twenty one plus three

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

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.

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.

Quote: 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.

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.

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.

Quote: AxiomOfChoice

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.

Quote: teliot

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.

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.

Quote: teliot

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.

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.

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?".

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.

Quote: AxiomOfChoice

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.

Quote: teliot

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!

Quote: AxiomOfChoice

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!

It's a contrived example to demonstrate the limits of just card counting. No decent AP has a max bet of $100, we all know that. In addition, no card counter is playing 40 hours per week. That's just a ridiculous notion.

Quote: AcesAndEights

It's a contrived example to demonstrate the limits of just card counting. No decent AP has a max bet of $100, we all know that. In addition, no card counter is playing 40 hours per week. That's just a ridiculous notion.

My point is that talking about 0.337 table-max-bets per 100 hands like it's nothing is silly. 0.337 table-max-bets per 100 hands is a lot of money at any decent casino with decent limits.

If you are not betting the table max whenever you have the edge then the whole example is silly, and calling your max bet "units" is misleading. You are going to bet proportionally to your edge (or, as close as you can get away with), and you will probably refer to your minimum bet (not your max) as a "unit". Like if I am betting at a black-chip game and spreading $100-$1000 my "units" are black chips (not yellows) and I am making a lot more than 0.337 units per 100 hands.

My point is, if you can get a decent bet spread down at a black-chip game with good rules, you can make good money. Is it the best advantage play in the casino? Maybe, maybe not, depending on the casino and what else is available. Should you limit yourself to it? Definitely not. There's nothing that says that you can't look at the hole card if the dealer shows it, and there's nothing that says that you can't go play in another game too if there is an advantage there. But does that mean that card counting at blackjack is worthless, or practically worthless? No, not at all.

teliot, have you done any analysis of using a 10-count and attempting to cash-in on three of a kinds / straights of 10 value cards only?

Quote: wudged

teliot, have you done any analysis of using a 10-count and attempting to cash-in on three of a kinds / straights of 10 value cards only?

You can never do better than perfect play, which is 0.2748. The suit count gets 0.1777. Your count above will get far less.

Quote: AxiomOfChoice

My point is that talking about 0.337 table-max-bets per 100 hands like it's nothing is silly. 0.337 table-max-bets per 100 hands is a lot of money at any decent casino with decent limits.

If you are not betting the table max whenever you have the edge then the whole example is silly, and calling your max bet "units" is misleading. You are going to bet proportionally to your edge (or, as close as you can get away with), and you will probably refer to your minimum bet (not your max) as a "unit". Like if I am betting at a black-chip game and spreading $100-$1000 my "units" are black chips (not yellows) and I am making a lot more than 0.337 units per 100 hands.

My point is, if you can get a decent bet spread down at a black-chip game with good rules, you can make good money. Is it the best advantage play in the casino? Maybe, maybe not, depending on the casino and what else is available. Should you limit yourself to it? Definitely not. There's nothing that says that you can't look at the hole card if the dealer shows it, and there's nothing that says that you can't go play in another game too if there is an advantage there. But does that mean that card counting at blackjack is worthless, or practically worthless? No, not at all.

I agree with you. Well said.