Hitting 16 against 7-10

Please help me see this correctly.
If only me and the dealer only (or I am last to play) are playing BJ and I hit 16 against his 10 and am fortunate enough to get a 5 or 6 it seems to me that if I had not hit then the dealer would have got this card making his hand (particularly with a 10) very poor. It seems to me that the odds are correct if the cards are shuffled after every card turned, but in the above case the Dealer would definitely get the card which would have been a good one for me and therefore a bad one for him. Am I talking rubbish?

The dealer has another card in the hole. It can very well be a 7-10, so he'll never have to take that 5 you are stealing.

Quote: kookumber

Please help me see this correctly.
If only me and the dealer only (or I am last to play) are playing BJ and I hit 16 against his 10 and am fortunate enough to get a 5 or 6 it seems to me that if I had not hit then the dealer would have got this card making his hand (particularly with a 10) very poor. It seems to me that the odds are correct if the cards are shuffled after every card turned, but in the above case the Dealer would definitely get the card which would have been a good one for me and therefore a bad one for him. Am I talking rubbish?

First, let's clarify that you're talking about Europen (no hole card) rules.

If the next card is a 7 to 10, it won't make any difference, you're doing to lose either way. Stand, and the dealer makes a pat hand beating your 16, hit and you bust. The following table shows the expected value according to each next card in the deck, assuming an infinite deck.

Next card	Stand	Hit
2	-0.034654572	-0.241508831
3	0.039249326	-0.018660154
4	0.107874374	0.434957754
5	0.171597633	0.811652585
6	0.230769231	-1
7	-1	-1
8	-1	-1
9	-1	-1
10	-1	-1
A	-1	-0.464357508

If you take a weighted average, the expected value of standing is -0.575782, and hitting is slightly not as bad at -0.575224.

Basically, an unseen card is a random variable. The order doesn't matter in the long run. For the same reason it is nonsense to play to avoid taking the dealer's card, or anything that alegedly messes up the order.

One thing we can learn from this is what to do if the dealer accidentally shows you the next card. The cards you should take are 4, 5, and ace, refuse a 2, 3, and 6, and 7-10 you're doomed either way. It seems a little surprising that you would refuse a 3, but you should.

according to your chart, shouldnt you stand if the next card is a 3?

Quote: rudeboyoi

according to your chart, shouldnt you stand if the next card is a 3?

Yes, thanks, I just fixed that comment.

Sorry but yes I am talking about European BJ with no hole card.
Thanks for replies.

Quote: Wizard

It seems a little surprising that you would refuse a 3, but you should.

I think this is kind of cute, because it illustrates just how lousy a 19 against a dealer 10 really is--in other words, you're better off with a stiff against a dealer 13 (even though you only have a, what is it, 42% chance of winning?) then you are with a 19 against a dealer 10 (of course, with Euro-rules, you're worse off in this situation than otherwise, because the dealer could still slide an Ace under that 10).

By the way, why does any sane person play Euro-no hole card BJ?