Insurance Paradox

Suppose you're playing a double deck game with a half deck left and a count in which 9s are negative. Before the hand is dealt the count is just above your insurance index. You get dealt 9,9 v A. The count is now below your insurance index. Do you take insurance?

The no argument is pretty obvious, count is below index, no insurance.

But the count was above the insurance index and then you saw 3 more non-face cards.

Thoughts?

The only thing that matters for insurance is the ratio of 10s to non-10s (or ratio of 10s to everything), because insurance is really just a 2-1 bet that the next card is a 10. If you saw 9,9,A and your count moved in the wrong direction vis-a-vis insurance, then your count and index system is not well-correlated to the insurance bet. As a result, I wouldn't put any faith in your premise -- that the count being above your insurance index was a valid indicator of insurance being a +EV play before the hand.

In other words, use a side count.

Right, so for insurance, Hi-Lo incorrectly counts aces as being advantageous, and doesn't count 7-9 as being advantageous.

If you are using HiLo, and this situation comes up, I'd say it's safe to say that insurance is closer to even money, and may be marginally profitable. I would insure a big bet.

My answer is "yes." Given the information you have it is the right play. For the same reason if you were playing a full table of face-up single-deck and every card was a 7 to 9 after the shuffle. Although the hi-lo count is neutral, just eyeballing the table indicates a surplus of tens in the remaining cards. If you remove any five non-tens from a single deck, and nothing else, then insurance is a good bet.

Quote: vetsen

Suppose you're playing a double deck game with a half deck left and a count in which 9s are negative. Before the hand is dealt the count is just above your insurance index. You get dealt 9,9 v A. The count is now below your insurance index. Do you take insurance?

Of course you do take insurance.

Before the dealt hand (given no other information), you have positive EV on the insurance bet (as this is the threshold of the insurance index given that particular counting scheme). After the hand is dealt, the probability for a dealers blackjack increases, as you see no face card.

If you think you should not take insurance because the count drops below the index: this would be the right move if the cards were dealt face down and someone announces the new count (somehow knowing the count of these cards).

In your situation you have additional information besides the count (no tens dealt). If you use this information correctly, you can make the better decision (do take insurance).

Not a paradox at all. As others have noted, it's what the situation is at the moment you make the bet that matters.

Example: Suppose a VP machine offered a 50-1 side bet on whether or not you would get a Royal Flush, and it would be offered both before the deal and after (but before any draw, of course). The probability of getting a Royal is far more than 1/51, so you don't take the bet before the deal. However, you are then dealt AKQJ of spades and 3 of hearts. Assuming you keep the 4/royal, the RF probability is now 1/47, so you go for the side bet - you don't say, "Well, the probability was lower than 1/51 at the start of the hand, so I shouldn't." The same applies with your insurance bet.

I guess the OP is confused by the index result to not play insurance due to the updated situation, where in fact playing insurance is advised.