true-count insurance

I'm hoping someone can help me determine how a true count of '+3' for insurance wagers was derived for hi-lo..

It would seem to me that a true-count of '+4' would be a garantee of the appropriate 10/'other' ratio... but I'm also able to take certain cards from the deck that yield a negative true count (aces with neutral cards) while still making buying insurance correct...

So I guess I'm asking what the logic is used for determining the best overall 'average' true-count...

Thanks in advance...

index

There are two components to computing the insurance index. First, suppose have a wager that the net card will be a 10. What would our HiLo index for that?

When the count goes up 1 High Low True point, on average there are 0.1 more Aces, 0.4 more tens, and 0.1 low cards per deck. So we can estimate the density of 10s to be 4/13 + 2/5 * (TC/52) . (The factor of 52 is used to convert points per deck to points per card). We set this equal to 1/3, the break even point for insurance and solve. You will see that the critical number is 10/3 or 3.33 points per deck.

Now this is not quite the same as the Insurance Bet. WE only get to take Insurance when there is a dealer Ace in front of us. We can adjust our index to reflect the fact that we have counted that Ace. The adjustment per Ace is about 2/N, where N is the number of decks. This gives us the following approximation for the insurance index:

10/3 - 2/N

You can see that this give 3.0 for 6 decks, 2.3 for 2 decks, and about 1.3 for 1 deck.

in this admittedly special situation, you can make a perfect insurance decision if you can see all the players' cards before making your insurance bet - this is done by doing a "ten-count" for this round only. It is fairly easy, as follows:

If you can see a total of 5 cards (your hand, another player hand, plus the dealer's Ace) and you see no tens...take insurance. The ratio of non-tens to tens is 31/16.

If you can see a total of 7 or 9 cards (your hand, and two or three other player hands, plus the dealer's Ace), and you see ONE TEN or less...take insurance. The ratio of non-tens to tens is no more than 30/15.

If you can see a total of 11 cards (your hand, four other players hands, plus the dealer's Ace) and you see TWO TENS or less, take insurance. The ratio of non-tens to tens is 27/14.

Sometimes you can infer what the other players are holding even if your can't actually see their hands. If they tuck their cards, this could mean that they have 17 or higher, so there is probably at least one ten hiding under there.

Thanks to Lawrence Revere and Stanford Wong for this advice from some really old editions of their books.

AB

there is one very special situation where you would take insurance and that is if you can see a total of 9 cards or more (your hand, three other players hands, and the dealer's Ace). If you see NO TENS you should insure your hand. The ratio is no more than 63/32, which is less than 2:1.

AB

MathProf, thank you for your response... yours was exactly the type of answer I was looking for.... but.. I still have questions!

first...

"10s to be 4/13 + 2/5 * (TC/52)".... I set this to 1/3, but wound up with 12/13 or 1.08... it may just be me... I'll try it again..

second...

Is this formula suitable for working with any kind of count? Or is it particular to Hi Lo? It would seem that the ratios are universal.. but just wanted to check.....
I did want to ask you... is" * (tc/52) " a required step? Converting to points per card seems to be where I lose it....
also.. in your last line:

You can see that this give 3.0 for 6 decks, 2.3 for 2 decks, and about 1.3 for 1 deck

Is this to say that it is correct to buy insurance at "plus 2" true count in a single deck game? I thought it was always +3 .....

MathProf, thank you once again, I truely appreciate your help....

index

I don't see how you came up with 12/13. Subtract the 4/13 from 1/3 and you should get 13/39-12/39 =1/39. Multiply by 5/2 to get 5/78. This is the index expressed in terms of points per card. Multiply by the 52 to get points per deck.

The 2/5 comes from HiLo. It is really 4/10, and is based upon the fact that HiLo tracks 10 denominations of cards, and 4 of them are 10s. For HiOpt, the figure would be 4/8 or 1/.2.

In single deck, you can take insurance when the RC is +2. Deeper in the deck, you can take it at +1. The transition occurs after approximately the first quarter deck. This is a quarter deck of seen cards.

uuhhg!! I found my error...

4/13 + 2/5*(TC/52) = 1/3

4/13 + 2TC / 260 = 1/3

4/13 + TC / 130 = 1/3

40/130 + TC / 130 = 1/3

40 + TC / 130 = 1/3 _ _ _ _ not: 40TC/130 = 1/3

120 + 3TC = 130

3TC = 10

TC = 10/3

I think I'm getting it MathProf.... you have my utmost respect and appreciation for your time....

One more! ;-)

Where is the ace adjustment of "2/N where N is the number of decks" derived from? And would that value change for different counts? Say.. one that valued the Ace at '-2'?

index

and you see a total of 15 cards (your hand, 6 other players hands and the dealers Ace, it's a full table and it's face up, remember?) Should you take insurance???

See Wong's book Blackjack Secrets, Chapter 4, if you don't know the answer (it depends on your situation).

AB