Alternative Index Calculation Method

[k_c]

Or, more specifically, the index (the decision) is dependent not only on the TC but also on the current depth. This is probably non-linear, in as the deeper you are, the more the depth becomes important.

I agree.

I suspect that for the most part indices will be fairly stable but when you approach running out of cards they could flop around like a fish out of water.

I used to have a bunch of tables on my website that showed how insurance indices varied for Hi-Lo and KO as a function of hand composition, running count and number of cards remaining for 1,2,4,6,8 decks. Insurance indices are simpler because all that is needed is probability of a ten as dealer's hole card.

Below is data for insuring A-A and T-T for single deck and 8 decks using Hi-Lo.
Hand composition is much more of a factor for single deck.
Indices may be most stable when 50% of shoe is dealt.

Single deck Hi-Lo
	[u]RC	Num Cards	TC[/u]

A-A	<=-3	Never insure	<=-3
	-2	>=42		-2.48
	-1	>=22		-2.36
	0	Exactly 2, >=4	0
	+1	Always insure

T-T	<0	Never insure	<0
	0	Exactly 2	0
	+1	<=17		+3.06
	+2	<=34		+3.06
	+3	<=42		+3.71
	+4	Always insure

8 decks Hi-Lo
	[u]RC	Num Cards	TC[/u]

A-A	<0	Never insure	<0
 	0  	Exactly 2 	0  
 	+1  	<=17 		+3.06  
 	+2  	<=38 		+2.74  
  	+3  	<=58 		+2.69  
  	+4  	<=78 		+2.67  
  	+5  	<=98 		+2.65  
  	+6  	<=119 		+2.62  
  	+7  	<=139 		+2.62  
  	+8  	<=159 		+2.62  
  	+9  	<=179 		+2.61  
  	+10  	<=198 		+2.63  
  	+11  	<=218 		+2.62  
  	+12  	<=238 		+2.62  
  	+13  	<=257 		+2.63  
  	+14  	<=276 		+2.64  
  	+15  	<=294 		+2.65  
  	+16  	<=312 		+2.67  
  	+17  	<=329 		+2.69  
  	+18  	<=344 		+2.72  
  	+19  	<=357 		+2.77  
  	+20  	<=367 		+2.83  
  	+21  	<=374 		+2.92  
  	+22  	<=379 		+3.02  
  	+23  	<=381 		+3.14  
  	+24  	<=383 		+3.26  
  	+25  	<=384, 384* 	+3.39  
  	+26  	Always insure 

T-T	<0	Never insure	<0
  	0  	Exactly 2 	0  
  	+1  	<=14 		+3.71  
  	+2  	<=30 		+3.47  
  	+3  	<=46 		+3.39  
  	+4  	<=62 		+3.35  
  	+5  	<=78  		+3.33  
  	+6  	<=94 		+3.32  
  	+7  	<=110 		+3.31  
  	+8  	<=126 		+3.30  
  	+9  	<=142 		+3.30  
  	+10  	<=158 		+3.29  
  	+11  	<=174 		+3.29  
  	+12  	<=189 		+3.30  
  	+13  	<=205 		+3.30  
  	+14  	<=220 		+3.31  
  	+15  	<=236 		+3.31  
  	+16  	<=251 		+3.31  
  	+17  	<=266 		+3.32  
  	+18  	<=281 		+3.33  
  	+19  	<=295 		+3.35  
  	+20  	<=309 		+3.37  
  	+21  	<=322 		+3.39  
  	+22  	<=334 		+3.43  
  	+23  	<=345 		+3.47  
  	+24  	<=354 		+3.53  
  	+25  	<=362 		+3.59  
  	+26  	<=367 		+3.68  
  	+27  	<=371 		+3.78  
  	+28  	<=374 		+3.89  
  	+29  	<=376 		+4.01  
  	+30  	<=377 		+4.14  
  	+31  	<=378, 378* 	+4.26  
  	+32  	Always insure

 

[jack.jackson]

Or, more specifically, the index (the decision) is dependent not only on the TC but also on the current depth. This is probably non-linear, in as the deeper you are, the more the depth becomes important.

I also believe depends on the hand. For example, i believe splits, insurance, and soft doubles are only affected by 1/2 as much as Hard Doubles. Its amazing how far past your index you can go when theres about 1/2 deck remaining when it comes to doubling a hard hand.

 

[Gramazeka]

http://www.blackjackinfo.com/bb/showthread.php?p=196261#post196261

 

[blackjack avenger]

Over Double Kelly a Bad Thing

In essence there is no such thing as overbetting +EV (with the caveat that what's right for an individual is a subjective decision.)

If you bet over double kelly doesn't your bank shrink?

:joker::whip:
good cards

 

[blackjack avenger]

It's probably useful to remind that the matter is not about just EV loss, split/stand, but the effect from burning the cards. About losing EV by pulling other two cards from the positive slug when splitting TT vs 6. I believe, Casino Verite creators should help (if they understand the subject, of course). It's very difficult to solve the task analitically.
Polevoy and others could understand the problem better if they had talked aluod: "WE CONSIDER COUNT TAKING INTO ACCOUNT THE NUMBER OF REMAINING CARDS!!" The point is that immediately arises the parameter "price of taken card", in lack of such a few pages of this forum are quite useless.
Indeed, the count of +5 with one deck left (say, there's no penetration), and ten decks left (infinite deck as a bound) are different game situations. In the first case any pulled card may change the count significantly, unlike in the latter.
Limited number of remaining cards brings out "index drift" effect. In my opinion there'll be different data for different situations:

1.Penetration.

2.Number of cards left before and after the cut card, the number of taken cards (depends on the two).

3.TrueCount exact to tenths (it's probably better to take running count then)

4. Cards in play zone.

Accordingly, when one of the parameters changes we'll have different value of the burned card. And because in reality the count frequency is different from theoretical, the solution gets even harder. How shall we count the variance? That's why this task is analitically solvable, I believe, though very difficult.
Once again, I remind the question, which is "EV loss when burning cards in TTvs6 situation.

A sim that plays hands and shoes would address your points?
:joker::whip:
good cards

 

[zengrifter]

The traditional method for computing an index was to try different indices, and determine which value resulted in the highest EV (expected value).

Then came RA indices, in which one would try different indices, and determine which value resulted in the highest CE (certainty equivalent), which is based on one's bankroll, kelly factor, etc.

I propose another method for index generation, based on minimizing N0. N0 = Var/EV^2. So essentially we are maximizing (EV^2/Var). The reason I propose this, is because this is what we aim to maximize every time we calculate the optimal bets. The entire optimal bet theory is based on minimizing N0, and I see no reason why we shouldn't minimize N0 when we generate indices.

So to summarize, possible methods for indices:
1. (Traditional) Maximize EV
2. (Risk Averse) Maximize EV - Var/(2 * KellyFraction * Bankroll)
3. (Proposed) Maximize EV^2/Var

Thoughts? Criticisms? Comments?

I would say that #3 is a weaker effect than #2. #1 is the weakest.
And the results in real play will pretty much be the same using any.

I know of more than one pro who don't even use indices as such anymore. Just 'zones' so to speak. zg

 

[aslan]

I am no statistical guru but from what I understand standard deviation = sqrt(variance)

Standard deviation is a measure of how spread out a series of data points are from the mean.
If data points are 1,3,5,7,9 then mean = (1+3+5+7+9)/5 = 5
Variance is defined as ((1-5)^2+(3-5)^2+(5-5)^2+(7-5)^2+(9-5)^2)/5 = 8
Standard deviation = sqrt(variance) = sqrt(8) = 2.83
So data points from (5-2.83) to (5+2.83) = (2.17 to 7.83) are within 1 standard deviation of the mean in this example.

The point is that variance and standard deviation are just constant characteristics. So it would seem maximizing EV^2/var is the same as maximizing EV^2/SD^2 which is the same as maximizing EV^2/(constant value).

So I would say maximizing EV^2/var boils down to the same thing as simply maximizing EV.

I'll take that as a YES? Or NO?

Break it down fellows. Should us less mathematically endowed players surmise that current indexes should suffice, or if not, what gains could be made by adjusting them and at what cost?

 

[k_c]

If you bet over double kelly doesn't your bank shrink?

:joker::whip:
good cards

Setting Kelly aside for a moment I think the more you wager in a positive EV situation, the more you can expect to win in the long run. A big wager comes with the cost of losing your entire bankroll though.

To try and describe this statistically suppose there are X number of people that all bet the same way on positive EV and bet big. Maybe the big betting results in all but 1 of the people going broke. Although most go broke the 1 that succeeds is wildly successful and brings the average winnings of all up. The larger the betting the more bankruptcies but also the larger the average winnings are.

http://www.marvinfrench.com/p1/blackjack/optimal.pdf

 

[assume_R]

I would say that #3 is a weaker effect than #2. #1 is the weakest.

Why do you say that? I would guess 3. would be the strongest, but perhaps that is just because I want to taut my own idea 2 is personalized to your own bankroll, while 3 takes into account variance in an objective fashion (minimizing N0).

And the results in real play will pretty much be the same using any. I know of more than one pro who don't even use indices as such anymore. Just 'zones' so to speak.

Agreed. This was an older post of mine, and since then I have just been focusing most of my energy on finding better opportunities than using better indices. "Zones" are perfectly fine, but realize that I am playing with a pretty small bankroll and hence I have been looking for every possible edge I can get to reduce my RoR, and maximize my EV.

 

[blackjack avenger]

EV Not Quite the Right Guide

I am playing with a pretty small bankroll and hence I have been looking for every possible edge I can get to reduce my RoR, and maximize my EV.

I think you know this, you want to maximize SCORE and minimize NO. To think max EV even if considering ror is not optimal. So look to RA indices over EV indices. As far as betting play a fraction of kelly, probably .5 to .25. Try to use an optimal bet ramp and avoid negative hands.

:joker::whip:
good cards

 

[assume_R]

I think you know this, you want to maximize SCORE and minimize NO. To think max EV even if considering ror is not optimal. So look to RA indices over EV indices. As far as betting play a fraction of kelly, probably .5 to .25. Try to use an optimal bet ramp and avoid negative hands.

:joker::whip:
good cards

Yup, doing all that, thanks.

However, it should be noted that that maximizing SCORE and minimizing N0 is NOT the same as minimizing RoR. Simple example - run cvcx. Then, notice as you increase the spread, you can get an extremely high SCORE and extremely low N0, but these don't necessarily correlated with the lowest RoR. For example, a 1-8 spread might have the minimum RoR, but a 1-10 spread will have a higher SCORE and RoR.

 

[blackjack avenger]

Yes & No

Yup, doing all that, thanks.

However, it should be noted that that maximizing SCORE and minimizing N0 is NOT the same as minimizing RoR. Simple example - run cvcx. Then, notice as you increase the spread, you can get an extremely high SCORE and extremely low N0, but these don't necessarily correlated with the lowest RoR. For example, a 1-8 spread might have the minimum RoR, but a 1-10 spread will have a higher SCORE and RoR.

Remember SCORE is suppose to be 10g, kelly (fixed?), optimal betting.

One can have an optimal bet ramp, kelly
One can also have an optimal 1-4 or 1-10 etc. bet ramp, kelly
They can be the same but not necessarily.

Once that is established, then one cuts the bets to correspond with half, third or fourth kelly or if your sim allows you to set whatever ror you want with your starting bank.

:joker::whip:
good cards

 

[blackjack avenger]

Sim TC Conjecture

it will be rare to make a min bet and then end up with a +4 TC by the time you make your playing decision, and likewise it will be rare to have a max bet out and yet be at a TC of 0 or +1 by the time you make your decision. I suppose that would happen more often in a pitch game, in which case you may be right that the current bet size may impact the optimal index value.

Every double and split indice has an EV/RA barrier where you act or not. The extra bet size may be large compared to the EV and not optimal, but as you point out this should not happen often. Somtimes based on original bet size when you act you will be more risk averse and sometimes more ev producing with regard to optimal play. This is perhaps another reason to bet conservatively.
:joker::whip:
good cards