Taking insurance at +3> doesn't make sense . . . ?

[MagicianJS]

If I understand this correctly, insurance is a completely different side bet on whether the dealers hole card is a ten or not. If so, it'd stand to reason that chances would only be in your favor to take the bet if there are more ten cards in the shoe than non-ten cards. But a true count of plus 3 or higher is nowhere near high enough of a count for the rest of the shoe to be more tens than non-tens.
If I take a deck of cards and take out 3 positive cards, the ratio of tens to non-tends is still far below 50/50.
We'd have to assume that all of the neutral cards in the deck have already been dealt in order to make an accurate judgement of whether it's advantageous to take insurance or not.
Where am I going wrong in my thinking?

 

[tthree]

If I understand this correctly, insurance is a completely different side bet on whether the dealers hole card is a ten or not. If so, it'd stand to reason that chances would only be in your favor to take the bet if there are more ten cards in the shoe than non-ten cards. But a true count of plus 3 or higher is nowhere near high enough of a count for the rest of the shoe to be more tens than non-tens.
If I take a deck of cards and take out 3 positive cards, the ratio of tens to non-tends is still far below 50/50.
We'd have to assume that all of the neutral cards in the deck have already been dealt in order to make an accurate judgement of whether it's advantageous to take insurance or not.
Where am I going wrong in my thinking?

The bet pays 2:1 so half as many tens make it break even.

 

[Thunder]

Here's something to think about...

in a single deck game, there are 52 cards. If you're using HI-Opt I, it says to take insurance at +3 (yes I realize it's actually lower than +3 at single deck but ignore that for one minute) This essentially means that if there are 16/49 cards left that are 10 cards. However 16/49= .3265 Since we only get 2-1, we need a ratio of higher than .33333 to make it worth taking the bet. 16/48 (.33333) would be +4 TC, so if this is the case, why do we generally take insurance at +3 instead of over +4????

 

[FLASH1296]

I take an opposite stance to those looking to split hairs and take insurance solely when it is a profitable action.

There are other considerations.

None other than the redoubtable A.P. demi-god James Grosjean promulgates taking Insurance for reasons of variance reduction.

I add to that the good value it has as a "cover play"

I suggest taking "even money" at (Hi-Lo) ≥+1 and insuring your "20's" at (Hi-Lo) ≥+2.

 

[tthree]

Here's something to think about...

in a single deck game, there are 52 cards. If you're using HI-Opt I, it says to take insurance at +3 (yes I realize it's actually lower than +3 at single deck but ignore that for one minute) This essentially means that if there are 16/49 cards left that are 10 cards. However 16/49= .3265 Since we only get 2-1, we need a ratio of higher than .33333 to make it worth taking the bet. 16/48 (.33333) would be +4 TC, so if this is the case, why do we generally take insurance at +3 instead of over +4????

Most people floor their TC estimates and many cards are neutral. The play assumes the neutral cards are depleted as average would expect. If your TC is +3 because three 3 to 6 cards are played and no face cards the assumption is 1 neutral card is played. That gives 16/48 for a TC of +3 were 3 cards are counted. You may know the assumption is wrong but that's why the index is +3.

 

[overtheedge]

On average the assumption is right. Sometimes 7,8, and 9 will be under-depleted making the +3 index too low, but sometimes they'll be over-depleted making it unnecessarily high. So yes, there is some "noise", but in the long run it should balance out. Likewise if you placed just 10 bets you're likely to be very far away from your EV (relative to amount bet), but if you placed 10,000,000 you'll very probably be at almost exactly your EV.

Additionally ANY positive count will make the insurance bet "less bad" than it normally is. An EXTREME positive count will make the insurance bet very valuable.