Deriving Perfect Insurance (for any count)

[k_c]

It's possible to derive perfect insurance for most any given counting system by maintaining 2 simultaneous running counts. When I played I found I was able to maintain a side count of aces for 2 decks but not for 6 decks. I'm not sure I could now do this for insurance in a real game but I can see that I may with practice. This is simpler than side counting for insurance purposes. If mastered, once the 2 running counts are known the decision to insure or not is immediately known.

http://www.bjstrat.net/perfectIns.html

k_c

[Cacarulo]

It's possible to derive perfect insurance for most any given counting system by maintaining 2 simultaneous running counts. When I played I found I was able to maintain a side count of aces for 2 decks but not for 6 decks. I'm not sure I could now do this for insurance in a real game but I can see that I may with practice. This is simpler than side counting for insurance purposes. If mastered, once the 2 running counts are known the decision to insure or not is immediately known.

http://www.bjstrat.net/perfectIns.html

k_c

Your method is perfectly valid, although it's not easy to maintain the secondary count. It also happens that you count several cards twice.
However, it has an important advantage, which is that you don't need to convert to true count.
Another idea that I consider a bit simpler, especially in 2D, would be to count only the tens. That count should start at +32,
and every time you see a ten, you subtract one. Then, you divide that running count (RC) by the remaining decks.
If the TC is greater than +16, you should buy insurance.

Sincerely,
Cac

[Secretariat]

Each mind works differently

Personally, I find it mentally easier to use two or three side counts than using a second count involving additions and subtractions to achieve perfect insurance... and other benefits.

Here’s another option for the visually inclined, provided that one can accurately estimate the number of unplayed cards, preferably within a margin of error of 3 cards or less.

If, as a second count, one counts down the tens (starting at 96 for 6D), one knows that with 5, 4 and 3 decks unplayed, the insurance thresholds are respectively above 86, 69 and 51. With a separate count of tens, the sharp eye will visually know when to take insurance or not. This works with level 2 and level 3 counts too. No calculation required. The downside is the need/tell for a serious look at the discard.

Also consider that perfect insurance is automatically signaled with the jungle count, even at its basic level. No additional effort required, not even a look at the discard.

[Cacarulo]

Each mind works differently

Personally, I find it mentally easier to use two or three side counts than using a second count involving additions and subtractions to achieve perfect insurance... and other benefits.

Here’s another option for the visually inclined, provided that one can accurately estimate the number of unplayed cards, preferably within a margin of error of 3 cards or less.

If, as a second count, one counts down the tens (starting at 96 for 6D), one knows that with 5, 4 and 3 decks unplayed, the insurance thresholds are respectively above 86, 69 and 51. With a separate count of tens, the sharp eye will visually know when to take insurance or not. This works with level 2 and level 3 counts too. No calculation required. The downside is the need/tell for a serious look at the discard.

Also consider that perfect insurance is automatically signaled with the jungle count, even at its basic level. No additional effort required, not even a look at the discard.

Hi Sec,

Your method is practically the same as the one I mentioned earlier (only that I used an integer index, +17, instead of a decimal one). If we take +17.3333 as the exact index for any number of decks, you can buy insurance simply by knowing
exactly how many tens are left in the shoe divided by the remaining decks. Notice that if there are 86 tens left and 5 decks remaining, we still couldn't buy insurance (+17.2). However, with 87 tens, we could (+17.4).
The same applies to 70/4 = +17.5 and 52/3 = +17.3333.
Note: If the TC is calculated by dividing by full decks, the index is +17.3333. However, if the TC is calculated by dividing by half decks, the index is +8.6666.

Sincerely,
Cac

[Secretariat]

Hello Cac

I wrote above 86, 69 and 51 with 86,6/69,33/52,0 in mind for simplicity
It would probably be clearer to say at 87/70/52 or above.

Using half decks, or quarter decks is increasingly difficult but it could be done visually to near perfection.
One thing is sure, as you said a while ago double counting tens can be valuable.

[Freightman]

Using half decks, or quarter decks is increasingly difficult but it could be done visually to near perfection.
One thing is sure, as you said a while ago double counting tens can be valuable.

Using 6 deck hi lo, strike point is 33.33333% 10 value cards remaining.
By 1/2 decks
5.5 decks 286 cards 96-10 33.33%
5.0 decks 260 cards 87-10 33.46% reduced 9 cards
4.5 decks 234 cards 78-10 33.33% reduced 9 cards
4.0 decks 208 cards 70-10 33.65% reduced 8 cards
3.5 decks 182 cards 61-10 33.51% reduced 9 cards
3.0 decks 156 cards 52-10 33.33% reduced 9 cards
2.5 decks 130 cards 44-10 33.84% reduced 8 cards
2.0 decks 104 cards 35-10 33.65% reduced 9 cards
1.5 decks 78 cards 26-10 33.33% reduced 9 cards
1.0 decks 52 cards 18-10 34.61% reduced 8 cards
0.5 decks 26 cards 9-10 34.61% reduced 9 cards


Mostly a reduction of 9 (sometimes 8) 10 value cards per 1/2 deck starting from 5.5 decks. Note, no 10 value cards appear in first 1/2 deck in order for insurance to be justified.

[Cacarulo]

Using 6 deck hi lo, strike point is 33.33333% 10 value cards remaining.
By 1/2 decks
5.5 decks 286 cards 96-10 33.33%
5.0 decks 260 cards 87-10 33.46% reduced 9 cards
4.5 decks 234 cards 78-10 33.33% reduced 9 cards
4.0 decks 208 cards 70-10 33.65% reduced 8 cards
3.5 decks 182 cards 61-10 33.51% reduced 9 cards
3.0 decks 156 cards 52-10 33.33% reduced 9 cards
2.5 decks 130 cards 44-10 33.84% reduced 8 cards
2.0 decks 104 cards 35-10 33.65% reduced 9 cards
1.5 decks 78 cards 26-10 33.33% reduced 9 cards
1.0 decks 52 cards 18-10 34.61% reduced 8 cards
0.5 decks 26 cards 9-10 34.61% reduced 9 cards


Mostly a reduction of 9 (sometimes 8) 10 value cards per 1/2 deck starting from 5.5 decks. Note, no 10 value cards appear in first 1/2 deck in order for insurance to be justified.

Correct, if you don't want to do the division for the remaining decks (5.5, 5.0, 4.5, 4.0, 3.5, 3.0, 2.5, 2.0, 1.5, 1.0, 0.5), you have to memorize the thresholds for each of them:
96, 87, 78, 70, 61, 52, 44, 35, 26, 18, and 9.
Otherwise, you divide the remaining tens by the remaining decks, and if the resulting value is greater than or equal to +17.3333, you buy insurance.

Sincerely,
Cac

[Cacarulo]

Hello Cac

I wrote above 86, 69 and 51 with 86,6/69,33/52,0 in mind for simplicity
It would probably be clearer to say at 87/70/52 or above.

Using half decks, or quarter decks is increasingly difficult but it could be done visually to near perfection.
One thing is sure, as you said a while ago double counting tens can be valuable.

Sure! Keeping a separate count of tens is very beneficial. Not only for insurance but it can also be applied to other plays.

Cac

[Freightman]

Not only for insurance but it can also be applied to other plays.

Index plays for indices, a not well understood concept. SOP for QTC.

[k_c]

If I only want insurance I would use insurance count. Insure when running count is greater than 0. Nothing is simpler. I am very good with insurance count. Problem is that by itself it does a poor job determining betting opportunities.

k_c

[Cacarulo]

Index plays for indices, a not well understood concept. SOP for QTC.

Keeping a side count of tens, in addition to being excellent for Insurance, in which case the correlation is perfect,
can also be used in other plays such as 12 vs 6/5/4/3/2, 9 vs 2, and 11 vs A, instead of using the primary system.
In these cases, the correlation is also very high.

Sincerely,
Cac

[Cacarulo]

If I only want insurance I would use insurance count. Insure when running count is greater than 0. Nothing is simpler. I am very good with insurance count. Problem is that by itself it does a poor job determining betting opportunities.

k_c

Something interesting that you could try is using your system in the plays I mentioned to Freightman. By doing that, you would be maximizing your system's potential.
As for the betting opportunities, they are not important because you already have the primary count (Hi-Lo in your example) for that.

Sincerely,
Cac

[k_c]

Something interesting that you could try is using your system in the plays I mentioned to Freightman. By doing that, you would be maximizing your system's potential.
As for the betting opportunities, they are not important because you already have the primary count (Hi-Lo in your example) for that.

Sincerely,
Cac

The idea of this thread is to show that any count can attain perfect insurance by relating to the insurance count.

In the case of the insurance count, 1 running count and nothing else is needed to perfectly decide if buying insurance is +EV no matter how many cards have been dealt.

In the case of a count other than insurance count, 2 running counts and nothing else are needed to perfectly decide if buying insurance is +EV no matter how many cards have been dealt.

I'm sure there may be more specific ways to approach this. Above is general case, that's all.

k_c