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Originally Posted by DSchles
But I said something different???

Don
Not different, just phrased in a way that helped me see the distinction I was missing.

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Originally Posted by Craigrow
I believe I understand now. Thanks. I still would be interested in the math. I don’t see how taking one low card from a single deck would make the insurance a positive EV situation. At risk of getting more abuse, here’s my math...

Single deck:
16/52 * 2 = .615
36/52 * -1 = -.692
====
-.077

Single deck missing one low card: TC=1
16/51 * 2 = .627
35/51 * -1 = -.686
====
-.059

What am I missing?
What you're missing is you can't remove a single card and play blackjack! At the very least, you have to remove the dealer's ace, and the player's two cards in his hand. But, as we all know, it is never correct to take insurance off the top of the pack if playing alone. So, what you might have observed was, if the dealer has an ace, and I have, say, 6,4, the Hi-Lo RC is +1, the TC is slightly more than +1, but it is still incorrect (33/16) to take insurance. And, that would be right. But, it doesn't mean that the SD insurance index shouldn't be +1 (actually it's 1.4).

There are many more scenarios beyond the one above. Suppose you had a player next to you, and you could see his cards. He has 9,8, and stands. You have the same hand as above. The RC is STILL +1, the TC is 1.10, and now the ratio is 31/16 and insurance is correct!

So the +1 SD index represents an entire gamut of possible situations, not just one. And, when any index is given, it represents not a single point but rather an entire interval of TCs (in this case from 1 to <2). So, the +1 also refers to TCs of, say, 1.8 or 1.9, which are floored to +1 but where insurance, once again, is the correct play. So, over the entire interval, it is more profitable to insure than not to.

Do you understand? (If not, maybe my good friend Gronbog will explain it better! )

Originally Posted by Craigrow
Also curious why one deck to play would make any difference v. playing with a single deck only. Either way you have 52 cards and if the count is zero you have the same math regardless, right?
No, not right. Do you have BJA3? I'm thinking no. In any event, having a count of zero with one deck to play in a multi-deck game (although I don't know why we're back to how many decks are left to play, as that has nothing to do with the discussion) is NOT the same thing as playing single-deck blackjack. Nor would you use SD BS if you were playing against a 6-deck game, weren't counting, but got down to the final deck of the shoe.

Don

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