sagefr0g said:
Just curious -- why the +3.5 for insurance? usually i think of it as 3 .
Admittedly, I've always been perplexed by that too. Hopefully, Norm can shed some light on this:
If you take six decks of cards, play out three of them and find that there are exactly 52 Tens in the remaining three decks, Insurance will now be a dead even bet. But the question is -- what will that running count most likely be???
It will vary some with the number of "zero" valued cards contained in the pack, but I don't suppose there'd be any reason to assume their population is abnormal. You simply know that you have more high cards and fewer low cards among the 156 that remain. Assuming then, that the "zero" cards number 12 each, there would be 52 Tens, 13 Aces and 11 each of the 2's through 6's
(using Hi/Lo as a test case). That leaves a running count of +10 -- divided by three remaining decks -- or a +3.33 true count.
Since there's no advantage in taking Insurance at a break even bet
(except probably Even Money), I generally begin insuring at around +3.5 true, which would yield about a half percent edge.
Now with systems that neutralize the Ace in the main count, Insurance becomes a play at a lower true count, since more or all of the surplus high cards consist of Tens. Using the same calculating method with Hi Opt I for example, Insurance becomes break even at +2.66 true.
To add to my frustration on this topic, I've read in various places over the years
(most profoundly in Wong's Professional Blackjack), that the correct true count for Insurance depends upon the number of decks used in the game. Wong states that the Insurance true count for single deck is +1.4 with Hi/Lo, and +1.7 with Halves -- and for six decks it's +3.0 with Hi/Lo and +3.3 with Halves. With Hi/Lo, to get one third of the remaining cards to be Tens and have only a +1.4 true count, you'd need to have fewer 7's, 8's and 9's in the pack than 2's thru 6's -- which are already in short supply. That confounds me.
I'll try to post this question elsewhere and see if we can get Don Schlesinger to chime in.