Blackjack: Expected Value of Standing 10,6 vs. Dealer 10

It's my first post here. Apologies in advance if this question has been answered previously. I tried the search function but couldn't lock-on to a post.

Anyway, I am running into trouble calculating the expected values for standing when the dealer is showing a 10. When I calculate the expected value, I am slightly off when compared to Appendix 9.

Assuming a single deck and the dealer stands on soft 17, a hand of 10,6 vs. 10 should have an EV = -.542952. I calculate is EV=-.5803. The algorithm I wrote works fine for upcards 2-9.

The general equation I'm using is EV = 2[P(T > 21) + P(T < j)] + P(T = j) - 1 where T are all possible dealer hands 17-21+ (including busts) and j is the value of the player hand. Does it have something to do with the fact that we know the dealer's second card will not be an ace, we calculate the probabilities slightly differently?

A post on Blackjackinfo has it at - 0.580261906574.

Quote: Riptide

Does it have something to do with the fact that we know the dealer's second card will not be an ace, we calculate the probabilities slightly differently?

Yes, yes, very much yes.

Quote: Riptide

It's my first post here. Apologies in advance if this question has been answered previously. I tried the search function but couldn't lock-on to a post.

Anyway, I am running into trouble calculating the expected values for standing when the dealer is showing a 10. When I calculate the expected value, I am slightly off when compared to Appendix 9.

Assuming a single deck and the dealer stands on soft 17, a hand of 10,6 vs. 10 should have an EV = -.542952. I calculate is EV=-.5803. The algorithm I wrote works fine for upcards 2-9.

The general equation I'm using is EV = 2[P(T > 21) + P(T < j)] + P(T = j) - 1 where T are all possible dealer hands 17-21+ (including busts) and j is the value of the player hand. Does it have something to do with the fact that we know the dealer's second card will not be an ace, we calculate the probabilities slightly differently?

I spent about 30 minutes trying to figure out where everyone went wrong, until I realized that you are calculating the ev of STANDING on 10,6 vs 10.

If the dealer hasn't checked for blackjack yet, the ev is -0.580261907, which matches Blackjackinfo.
If the dealer has checked for blackjack, and you know that the dealer doesn't have a blackjack, the ev is -0.542951854, which matches Appendix 9.

But, the player should hit, so the ev is as follows:
Dealer hasn't checked for blackjack: ev = -0.5471799166540101
Dealer checked and doesn't have blackjack: ev = -0.5071033260810114

Should surrender be available, ev = -0.5, which is the best option.