1. ## blackjack crusader: Grosjean VS Cacarulo on 10,10 Insurance

Grosjean on page 12 of "Beyond Counting" recommends taking insurance when holding 10,10 at below the indice value in order to lower variance. I believe Griffin in the "elephant edition" was also a proponent of this strategy?

Cacarulo on this site recommends taking 10,10 RA insurance at a higher indice value.

I can see how both are right, but which is superior?

2. ## Don Schlesinger: Re: Grosjean VS Cacarulo on 10,10 Insurance

> Grosjean on page 12 of "Beyond Counting"
> recommends taking insurance when holding 10,10 at
> below the indice value in order to lower variance. I
> believe Griffin in the "elephant edition"
> was also a proponent of this strategy?

James mentions this as a diversionary tactic, to deflect heat. It isn't meant to be mathematically rigorous.

> Cacarulo on this site recommends taking 10,10 RA
> insurance at a higher indice [index] value.

Cac's numbers are mathematically precise. They take into account the two-card hand combination, and he furnishes both an e.v.-maximizing index and a risk-averse index for each possible holding.

> I can see how both are right, but which is superior?

What does "superior" mean? E.v. maximizing? Optimal risk-averse? Best for cover?

Don

3. ## Rukus: But Don...

I understand Cacarulo calculated precise indices (RA and EVmax) for the SIDE BET of insurance. I think what the OP is asking (and Grosjean is suggesting beyond mere heat considerations) is that when taking insurance, should we consider our total action on the table, not just the side bet of insurance.

Grosjean seems to suggest that taking insurance early on some strong hands lowers your overall variance for the round, but as a consequence of taking insurance slightly early also lowers your EV for the round. He argues that the drop in variance is enough to outweigh the drop in EV, thus producing a greater EV/variance ratio (or SCORE proxy) for the your total round action than had you not taken the insurance early.

Now for other side bets like say lucky ladies, when we have to place that side bet before we see our cards, i agree we need to size our bets and determine our index plays as if the side bet and main bet are independent. BUT with insurance, we are able to make a decision with MORE information in our hands (literally! at least in pitch games ) and thus it seems to me like the two bets, insurance side + main, should be linked when making bet/play decisions.

So Don, what do you think about the idea that maybe we need to consider overall main bet + insurance side bet when determining our optimal play (since one bet is actually linked to the other with additional card knowledge).

So to repeat, all variables being the same, we need to choose the decision that leads to the highest SCORE. I think what grosjean is saying is that:
1. for a bet like insurance, when it is implicitly linked to our main bet by knowledge of additional cards, we should consider both bets/decisions when considering our total possible money/decisions for a round of blackjack, and
2. the reduction in overall variance from taking insurance early on certain hands is greater than the reduction in overall EV from placing a negative EV bet, hence a greater SCORE for that play (if it is even possible to have a SCORE for a single play).

Did that rambling make sense?

I've always used RA insurance indices as calculated with CVData, but since happening upon the Grosjean thoughts it has made me reconsider this...

Thanks for the time,
Rukus

> James mentions this as a diversionary tactic, to
> deflect heat. It isn't meant to be mathematically
> rigorous.

> Cac's numbers are mathematically precise. They take
> into account the two-card hand combination, and he
> furnishes both an e.v.-maximizing index and a
> risk-averse index for each possible holding.

> What does "superior" mean? E.v. maximizing?
> Optimal risk-averse? Best for cover?

> Don

4. ## Don Schlesinger: Re: But Don...

> I understand Cacarulo calculated precise indices (RA
> and EVmax) for the SIDE BET of insurance. I think what
> the OP is asking (and Grosjean is suggesting beyond
> mere heat considerations) is that when taking
> insurance, should we consider our total action on the
> table, not just the side bet of insurance.

I don't understand what you're saying. The insurance bet is half your bet. Are you asking about taking partial insurance?

> Grosjean seems to suggest that taking insurance early
> on some strong hands

What does "early" mean? You mean below the e.v.-maximizing index, right?

> lowers your overall variance for
> the round,

It's not as simple as that. Some risk-averse insurance indices are actually higher than the e.v.-maximizing one.

> but as a consequence of taking insurance
> slightly early also lowers your EV for the round. He
> argues that the drop in variance is enough to outweigh
> the drop in EV, thus producing a greater EV/variance
> ratio (or SCORE proxy) for the your total round action
> than had you not taken the insurance early.

All that you're stating, above, is that you're discussing the value of risk-averse insurance indices.

> Now for other side bets like say lucky ladies, when we
> have to place that side bet before we see our cards, i
> agree we need to size our bets and determine our index
> plays as if the side bet and main bet are independent.
> BUT with insurance, we are able to make a decision
> least in pitch games ) and thus it seems to me like
> the two bets, insurance side + main, should be linked
> when making bet/play decisions.

That's why Cac calculated a different insurance index for every possible starting two-card combination. And then, r-a indices as well. Either I'm not understanding your point, or we're talking at cross-purposes.

> So Don, what do you think about the idea that maybe we
> need to consider overall main bet + insurance side bet
> when determining our optimal play (since one bet is
> knowledge).

See above.

> So to repeat, all variables being the same, we need to
> choose the decision that leads to the highest SCORE. I
> think what grosjean is saying is that:
> 1. for a bet like insurance, when it is implicitly
> cards, we should consider both bets/decisions when
> considering our total possible money/decisions for a
> round of blackjack, and
> 2. the reduction in overall variance from taking
> insurance early on certain hands is greater than the
> reduction in overall EV from placing a negative EV
> bet, hence a greater SCORE for that play (if it is
> even possible to have a SCORE for a single play).

> Did that rambling make sense?

The "rambling" is nothing more than a description of r-a insurance indices. I believe Cac has furnished those, but maybe I will drop him a line and ask him if he has anything to add to this discussion.

Don

> I've always used RA insurance indices as calculated
> with CVData, but since happening upon the Grosjean
> thoughts it has made me reconsider this...

> Thanks for the time,
> Rukus

5. ## Rukus: Confusion abounds! Cac, Grosjean, others feel free to comment!

Thanks for your response Don --

I think you are right, we are just experiencing a crossing of the internet cables (or do we all use wireless these days?). I will try and take it step by step to avoid further confusion I may be causing. Appreciate your time, please stay with me on this long post!

I understand risk-averse indices. I understand that they often push an index a bit higher than EVmaximizing indices to account for additional variance, particularly for doubles/splits/insurance. I further understand that each decision is calculated by evaluating that play in isolation. For instance and to simplify things, when determining an index with simulations, the decision to hit or stand on say 16 v 10 will be evaluated at many different TCs. The TC at which standing produces a positive EV (or in this case, rather, less negative EV) will be given as the "optimal" EV maximizing index. The TC at which the EV/variance ratio (or something to that effect) is maximized will be the optimal risk-averse index. I think we are in agreement here . Thus, I am not talking about RA indices here and will attempt to clarify.

Cac has calculated both EVmax and RA indices for insurance, I agree. They are in the archives and I've been using the idea for a while now.

What I was trying to explain is that the "optimal" index (whether we are talking EVmax or RA type, it does not matter) for taking insurance is calculated independently, just as for any other playing decision:

Taking insurance will be simulated at a range of TCs. The TC at which your EV is maximized is called the EV-maximizing index. The TC at which the ratio of EV/variance (or something to this effect, I actually admit I am not positive what ratio is used) is maximized is called the Risk-averse index. Agreed so far?

My point (and I think Grosjean's, et al) is that this index is calculated *solely considering the money bet on the insurance bet*. So if you had flat-bet one unit on each main hand, when simulating insurance to determine the proper index, Cac or any program like CVData, will look at what index will get you maximum EV or EV/Variance with respect to JUST the ensuing half-unit insurance bet. Cac or CVData will ignore the results of the main hand (at least this is what I believe is being done).

Now! If that is the case, as I believe it is (i.e. that calculating the insurance index takes into account only the EV or EV/Variance ratio of just the insurance bet), there may be room for improvement when considering risk-averse decisions and bets. Would you agree that the insurance bet is somehow "linked" to our main hand since we have additional information before making this side bet? If so, Grosjean seems to suggest, and I and the OP are thinking, that we should not calculate the insurance index in the traditional sense, based solely on the TC that maximizes the EV/variance ratio of just the half unit insurance bet - we should determine an index that maximizes the EV/variance ratio of our entire hand consisting of our main bet plus the insurance bet if it is made. Does that make sense?

> I don't understand what you're saying. The insurance
> partial insurance?

No, I am talking about full insurance (though partial is also a possibility). Hopefully what I wrote above clraifies what I was trying to say

> What does "early" mean? You mean below the
> e.v.-maximizing index, right?

Well, yes. However, after further thought, we should probably limit the discussion to the risk-averse index since the whole idea behind Grosjean's comments are to lower variance... But yes, by "early" I mean taking insurance before the risk-averse index would say to.

> It's not as simple as that. Some risk-averse insurance
> indices are actually higher than the e.v.-maximizing
> one.

Agreed here . They usually are for doubles, spits, and insurance or any other variance-increasing bet/decision.

> All that you're stating, above, is that you're
> discussing the value of risk-averse insurance indices.

Not quite, hopefully I clarified my thoughts above. You'll let me know I guess .

> That's why Cac calculated a different insurance index
> for every possible starting two-card combination. And
> then, r-a indices as well. Either I'm not
> understanding your point, or we're talking at
> cross-purposes.
Agreed, he did a great job calculating insurance indices, both EVmax and RA, in the traditional sense. I have used this to-date. I think I just caused misunderstanding in my last post.

> The "rambling" is nothing more than a
> description of r-a insurance indices. I believe Cac
> has furnished those, but maybe I will drop him a line
> and ask him if he has anything to add to this
> discussion.
I hope I clarified my thoughts that what I was describing is a risk-averse concept, but not quite just the risk-averse index for insurance in the traditional sense. The index needs to be calculated accounting for results of the full hand, main bet plus insurance, and not just the insurance portion. This is the crux of the issue and what Grosjean was trying to say I think.

Thoughts?

THANKS!
Rukus

6. ## Don Schlesinger: Re: Confusion abounds! Cac, Grosjean, others feel free to comment!

> Taking insurance will be simulated at a range of TCs.
> The TC at which your EV is maximized is called the
> EV-maximizing index. The TC at which the ratio of
> EV/variance (or something to this effect, I actually
> admit I am not positive what ratio is used) is
> maximized is called the Risk-averse index. Agreed so
> far?

Yes. No different from any other r-a index.

> My point (and I think Grosjean's, et al) is that this
> index is calculated *solely considering the money bet
> on the insurance bet*.

No, it isn't. Just as r-a indices can be different depending on what percent of your bank is risked on the hand, the same can be trueof insurance r-a indices. They could be different depending on the amount of the original wager, as a percent of total bank. And, obviously, the amount of the original wager immediately impacts the amount of the insurance wager.

> So if you had flat-bet one unit
> on each main hand, when simulating insurance to
> determine the proper index, Cac or any program like
> CVData, will look at what index will get you maximum
> EV or EV/Variance with respect to JUST the ensuing
> half-unit insurance bet.

No, that isn't true. If it were, why would all the indices for the different two-card holdings of the various hands be different?? To calculate the variance, you obviously have to include the result of the main hand. How else could you get different variances, if you were just considering whether the dealer had a natural or didn't? I don't think you understand this point.

> Cac or CVData will ignore the
> results of the main hand (at least this is what I
> believe is being done).

I believe you are wrong.

> Now! If that is the case, as I believe it is (i.e.
> that calculating the insurance index takes into
> account only the EV or EV/Variance ratio of just the
> insurance bet),

See above. I believe your premise is wrong.

> there may be room for improvement when
> considering risk-averse decisions and bets. Would you
> agree that the insurance bet is somehow
> "linked" to our main hand since we have
> additional information before making this side bet?

Of course. But, I can't believe that you think that Cac didn't take this into account.

> If so, Grosjean seems to suggest, and I and the OP are
> thinking, that we should not calculate the insurance
> index in the traditional sense, based solely on the TC
> that maximizes the EV/variance ratio of just the half
> unit insurance bet - we should determine an index that
> maximizes the EV/variance ratio of our entire hand
> consisting of our main bet plus the insurance bet if
> it is made. Does that make sense?

It makes sense, because that's what everyone is doing! :-)

> Now to your individual points/questions:

> No, I am talking about full insurance (though partial
> is also a possibility). Hopefully what I wrote above
> clarifies what I was trying to say

OK.

> Well, yes. However, after further thought, we should
> probably limit the discussion to the risk-averse index
> since the whole idea behind Grosjean's comments are to
> lower variance... But yes, by "early" I mean
> taking insurance before the risk-averse index would
> say to.

Fine.

> Agreed, he did a great job calculating insurance
> indices, both EVmax and RA, in the traditional sense.
> I have used this to-date. I think I just caused
> misunderstanding in my last post.
> I hope I clarified my thoughts that what I was
> describing is a risk-averse concept, but not quite
> just the risk-averse index for insurance in the
> traditional sense. The index needs to be calculated
> accounting for results of the full hand, main bet plus
> insurance, and not just the insurance portion. This is
> the crux of the issue and what Grosjean was trying to
> say I think.

> Thoughts?

I don't think James has done anything different from what was already done.

Don

7. ## Rukus: Oy :)

Thanks again Don, and i apologize if i am truly missing something or causing you headaches . But that said, I must apologize for continuing to belabor the point here...

> No, it isn't. Just as r-a indices can be different
> depending on what percent of your bank is risked on
> the hand, the same can be trueof insurance r-a
> indices. They could be different depending on the
> amount of the original wager, as a percent of total
> bank. And, obviously, the amount of the original wager
> immediately impacts the amount of the insurance wager.

100% agreed with this point. the fraction of your BR bet on the main hand affects what you bet on the insurance and can affect what we are agreeing to call the "traditional" index.

> No, that isn't true. If it were, why would all the
> indices for the different two-card holdings of the
> various hands be different?? To calculate the
> variance, you obviously have to include the result of
> the main hand. How else could you get different
> variances, if you were just considering whether the
> dealer had a natural or didn't? I don't think you
> understand this point.

I do not agree that to calculate variance of the sidebet you need to include the results of the main hand. see my example below of someone just standing behind a table and ONLY playing the insurance bet when he feels like it. his EV and variance will not be tied to the whether the main hand he is back-betting wins. it cannot be so since insurance is checked for and bets paid/collected before the main hand is even played.

> I believe you are wrong.
> See above. I believe your premise is wrong.
I am trying to confirm this, and would love to know whether or not i am wrong here. this can answer the question, if we know what EV and variance Cac or even Norm/CVData use. It is my thesis that they are using the insurance bet's independent EV and variance (that i describe below can be obtained by just simulating a player only playing the insurance bet but not the main hand). You say I may be mistaken. I would LOVE to know for sure if you can confirm with Cac and/or Norm.

> Of course. But, I can't believe that you think that
> Cac didn't take this into account.

This is exactly what I would like to have clarified if you can be in touch with Cac and confirm.

I think Cac takes into account the main hand only to say, "ok i see a TC of, say 3, but i know i am holding two tens in my hand, which is different than me seeing a TC of 3 and holding no tens in my hand". thus the probability the dealer is holding a 10 in the hole differs for a given TC depending on what you are holding in your own hand. that is what i believe Cac uses the main hand's information for, purely for determining the change in probability of dealer holding a 10 in the hole as well. This is part of what i am trying to confirm with Cac and/or Norm.

i guess what i am TRULY asking is this: is the EV and variance Cac is using in his sims coming from the main hand or just the side bet. in my mind, it is perfectly understandable to believe that when looking at when to make a side bet you would just look at the EV of that side bet and the variance of just that side bet. i would like confirmed whether this is what Cac has done. if it is what he has done, than Grosjean's point has not been addressed.

what you are saying i do not understand is what i am arguing for: the side bet itself does have its own EV and variance.

imagine we are in a casino that allows someone who just stands behind a table without playing a hand himself to take insurance on another person's hand. his EV and variance will be purely based on the insurance side bet.

agreed? if you say i am wrong on this point and say that someone purely playing the insurance bet (but not the main bet) does not have an EV and variance different from someone playing a regular blackjack hand, then you can stop reading and i will drop the argument.

but i am maintaining that since this player is only betting on the side bet, not the main bet, his wins and losses are not tied to whether the main bettor wins or loses. It is this "independent" EV and variance of someone only playing the insurance side bet that i believe, and would love to have confirmed, Cac is using in his index calculations. as a matter of fact, this SHOULD be the EV and variance he looks at while calculating his indices according to what we agree is the "traditional" way to calculate indices.

What i am saying is now take a typical player who plays the main hand and the insurance bet at times. his EV is a combination of the EV from playing the blackjack hand plus the EV from playing the insurance side bet and his variance is a combination of the variance from playing the main blackjack hand plus the variance of the insurance side bet itself. I think Grosjean is commenting that it is this "global" or "total" EV and variance that should be taken into account when determining a risk-averse insurance index.

> I don't think James has done anything different from

He must be doing something different if he is recommending taking insurance "earlier", ie at a lower TC, than the index (for reasons other than heat diffusion) when holding say 10,10 vs Cac's original sims that say take insurance "later" than the normal insurance index for that same hand!

Thanks again Don,
Rukus

8. ## blackjack crusader: Muddying the Waters?

> Thanks again Don, and i apologize if i am truly
> missing something or causing you headaches . But
> that said, I must apologize for continuing to belabor
> the point here...

> 100% agreed with this point. the fraction of your BR
> bet on the main hand affects what you bet on the
> insurance and can affect what we are agreeing to call

> I do not agree that to calculate variance of the
> sidebet you need to include the results of the main
> hand. see my example below of someone just standing
> behind a table and ONLY playing the insurance bet when
> he feels like it. his EV and variance will not be tied
> to the whether the main hand he is back-betting wins.
> it cannot be so since insurance is checked for and
> bets paid/collected before the main hand is even
> played.
> I am trying to confirm this, and would love to know
> whether or not i am wrong here. this can answer the
> question, if we know what EV and variance Cac or even
> Norm/CVData use. It is my thesis that they are using
> the insurance bet's independent EV and variance (that
> i describe below can be obtained by just simulating a
> player only playing the insurance bet but not the main
> hand). You say I may be mistaken. I would LOVE to know
> for sure if you can confirm with Cac and/or Norm.

> This is exactly what I would like to have clarified
> if you can be in touch with Cac and confirm.

> I think Cac takes into account the main hand only to
> say, "ok i see a TC of, say 3, but i know i am
> holding two tens in my hand, which is different than
> me seeing a TC of 3 and holding no tens in my
> hand". thus the probability the dealer is holding
> a 10 in the hole differs for a given TC depending on
> what you are holding in your own hand. that is what i
> believe Cac uses the main hand's information for,
> purely for determining the change in probability of
> dealer holding a 10 in the hole as well. This is part
> of what i am trying to confirm with Cac and/or Norm.

> i guess what i am TRULY asking is this: is the EV and
> variance Cac is using in his sims coming from the main
> hand or just the side bet. in my mind, it is perfectly
> understandable to believe that when looking at when to
> make a side bet you would just look at the EV of that
> side bet and the variance of just that side bet. i
> would like confirmed whether this is what Cac has
> done. if it is what he has done, than Grosjean's point

> what you are saying i do not understand is what i am
> arguing for: the side bet itself does have its own EV
> and variance.

> imagine we are in a casino that allows someone who
> just stands behind a table without playing a hand
> himself to take insurance on another person's hand.
> his EV and variance will be purely based on the
> insurance side bet.

> agreed? if you say i am wrong on this point and say
> that someone purely playing the insurance bet (but not
> the main bet) does not have an EV and variance
> different from someone playing a regular blackjack
> hand, then you can stop reading and i will drop the
> argument.

> but i am maintaining that since this player is only
> betting on the side bet, not the main bet, his wins
> and losses are not tied to whether the main bettor
> wins or loses. It is this "independent" EV
> and variance of someone only playing the insurance
> side bet that i believe, and would love to have
> confirmed, Cac is using in his index calculations. as
> a matter of fact, this SHOULD be the EV and variance
> he looks at while calculating his indices according to
> what we agree is the "traditional" way to
> calculate indices.

> What i am saying is now take a typical player who
> plays the main hand and the insurance bet at times.
> his EV is a combination of the EV from playing the
> blackjack hand plus the EV from playing the insurance
> side bet and his variance is a combination of the
> variance from playing the main blackjack hand plus the
> variance of the insurance side bet itself. I think
> Grosjean is commenting that it is this
> "global" or "total" EV and
> variance that should be taken into account when
> determining a risk-averse insurance index.

> He must be doing something different if he is
> recommending taking insurance "earlier", ie
> at a lower TC, than the index (for reasons other than
> heat diffusion) when holding say 10,10 vs Cac's
> original sims that say take insurance
> "later" than the normal insurance index for
> that same hand!

> Thanks again Don,
> Rukus

Cacarulo composition dependent RA insurance 10,10 vs dealer A at TC 4

Griffin
"Insure a Good Blackjack Hand part 2"
If I understand. At precisely the insurance index (borderline decision) insure 20, 19, 18, 11, 10, 9 in order to reduce variance.
and
Grosjean page 12 "beyond counting"
"if the insurance count is exactly 0, you will lower your variance by insuring any soft hand, any 8-11 and 18-21.

These seem to contradcit each other?
Cac as opposed to Griffin and Grosjean

Let's assume optimal betting. However, Don I believe you state in BJA 3 that whatever fraction of kelly is used the RA indices would remain the same. page 374 3rd paragraph.

Don thanx for your time. I am sure we are driving you to the brink!

9. ## Don Schlesinger: Re: Oy :)

I have written to Cac and to Zenfighter, inviting them to look at this thread. If they have anything to add, they will surely post here.

In the meantime, I saw nothing in Beyond Counting to imply that James was doing something different. When you take insurance early, you may or may not reduce variance. Clearly, if the r-a index is higher than the normal index, then taking insurance early has just the opposite effect: it increases variance!

I understand all of your arguments, and I understand the concept of a person not playing the main hand but just taking insurance. Of course his results have nothing to do with the main hand. But, yet again, I do NOT believe that this is what Cac is doing.

Either way, it will be great to hear from him here.

Don

10. ## Don Schlesinger: Ethier/Canjar

Stewart Ethier has edited a wonderful new book entitled "Optimal Play: Mathematical Studies of Games and Gambling," in which there are new papers published by some of our best theoreticians.

The first paper is "Advanced Insurance Play in 21: Risk Aversion and Composition Dependence," by R. Michael Canjar. I read it awhile ago, when Stewart sent me the book, but would have to reread it to best answer the questions in the above discussion.

In any event, all the answers -- and then some! -- can be found in this article. In addition, there is a table giving the adjustments to the e.v-maximizing Hi-Lo insurance indices, when hand composition and risk-aversion are BOTH taken into account, for every starting holding!

I'll try to reread the article, but, in the meantime, for 6 decks, S17, DAS, and a player T,T, the CD adjustment is to ADD 0.26, but the RA/CD index adjustment is to SUBTRACT 0.3 for a 2% wager and subtract 1.1 for a 5% wager. Of course, the Hi-Lo standard index is 3.0.

Hope this helps a little.

Don

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