting. The example that you give on the linked page is a little ridiculous.

Twenty One Plus Inc

Why would a counter who knows that he gets no heat at all ignore the Kelly Criterion? The Kelly Criterion is the optimal way to bet. It's the answer to the question 'how should you bet if you can bet however you want with no heat?'.

Twenty One Plus Three Blackjack Online


Flat-betting only when you have the edge is an extremely expensive form of cover. It's nowhere near the best you can do. The 6-deck game that you described has extremely good penetration, which is extremely profitable, if you bet big when you have a big edge. If you don't get the chips out there with the large edges that you will sometimes get with that penetration, then it's not worth that much.
teliot

The Kelly Criterion is the optimal way to bet.

The optimal way to maximize the amount you win is to have a sufficiently large bankroll so that the Kelly Criterion does not apply; you can bet table max whenever you have the edge, which is at +1 or higher. Most big teams and top APs can easily play at this level.
For a fixed maximum bet (I chose $100), if you use a bet ramp then you will earn at a rate that is less than 0.337 units per 100 hands.
AxiomOfChoice

The optimal way to maximize the amount you win is to have a sufficiently large bankroll so that the Kelly Criterion does not apply; you can bet table max whenever you have the edge, which is at +1 or higher. Most big teams and top APs can easily play at this level.
For a fixed maximum bet (I chose $100), if you use a bet ramp then you will earn at a rate that is less than 0.337 units per 100 hands.


There is no bankroll that will make it correct to bet table max for an arbitrarily small edge, so I'm not really sure what you mean by your statement.
Ignoring that, in a decent strip casino with a table max of, say, $10k, 0.337 max bets per 100 hands is a pretty good income that I would not be unhappy with at all. $33.70 per hand? I'll take it. Even in a slow game (say, 60 hands per hour) if we assume 40 hour weeks and 50 week years (standard work hours; not killing yourself or anything) is about 4.5 million dollars per year. Sign me up!!!
Also, why are we betting only one spot??? Table max on the 6 spots that the other guy isn't playing when we have the edge!
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