
steve waugh: card eating?
Don,
I just read through your comments on Prize Car's post (Nov 2008) relating to 1 hand and 2 hands playing heads on. I understand now that it makes no difference whether you play one or two hands if you bet appropriately. We would have 1.5 times the bet of a single hand in 2 hands (1*300 or 2*225) but the lower number of rounds for 2 hands will ensure that the EV and ROR are almost identical.
I have another question relating to negative counts though:
My question is: In negative counts, again playing heads up, is there a case for playing 2 hands?(card eating?) at table minimum as opposed to 1 hand at table minimum.
On ve counts: Will card eating not help if you can bet 2*table minimum and have 50% fewer rounds? I do understand that the total amount bet would be more.
Let table min be x;
With 2 hands on negative counts betting 2* table min, we have R Rounds: Total amount bet : 2*x*R=2xR
With 1 hand on negative count betting 1: table min, we have 1.5 R rounds. Total amoung bet =1*x*1.5R= 1.5xR.
Is is that straightforward to sayAlways play 1 hand on negative counts even if playing heads on?
Is that a appleapple comparison? The reason I ask is that, even though we bet 2xR playing 2 hands, the variance would have been reduced in the 2xR wagered playing 2 hands on negative counts as opposed to 1.5xR wagered playing 1 hand on negative counts.
If you recommend one hand on negative counts, when is card eating useful? Is it a concept unique when other players are present and you play as little as possible on negative counts or wong out?
regards
waugh

Don Schlesinger: Sorry for the delay
Sorry not to get back sooner. My wife broke her wrist, so things have been a bit hectic here for a couple of days.
I suppose that, over 30+ years, no question has ever been asked more than the one/two hands one, and, frankly, I usually don't have the patience to answer again and again. But yours, below, has a different twist, because of the negative e.v., so I will do my best to give you a thorough answer.
> I just read through your comments on Prize Car's post
> (Nov 2008) relating to 1 hand and 2 hands playing
> heads on. I understand now that it makes no difference
> whether you play one or two hands if you bet
> appropriately.
Alone, correct. With others, two will be better.
> We would have 1.5 times the bet of a
> single hand in 2 hands (1*300 or 2*225) but the lower
> number of rounds for 2 hands will ensure that the EV
> and ROR are almost identical.
Right.
> I have another question relating to negative counts
> though:
> My question is: In negative counts, again playing
> heads up, is there a case for playing 2 hands? (card
> eating?) at table minimum as opposed to 1 hand at
> table minimum.
My intuition tells me no, but we will do the math in a second. It may be very close.
> On ve counts: Will card eating not help if you can
> bet 2*table minimum and have 50% fewer rounds? I do
> understand that the total amount bet would be more.
It will help, but it will not be superior to playing one hand at table min. Again, we are assuming that you are alone at the table. And again, let's do the math later.
> Let table min be x;
> With 2 hands on negative counts betting 2* table min,
> we have R Rounds: Total amount bet : 2*x*R=2xR
> With 1 hand on negative count betting 1: table min, we
> have 1.5 R rounds. Total amoung bet =1*x*1.5R= 1.5xR.
So far, so good.
> Is is that straightforward to sayAlways play 1 hand
> on negative counts even if playing heads on?
Well, we haven't considered the risk yet, and since SCORE (for positivee.v. situations) is a riskadjusted measure, we would want to do the same thing here and consider e.v./s.d, or (e.v./s.d.)^2, as well. We'll do that in a minute.
> Is that an appleapple comparison? The reason I ask is
> that, even though we bet 2xR playing 2 hands, the
> variance would have been reduced in the 2xR wagered
> playing 2 hands on negative counts as opposed to 1.5xR
> wagered playing 1 hand on negative counts.
No, that isn't true. You can never reduce variance by betting more! You bet more, you have higher variance. Period.
> If you recommend one hand on negative counts, when is
> card eating useful? Is it a concept unique when other
> players are present and you play as little as possible
> on negative counts or wong out?
The maximum cardeating effect will be when you are alone. When going from two hands on the table (yours and the dealer's) to three hands (your two and the dealer's), you are adding 50% more cards per round. Of course, you are also betting twice as much per round, so you really have to consider the two together.
So, before we do any more complicated math, just consider the following: suppose there are just enough cards left to deal six hands. Playing one hand, that will be three rounds, and I will bet three units, until the shoe ends. Playing two hands, I will play only two rounds, but each will have two units bet, so a total of four. Why do I want to risk four units before the shoe ends, instead of three? Well, because we haven't yet factored in the variance.
Let's do some more math. Suppose the e.v. for a hand in this situation is 2%. You bet one unit. And suppose the s.d. is, say, 1.15 units. That makes the variance 1.15^2 = 1.32 squared units.
For two hands (total of two units wagered), the variance becomes 2*[1.32 + 0.48 (the covariance)] = 3.60 squared units.
But, in the second instance, we play R rounds per unit of time, while in the first, we play 1.5R rounds. So, playing one hand, the total e.v. is 2% x 1.5R = 0.03R and the total variance is 1.32 X 1.5R = 1.98R. So, the Sharpe ratio
(akin to the DI, Desirability Index, which I reserved for positivee.v. situations = e.v./s.d.) is 0.03R/1.41R = 0.021.
For the twohand situation, the e.v. is 2% x 2 x R = 0.04R, while the variance is 2 x 1.80R = 3.60R. Sharpe ratio becomes 0.04R/1.90R = 0.021!!
Ha! Same thing. Interesting, huh?
Don

steve waugh: Re: Sorry for the delay
Thanks Don,
I wish your wife a speedy recovery.
It is a pleasure to read your posts (and your wonderful book BJA3 which I have read multiple times).In fact , I would like to take this opportunity to let you know that that IMHO, it ranks amongst the top 3 books I would recommend to anyone on BJ. I am awaiting the next book of yours.
I am also thankful that you put my misery to rest by clarifying the 2 hands 1 hand puzzle for negative scenario. I happened to notice one thingin making the Sd calculation from the variance, you ignored the square root of R but that should not affect the results as it would affect both the cases in equal measure.
Are there any other articles that are not published in BJA3 that I can purchase or read?
regards
waugh
> Sorry not to get back sooner. My wife broke her wrist,
> so things have been a bit hectic here for a couple of
> days.
> I suppose that, over 30+ years, no question has ever
> been asked more than the one/two hands one, and,
> frankly, I usually don't have the patience to answer
> again and again. But yours, below, has a different
> twist, because of the negative e.v., so I will do my
> best to give you a thorough answer.
> Alone, correct. With others, two will be better.
> Right.
> My intuition tells me no, but we will do the math in a
> second. It may be very close.
> It will help, but it will not be superior to playing
> one hand at table min. Again, we are assuming that you
> are alone at the table. And again, let's do the math
> later.
> So far, so good.
> Well, we haven't considered the risk yet, and since
> SCORE (for positivee.v. situations) is a
> riskadjusted measure, we would want to do the same
> thing here and consider e.v./s.d, or (e.v./s.d.)^2, as
> well. We'll do that in a minute.
> No, that isn't true. You can never reduce variance by
> betting more! You bet more, you have higher variance.
> Period.
> The maximum cardeating effect will be when you are
> alone. When going from two hands on the table (yours
> and the dealer's) to three hands (your two and the
> dealer's), you are adding 50% more cards per round. Of
> course, you are also betting twice as much per round,
> so you really have to consider the two together.
> So, before we do any more complicated math, just
> consider the following: suppose there are just enough
> cards left to deal six hands. Playing one hand, that
> will be three rounds, and I will bet three units,
> until the shoe ends. Playing two hands, I will play
> only two rounds, but each will have two units bet, so
> a total of four. Why do I want to risk four units
> before the shoe ends, instead of three? Well, because
> we haven't yet factored in the variance.
> Let's do some more math. Suppose the e.v. for a hand
> in this situation is 2%. You bet one unit. And
> suppose the s.d. is, say, 1.15 units. That makes the
> variance 1.15^2 = 1.32 squared units.
> For two hands (total of two units wagered), the
> variance becomes 2*[1.32 + 0.48 (the covariance)] =
> 3.60 squared units.
> But, in the second instance, we play R rounds per unit
> of time, while in the first, we play 1.5R rounds. So,
> playing one hand, the total e.v. is 2% x 1.5R =
> 0.03R and the total variance is 1.32 X 1.5R = 1.98R.
> So, the Sharpe ratio
> (akin to the DI, Desirability Index, which I reserved
> for positivee.v. situations = e.v./s.d.) is
> 0.03R/1.41R = 0.021.
> For the twohand situation, the e.v. is 2% x 2 x R =
> 0.04R, while the variance is 2 x 1.80R = 3.60R.
> Sharpe ratio becomes 0.04R/1.90R = 0.021!!
> Ha! Same thing. Interesting, huh?
> Don

Don Schlesinger: Re: Sorry for the delay
> Thanks Don,
> I wish your wife a speedy recovery.
Very kind of you. Thank you.
> It is a pleasure to read your posts (and your
> wonderful book BJA3
It's nice to be appreciated! :)
>which I have read multiple times).
You're a glutton for punishment! :)
> In fact, I would like to take this opportunity
> to let you know that that IMHO, it ranks amongst the
> top 3 books I would recommend to anyone on BJ. I am
> awaiting the next book of yours.
Thank you. Better be careful; if you say any more nice things, you may wind up being quoted in the blurbs section of the next edition! :)
> I am also thankful that you put my misery to rest by
> clarifying the 2 hands 1 hand puzzle for negative
> scenario.
In fact, it actually was a fresh look at an old question, and one that I think has really not been studied all that carefully. The result was mildly surprising to me.
> I happened to notice one thingin making the
> Sd calculation from the variance, you ignored the
> square root of R but that should not affect the
> results as it would affect both the cases in equal
> measure.
I actually absolutely knew that and wrestled with whether or not I should bother to put it in, for fear of further complicating the explanation. But, as is often the case, no good deed goes unpunished (!), and you caught me! There really is no excuse for taking shortcuts like that; it's sloppy, and, if you know me, "sloppy" is definitely not me! Sorry.
> Are there any other articles that are not published in
> BJA3 that I can purchase or read?
Yes, I'm sure there are a couple floating around here and there, but they are probably of a more elementary level, like something I did for Casino Player magazine a while back. You're not missing anything. And, at 500+ pages, just about everything worthwhile that I've written is probably in BJA3.
Thanks for the kind words.
Don

Don Schlesinger: PLEASE DON'T crosspost
Steve,
As you must know, BJ21 is a competing site to ap.com. And this page is by invitation only, so not open to all readers.
You mustn't cut and paste replies and threads from this site to a rival site. No one ever does that, as it's considered very poor etiquette.
It's too late for you to just go and post it over at BJ21 and then ask me, on that site, no less, if it's OK with me! You should have asked me on THIS site, if it was OK, in which case, in all honesty, I would have probably said no.
Don

steve waugh: Re: PLEASE DON'T crosspost
Don,
I knew that it was a competing site but made an error of judgement because I have seen you post quite a bit on that site(still no reason to do what I did). I thought your post would complete the solution and clarify issues.
I do apologize and this would not repeat.
Thanks once again.
regards
Waugh
Steve,
> As you must know, BJ21 is a competing site to ap.com.
> And this page is by invitation only, so not open to
> all readers.
> You mustn't cut and paste replies and threads from
> this site to a rival site. No one ever does that, as
> it's considered very poor etiquette.
> It's too late for you to just go and post it over at
> BJ21 and then ask me, on that site, no less, if it's
> OK with me! You should have asked me on THIS site, if
> it was OK, in which case, in all honesty, I would have
> probably said no.
> Don

What about Bob?: Re: Sorry for the delay
> So, the Sharpe ratio
> (akin to the DI, Desirability Index, which I reserved
> for positivee.v. situations = e.v./s.d.) is
> 0.03R/1.41R = 0.021.
> For the twohand situation, the e.v. is 2% x 2 x R =
> 0.04R, while the variance is 2 x 1.80R = 3.60R.
> Sharpe ratio becomes 0.04R/1.90R = 0.021!!
> Ha! Same thing. Interesting, huh?
> Don
So it seems to me that playing two hands when heads up in a negative count would be the proper play since that would burn through the negative shoe more quickly. Thus you would get to the next, potentially positive shoe, more quickly and less time would be wasted with negative EV. Or did i misunderstand something?
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