Here's how I work it out:
Assuming A 9 held by player, dealer shows 5. There are 3 As out of 49 cards left, giving 6.12% odds for a score of 21. Here's the table:
Code:
A 3 - 21 - 6.12
2 4 - 12 - 8.16
3 4 - 13 - 8.16
4 4 - 14 - 8.16
5 3 - 15 - 6.12
6 4 - 16 - 8.16
7 4 - 17 - 8.16
8 4 - 18 - 8.16
9 3 - 19 - 6.12
10 16 - 20 - 32.65
Adding the under 17 hands, we get:
Code:
21 - 6.12
less than 17 - 38.78
17 - 8.16
18 - 8.16
19 - 6.12
20 - 32.65
Dealer will bust about 40% of the time, giving all of those scores wins. In other cases (leaving pushes out of it): 20 will beat the dealer 75%. 19 will beat the dealer 50%. 18 will beat the dealer 25%. 17 and under will lose or push 100%. So add those to the table and we get:
Code:
21 - 6.12 (6.12)
less than 17 - 38.78 (15.51)
17 - 8.16 (3.26)
18 - 8.16 (3.26 + 1.25 = 4.51)
19 - 6.12 (2.45 + 1.84 = 4.29)
20 - 32.65 (13.06 + 14.69 = 27.75)
Adding up all the win expectancies I get 61.41, making this a sure double situation. Where is my error?