Dynamic Insurance

[k_c]

What we still do not agree on is the way of presenting the data. It is very complicated to carry out a control that depends on each depth.

I kind of see what you may be doing but I likely don't know all of the details.

A card counter is aware of only 2 things - present running count and some sort of estimate of penetration. The data we agree on eliminates true count to find a strategy. The purpose of true count is to simplify a lot of data to a single value, although it may not be perfect. I have not given up on sticking with running count and avoiding true count, which wouldn't be perfect either.

Consider this solution for generic single deck insurance, no side counting.

let dR = decks remaining = (cards remaining)/52
let RCi = running count index

RCi = 52/36*dR - 1/18

if RCi turns out to be >0 and <1, round to 1
if RCi turns out to be >1 and <2, round to 2
etc.

if RCi=0 or RCi=1 then that is the index

if present RC>=RCi, buy insurance

I think the above approach yields the correct decision for all cards remaining except 1.

Instead of having to compute a true count, RCi is computed from decks remaining and constant values.

Just an idea. I can explain how I get the constant values. Also I think I can use this approach for RCi estimate when side counting aces.

k_c

[Cacarulo]

I kind of see what you may be doing but I likely don't know all of the details.

A card counter is aware of only 2 things - present running count and some sort of estimate of penetration. The data we agree on eliminates true count to find a strategy. The purpose of true count is to simplify a lot of data to a single value, although it may not be perfect. I have not given up on sticking with running count and avoiding true count, which wouldn't be perfect either.

Consider this solution for generic single deck insurance, no side counting.

let dR = decks remaining = (cards remaining)/52
let RCi = running count index

RCi = 52/36*dR - 1/18

if RCi turns out to be >0 and <1, round to 1
if RCi turns out to be >1 and <2, round to 2
etc.

if RCi=0 or RCi=1 then that is the index

if present RC>=RCi, buy insurance

I think the above approach yields the correct decision for all cards remaining except 1.

Instead of having to compute a true count, RCi is computed from decks remaining and constant values.

Just an idea. I can explain how I get the constant values. Also I think I can use this approach for RCi estimate when side counting aces.

k_c

If what you are interested in is finding an index that avoids the conversion to TC, you have to go for the RC side. In SD it is interesting to know that for insurance it would not be necessary to convert to TC. The trick is this: We shall buy insurance only when the RC >= +1 and the total remaining cards is less than or equal to 38. This captures ALL the positive EV available. For any other option the expected value is negative or zero. The only exception that will obviously never happen is when the RC is equal to zero and there are only two cards left. In that case there is also positive EV.
What is simpler than the above? Coincidentally +1 with 38 cards remaining matches the perfect index whose TC = +1/38 * 52 = +1.368421 that we had discussed earlier.

Sincerely,
Cac

[k_c]

We shall buy insurance only when the RC >= +1 and the total remaining cards is less than or equal to 38.

Sincerely,
Cac

As you stated if there are 2 cards left and RC >= 0 buy insurance, but nothing is perfect and this is certainly good enough.

Single deck is very simple to remember by just only considering RC but the method could hopefully apply to more complicated data with minimal inconsistencies. Still just an idea.

k_c

[aceside]

As you stated if there are 2 cards left and RC >= 0 buy insurance, but nothing is perfect and this is certainly good enough.

Single deck is very simple to remember by just only considering RC but the method could hopefully apply to more complicated data with minimal inconsistencies. Still just an idea.

k_c

Earlier I calculated this: insurance contributes a tiny portion to player's edge. The probability of a dealer ace/face/ten up card as a function of TC can be written as,


P(TC)=0.001966xTC + 0.07674.


At TC=+6.5, when the dealer shows an ace up card, the player edge gain from insurance is 7.4%, and therefore, the average player edge gain from insurance is 0.66%.


However, the player edge gain from additional blackjacks at TC=+6.5 is 0.5x(6.4%-4.7%)=0.85%.


This means player's blackjacks are about three times more important than dealer's ones, if the insurance bet is limited to 0.5 of the main bet.

[DSchles]

This means player's blackjacks are about three times more important than dealer's ones, if the insurance bet is limited to 0.5 of the main bet.

And this assumes a player's bet spread of???

Don

[Norm]

insurance contributes a tiny portion to player's edge.

Well, lots of little things have small effects. It's the sum of lots of little things that matter.

[DSchles]

So, just so that everyone knows how wrong egregiously wrong aceside is, consider the following: 4.5/6, S17, DAS, play-all, 1-12 spread. First, you play just BS--no deviations. Your SCORE is 11.837. Now, you add a single deviation--insurance. How much is that "tiny portion"? What does insurance add to your edge? Answer: 18.51%!

Let's look at it a different way: You now use 117 deviations above BS. Insurance is one of them. What percentage of all the gain that you can acquire from ALL the deviations is provided by insurance? That "tiny portion" of your gain above BS from using ALL indices is ... 23.85%!

Finally, it's obvious that you have no gain with flat betting BS, but you have a gain when you use BS and a spread. So, what percentage of ALL your gain (total SCORE), both from BS and using indices, is furnished by insurance alone? Answer: 10.98%.

Moral of the story: Don't rag on insurance!

Don

[Freightman]

Freightman recently said

The most valuable index of all based on frequency of occurrence combined with dollars on table is insurance

[aceside]

And this assumes a player's bet spread of???

Don

The above calculation of mine is independent of bet spread.

So, just so that everyone knows how wrong egregiously wrong aceside is, consider the following: 4.5/6, S17, DAS, play-all, 1-12 spread. First, you play just BS--no deviations. Your SCORE is 11.837. Now, you add a single deviation--insurance. How much is that "tiny portion"? What does insurance add to your edge? Answer: 18.51%!

I am not so confident with this part, and I brought up this topic to understand it. We consider a 6-deck, 4.5/6 pen, S-17, and DAS game. Let me calculate this number based on my theory. The total player edge gain from card counting is about 4% when TC=+6.5, while the player edge gain from insurance is 0.5*0.66%=0.33%; therefore, insurance produces 0.33%/4%=8.3% of the total player edge gain.

In comparison, player blackjack produces 0.85%/4%=21.3% of the total player edge gain when TC=+6.5.

[DSchles]

My comment had nothing to do with a TC of +6.5 or any other TC. It had to do with the contribution of insurance to our total edge playing the game that I described. I already had explained to you that the contribution of insurance to edge is linear and that, starting at +3, it adds about 2.3% per Hi-Lo TC. So, as (6.5 -3) x 2.3 = 8.05%, that is your edge from insurance at that one particular count. I'm not sure why anyone should care, but I've furnished you a value.

Don

[ShipTheCookies]

As far as I'm concerned, if you are not winning your insurance bets 100% of the time like we do, then you're just guessing and gambling.

[Secretariat]

As far as I'm concerned, if you are not winning your insurance bets 100% of the time like we do, then you're just guessing and gambling.

Playing perfect insurance is far from winning the insurance bet 100% of the time.
The worse it can be is 33.3% over the long haul and won't likely be over 40% overall.
Is that what you meant or are you referring to a non-mathematical technique?

By the way, Don how much does perfect insurance add to TC+3 index insurance?

[Cacarulo]

The above calculation of mine is independent of bet spread.



I am not so confident with this part, and I brought up this topic to understand it. We consider a 6-deck, 4.5/6 pen, S-17, and DAS game. Let me calculate this number based on my theory. The total player edge gain from card counting is about 4% when TC=+6.5, while the player edge gain from insurance is 0.5*0.66%=0.33%; therefore, insurance produces 0.33%/4%=8.3% of the total player edge gain.

In comparison, player blackjack produces 0.85%/4%=21.3% of the total player edge gain when TC=+6.5.

The edge at a TC of +6.5 is:

| 6.5 | 0.00083473498616494 | 0.08273895754443319 |

or, if you prefer: 8.27% and a frequency of 0.08347%

The edge at a TC of +6 is:

| 6 | 0.00603608732656385 | 0.08057113743332595 |

or, if you prefer: 8.057% and a frequency of 0.6036%

Hope this helps.

Sincerely,
Cac