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Thread: 98%: Optimal Betting

  1. #1
    98%
    Guest

    98%: Optimal Betting

    It has been repeatedly stated in blackjack literature that a Kelly betting approach is, in a purely theoretical sense, the fastest way to grow your bankroll. However, it is my understanding that the Kelly Criterion assumes an SD of exactly 1 or, in other words, a 1 unit up or down move at the conclusion of each trial. Has anyone ever corrected for this approximation and determined an exact optimal bet as a function of EV and BR size, assuming a goal of maximum bankroll growth, for blackjack with different numbers of decks in play and for different benchmark rules?

    Also, has anyone ever determined SD as a function of EV in blackjack? This would, of course, have to be approximated by evaluating the SD of a blackjack hand as a function of the count. This could also imply a sort of second-degree functionality of EV in determining an optimal bet size. I do not expect this change in SD to be very significant, but it is intuitively obvious that a change in deck composition can change SD.

    I'm not going to claim that any of this is actually useful, I'm merely curious.

  2. #2
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Optimal Betting

    > It has been repeatedly stated in blackjack
    > literature that a Kelly betting approach is,
    > in a purely theoretical sense, the fastest
    > way to grow your bankroll.

    Grow the logarithm of your bankroll, which isn't exactly the same thing, but I digress.

    > However, it is my
    > understanding that the Kelly Criterion
    > assumes an SD of exactly 1 or, in other
    > words, a 1 unit up or down move at the
    > conclusion of each trial.

    No, that isn't true. It has no such restriction, and, clearly, for blackjack, the variance of a hand is greater than 1.

    > Has anyone ever
    > corrected for this approximation and
    > determined an exact optimal bet as a
    > function of EV and BR size, assuming a goal
    > of maximum bankroll growth, for blackjack
    > with different numbers of decks in play and
    > for different benchmark rules?

    Yes, absolutely! You can read all about it in BJA3 -- in the greatest possible detail imaginable.

    > Also, has anyone ever determined SD as a
    > function of EV in blackjack? This would, of
    > course, have to be approximated by
    > evaluating the SD of a blackjack hand as a
    > function of the count. This could also imply
    > a sort of second-degree functionality of EV
    > in determining an optimal bet size. I do not
    > expect this change in SD to be very
    > significant, but it is intuitively obvious
    > that a change in deck composition can change
    > SD.

    See above. It's all been done -- years and years ago.

    > I'm not going to claim that any of this is
    > actually useful, I'm merely curious.

    It's very useful. You've just been somewhat out of contact.

    Don

  3. #3
    98%
    Guest

    98%: Re: Optimal Betting

    > No, that isn't true. It has no such
    > restriction, and, clearly, for blackjack,
    > the variance of a hand is greater than 1.

    So the Kelly Criterion is independent of SD? And here I had always thought, given the sensitivity of RoR calculations to both EV and SD, that the Kelly Criterion had a component of SD dependence as well.

    > See above. It's all been done -- years and
    > years ago.

    Yes, I'm just looking for a spoiler. I've always speculated that SD goes up with the count. I'm just curious if that's true and, if so, how much?

    > It's very useful. You've just been somewhat
    > out of contact.

    Is it? I'm not convinced. I've averaged between 1,000 and 1,500 hours of blackjack per year for several years now, and I don't think I've ever placed an optimal bet. The table maximum and other unfortunate constraints always get in the way. It would probably also be impossible and impractial to make exactly (to the dollar) optimal bets in a casino. I suppose I can qualify my previous statement and say that I don't think it is useful for me, I'm just curious.

  4. #4
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Optimal Betting

    > So the Kelly Criterion is independent of SD?

    Where did I ever say that? No, that's not true. I simply said that the variance of a hand of blackjack is not 1; it's greater than 1 (anywhere from 1.26 to 1.35).

    > And here I had always thought, given the
    > sensitivity of RoR calculations to both EV
    > and SD, that the Kelly Criterion had a
    > component of SD dependence as well.

    It does. There's just no reason to assume that the SD has to be 1 all the time. It doesn't.

    > Yes, I'm just looking for a spoiler. I've
    > always speculated that SD goes up with the
    > count. I'm just curious if that's true and,
    > if so, how much?

    See the BJA3 Chapter 10 charts. It goes up for a while (because of more frequent naturals), but then starts to drop again, because of the influence of more frequent ties (20 v. 20) at the very high counts.

    > Is it? I'm not convinced. I've averaged
    > between 1,000 and 1,500 hours of blackjack
    > per year for several years now, and I don't
    > think I've ever placed an optimal bet. The
    > table maximum and other unfortunate
    > constraints always get in the way. It would
    > probably also be impossible and impractial
    > to make exactly (to the dollar) optimal bets
    > in a casino. I suppose I can qualify my
    > previous statement and say that I don't
    > think it is useful for me, I'm just curious.

    Everyone understands that making precisely optimal bets is impractical in a casino environment. But, the statement was that it is "very useful" to know what the optimal betting ramp is. How else are you going to know how to scale your bets? Surely, you will bet convenient, chip-size multiples, and surely you will need to choose a max bet and use some camouflage, but would you have us ascertain a working guideline to all of the above in a void, or would you have us first determine what the precise optimal bets are and then construct a ramp that is as close to ideal as possible, while still respecting all of the constraints that we know exist?

    Don

  5. #5
    98%
    Guest

    98%: Re: Optimal Betting

    > Where did I ever say that? No, that's not
    > true. I simply said that the variance of a
    > hand of blackjack is not 1; it's greater
    > than 1 (anywhere from 1.26 to 1.35).

    Ah, my initial post must have been misunderstood. I'm well aware that the variance and/or SD of a hand of blackjack is not necessarily 1. My assumption was that the original Kelly Criterion application assumed a system wherein there was a variance of 1 and, as such, it has usually been "ballparked" when applied to blackjack. That is to say, a full Kelly bet of a percentage of your bankroll equal to your percent expectation on the next hand is not precisely optimal for blackjack.

    > See the BJA3 Chapter 10 charts. It goes up
    > for a while (because of more frequent
    > naturals), but then starts to drop again,
    > because of the influence of more frequent
    > ties (20 v. 20) at the very high counts.

    That's what I figured. The spread of the SDs for various counts is what I was interested in. Above, you mentioned 1.26 and 1.35 as being the range of the variance for a hand of blackjack and, thus, 1.12 to 1.16 for the SD. I guess that won't make a huge difference on bet sizing, but it is still interesting to know. How much bankroll growth do we miss out on in a year (call it 10,000 hands) of betting optimally assuming a 1.1 SD in a game where the real SD is between 1.12 and 1.16?

    > Everyone understands that making precisely
    > optimal bets is impractical in a casino
    > environment. But, the statement was that it
    > is "very useful" to know what
    > the optimal betting ramp is. How else are
    > you going to know how to scale your bets?
    > Surely, you will bet convenient, chip-size
    > multiples, and surely you will need to
    > choose a max bet and use some camouflage,
    > but would you have us ascertain a working
    > guideline to all of the above in a void, or
    > would you have us first determine what the
    > precise optimal bets are and then construct
    > a ramp that is as close to ideal as
    > possible, while still respecting all of the
    > constraints that we know exist?

    Well, when you are staring at a $500 maximum and your optimal bet is $5,000, working out the details down to the nearest $100 isn't that helpful, let alone the nearest $1. One could argue I'm playing in the wrong joints but, the world of casinos which will take bets over $1,000 gets really small really fast. That said, an optimal betting ramp is useful in many situations. Generally speaking, I'm definitely a proponent of many short, highly-optimal sessions as opposed to a few long, camo-heavy sessions.

  6. #6
    Sun Runner
    Guest

    Sun Runner: Re: Optimal Betting

    > Well, when you are staring at a $500 maximum
    > and your optimal bet is $5,000, working out
    > the details down to the nearest $100 isn't
    > that helpful, let alone the nearest $1.

    If I may ..

    If your optimal max bet is $5K and you are stuck playing at joints where the table max is $500, do you even need to calc a bet ramp?

    I've never played, nor will I most likely ever play, in the rarified air you do. Wouldn't the RoR flat betting $500 into your BR still be very very small; especially if you are able to avoid most (some) of the negative counts?

    Also, a related question.

    What kind of spread is tolerated (generally speaking) at a table where the table max exceeds $5,000? And generally what kind of game is being offered at that table?

    Thanks for any insites.


  7. #7
    98%
    Guest

    98%: Re: Optimal Betting

    > If your optimal max bet is $5K and you are
    > stuck playing at joints where the table max
    > is $500, do you even need to calc a bet
    > ramp?

    Not really. If you have no hope of reaching your optimal bet on account of table maximum or other constraints, a betting ramp is more a function of cover or act than anything else.

    > I've never played, nor will I most likely
    > ever play, in the rarified air you do.
    > Wouldn't the RoR flat betting $500 into your
    > BR still be very very small; especially if
    > you are able to avoid most (some) of the
    > negative counts?

    Yes, though I've found most casinos don't appreciate you walking up out of nowhere and blasting away at table maximum right out of the gate.

    > What kind of spread is tolerated (generally
    > speaking) at a table where the table max
    > exceeds $5,000? And generally what kind of
    > game is being offered at that table?

    I must confess to not being the most qualified person to answer this question. Perhaps there are others here with more experience in this arena? That said, I think a very high (1 to 30+) spread will be tolerated as long as you don't overstay your welcome. My last session involved a 1 to 2 x 20 spread, and nothing bad came of it. The most impressive spread I've witnessed was $20 to 3 x $1,000. I'm sorry I can't be anymore detailed than that, but I'd be worse off if I shared the specifics of various moves to achieve massive spreads. Obviously, shuffle tracking is a good means of doing this, but it's far easier to postulate about shuffle tracking than to actually go out and do it with competence.

    All that said, perhaps you could be more specific in what you mean when you say "tolerate." If I get backed off or 86'd or flyered but return to play another day, then I consider that a form of tolerance. To this day, there are only two casinos on earth where I've been asked to leave or asked not to play that I've not yet returned to play in again. And it is only a matter of time for those as well.

  8. #8
    Sun Runner
    Guest

    Sun Runner: Thanks so much.

    > If you have no hope of reaching
    > your optimal bet on account of table maximum
    > or other constraints, a betting ramp is more
    > a function of cover or act than anything
    > else.

    That was my thinking, and by extension, there really is no 'optimal ramp' in this situation, is there? The optimal ramp would seem to be get it out as fast as you can while staying welcome.

    > That said, I think
    > a very high (1 to 30+) spread will be
    > tolerated as long as you don't overstay your
    > welcome. My last session involved a 1 to 2 x
    > 20 spread, and nothing bad came of it. The
    > most impressive spread I've witnessed was
    > $20 to 3 x $1,000.

    This is a high limit table we are talking about right? Maybe it's me, but I'm nervous about heat when my max bet starts coming out and I'm just playing with the regular folk. Is it possible higher bet spreads are 'tolerated' in the high limit areas?

    > All that said, perhaps you could be more
    > specific in what you mean when you say
    > "tolerate."

    No -you got it right.

    Thanks again for the insites.

  9. #9
    Don Schlesinger
    Guest

    Don Schlesinger: Just for future reference ...

    ... it's "insights." :-)

    Don

    >Thanks again for the insites.


  10. #10
    98%
    Guest

    98%: Re: Thanks so much.

    > This is a high limit table we are talking
    > about right? Maybe it's me, but I'm nervous
    > about heat when my max bet starts coming out
    > and I'm just playing with the regular folk.
    > Is it possible higher bet spreads are
    > 'tolerated' in the high limit areas?

    I've never been certain enough to take a stand on this issue either way. On the one hand, betting through the roof with a bunch of red chip ploppies around you sort of looks bad but, on the other hand, high limit rooms theoretically get a lot more up-front scrutiny. Since, in the duration and style I usually play, I don't often hit a table maximum of more than $1,000, even though something much larger would theoretically be optimal, if the main pits offer something like $2,000 or $3,000 and the high limit is $5,000, the higher maximum in the high limit area will usually not color my decision of whether to play there or not. I have, however, declined an opportunity which presented itself on a $1,000 table in hopes of getting a chance later on a $3,000 table. At high stakes, you simply cannot pound away on the same casino ad infinitum. You have to make the most of the chances you get and only take the opportunities which offer solid expectation.

    One thing I really like to do is avoid playing with 'regular folk.' This is more for game speed reasons than anything else. When possible, I try to find empty tables, but not empty pits. I would much rather play an empty shoe from ground zero with a huge spread than hop into a juicy shoe with a lot of players. I think the difference in hand speed is huge. I'm certain slow ploppies cost me tens of thousands in expectation every year. The worst part is that slow ploppies get nervous and thus even slower when someone is betting more on one hand than they have in their bank accounts.

  11. #11
    Sun Runner
    Guest

    Sun Runner: Re: Just for future reference ...

    > ... it's "insights." :-)

    > Don

    Not when your goal is to type fast and get the point across.

    (And of course this is also my excuse for all other spelling goofs.)

    Have a good weekend!!

  12. #12
    Sun Runner
    Guest

    Sun Runner: Re: Thanks so much.

    > One thing I really like to do is avoid
    > playing with 'regular folk.'

    Me too.



    Thanks for the time and the insights.

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