Matrix Number For Insurance

[falseazure]

I'm new to card counting, and I hope that somebody could explain to me the reasoning behind the +3 matrix number for taking insurance, in a 6-deck game, while using the hi-low count, which is listed in the book "Play Blackjack Like the Pros." If I understand this correctly, this means that I should take insurance any time the true count is +3 or higher. But when I think about this, it doesn't make sense to me, and seems like the matrix number should be +4.

Since insurance pays 2 to 1, it seems like this is only a break-even or profitable bet if at least 1/3 of the remaining cards are tens. But an example of a deck with a true count of +3 would be a deck with three small cards removed, right? In which case, 16/49ths of the remaining cards would be tens, which would be less than 1/3, making insurance a losing bet. According to this logic, the real number should be +4. I'd greatly appreciate if someone could explain to me what I'm thinking about incorrectly.

 

[godeem23]

I'm new to card counting, and I hope that somebody could explain to me the reasoning behind the +3 matrix number for taking insurance, in a 6-deck game, while using the hi-low count, which is listed in the book "Play Blackjack Like the Pros." If I understand this correctly, this means that I should take insurance any time the true count is +3 or higher. But when I think about this, it doesn't make sense to me, and seems like the matrix number should be +4.

Since insurance pays 2 to 1, it seems like this is only a break-even or profitable bet if at least 1/3 of the remaining cards are tens. But an example of a deck with a true count of +3 would be a deck with three small cards removed, right? In which case, 16/49ths of the remaining cards would be tens, which would be less than 1/3, making insurance a losing bet. According to this logic, the real number should be +4. I'd greatly appreciate if someone could explain to me what I'm thinking about incorrectly.

With 3 cards low cards gone, although the running count may be +3, the true count is not because we are no longer dealing with a full deck. We are dealing with only 49 cards, bring the true count to 3.18. This might have something to do with the discrepancy.

 

[falseazure]

My bad. Anyway, if you start with 1 deck, and remove three small cards, then 16/49ths of the remaining deck are tens, so insurance is still going to lose money, and the true count is going to be above +3. I was thinking about this some more last night, and I thought that maybe the number was +3 instead of +4 because the simulation that determined it discovered that on average, in the process of naturally reducing a 6-deck shoe to a theoretical situation (where of course less than a deck is being burned) where 49 cards remain and the TC is +3, a greater number of zero-count cards (7, 8, 9) are going to also be removed than the zero in my example where you start with a full deck and remove three low cards. So, on average, with 49 cards left in a 6-deck game and a tc of +3, more than 16/49ths of the remaining cards are going to be tens, and in fact, more than 1/3rd, making the insurance bet profitable.

Is this analysis correct? Could somebody who understands these basic strategy deviations from a discrete mathematics perspective comment?

 

[Mimosine]

Is this analysis correct? Could somebody who understands these basic strategy deviations from a discrete mathematics perspective comment?

the best way to convince yourself of this is to get some good simulation software and crunch the numbers and see the results. yes you could logically go through an exercise and work out a rough guess for what the correct TC should be for insurance, but it has been done for you and the answer is +3. Before you step foot in a casino, if you are wavering on this, or if you think you have a better answer you should double check your back of the envelope calculation. INSURANCE above ALL OTHER index plays is the most important. Insurance is worth what the next 10-15 index plays are worth COMBINED. so if you're playing it at the wrong TC, the results will be measurable over the long term.

so, a word of caution, take insurance seriously, don't just wing it, or guess what it should be.

you're on the right track though, with your reasoning, the loss of a statistical number of uncounted cards will have an effect on the probability of the dealer having a 10 in the hole. as this probability exceeds a specific value, insurance becomes profitable. Taking insurance at +2 through +4 won't have a HUGE effect, in fact certain conditions will warrant it at +2, but +3 is the best average time to take it.

 

[k_c]

Math Analysis of Hi-Lo/KO insurance indices

My bad. Anyway, if you start with 1 deck, and remove three small cards, then 16/49ths of the remaining deck are tens, so insurance is still going to lose money, and the true count is going to be above +3. I was thinking about this some more last night, and I thought that maybe the number was +3 instead of +4 because the simulation that determined it discovered that on average, in the process of naturally reducing a 6-deck shoe to a theoretical situation (where of course less than a deck is being burned) where 49 cards remain and the TC is +3, a greater number of zero-count cards (7, 8, 9) are going to also be removed than the zero in my example where you start with a full deck and remove three low cards. So, on average, with 49 cards left in a 6-deck game and a tc of +3, more than 16/49ths of the remaining cards are going to be tens, and in fact, more than 1/3rd, making the insurance bet profitable.

Is this analysis correct? Could somebody who understands these basic strategy deviations from a discrete mathematics perspective comment?

I have done exactly that. I have analyzed the insurance decision for Hi-Lo and KO from a mathematical perspective rather than simulation. As far as I know nobody else has done this. Possibly I'm an idiot for doing this but it is more accurate than a sim. Maybe the accuracy is worth it, maybe not, but the analysis should answer your questions. The fewer the number of decks, the more volatile the insurance index is. You're using a single deck as an example: (Dead link: http://www.bjstrat.net/SDHiLoIns.htm) _Single Deck Data_. If you click the link to the home page you will find links to 1,2,4,6, and 8 deck data for both Hi-Lo and KO. My web site is pretty simple as I'm not much of a web designer.

k_c

 

[bj bob]

Good question

I have pondered that very same point myself and have come to the conclusion that the +3 TC index is accurate in that it "imputes" the relative average numbers of neutral cards which, of course are non-tens and thus the TC number reflects that , on average.

 

[blackjack avenger]

Insurance

Don Schlesinger "Blackjack Attack 3"
hi low:
1 deck Insure at TC 2
2 deck 3
6 deck 3
8 deck 3

The above are correct while using no decimals.

Stanford Wong "Professional Blackjack"
hi low:

1 deck insure at TC 1.4
2 deck 2.4
6 deck 3
8 deck 3.1

The above are correct if using decimals.

The difference is with Wong's you have to remember the decimal point aaaand be able to calculate the TC conversion. Also, the difference between which is superior would take many many hands played before it became obvious if there is a difference.

 

[Ferretnparrot]

I think somebody posted a chart for taking insurance based on the number of cards remaining in a 6 or 8 deck shoe, the number varied from 4 and got lower untill you reached the bottom of the deck, but the average was around and just a little over 3 as i remeber. so in general 3.1 is the number fro multideck but maybe 4 if its the first couple decks, it really doesnt matter though cause youll practically never see a +4 on the first couple decks ever yet alone a +3, but if you do your in for hell of a high count later in the shoe.