To, any one that can help?
As per my earlier thread, I have been trying to re-create infinite deck expected returns in my own Excel spreadsheet. I know there are sites with optimal play strategies but I wanted to crunch the numbers myself. I have been referring to Wizard of Odds, Appendix 1 to the Blackjack section:http://wizardofodds.com/blackjack/appendix1.html
I have been able to set up all the Dealer probabilities of either: (i) going bust; or (ii) reaching totals of 17-21 (and agree with the Wiz). But I can't reconcile all the expected returns for the Player when hitting. When calculating the Player's first two card totals of 16-21 I agree with the Wiz but then there doesn't appear to be any consistency where the Player's first two card totals are less than 16.
For example, Player is on Hard 15. I work out odds of hitting one more card: i.e. A, 2, 3, 4, 5, 6, 7, 8, 9 & T. Hitting for a 7, 8, 9 & T = bust, for 2, 3, 4, 5 & 6 I pick up the expected returns when the player sits on the new total which is 15 + 2 thru 6 = 17, 18, 19, 20 & 21. Problem I have is with the Ace??
I would have thought the returns I pick up were the same as the expected returns for sitting on 16. For each of the Dealer's cards I thought it would be:
2 = -0.2928
3 = -0.2523
4 = -0.2111
5 = -0.1672
6 = -0.1537
7 = -0.4754
8 = -0.5105
9 = -0.5431
T = -0.5404
A = -0.6670
This matches the Wiz for Dealer's up-card for 2, 3, 4, 5 & 6 but differs for the others 7, 8, 9, T & A. It looks like the Wiz for these numbers uses:
7 = -0.4148
8 = -0.4584
9 = -0.5093
T = -0.5398
A = -0.5171
, which if you look at the tables is picking up the expected returns for the previously derived expected returns for 16.
I would have thought this is inconsistent? Either you pick up the row for the previously derived expected returns or you use the sitting expected returns. Basically, I don't understand the logic used.
The way I think it should work is Player is on Hard 15 and hits, gets say a 2 which is the same expected returns as sitting on 17. Then you evaluate the expected returns for sitting and hitting on 17 to determine what to do, but it doesn't look like this is the way the Wiz has done it.
If any one is about to help it would be appreciated, I can always email my worksheet if that helps?