doubling on an A-A
If you can't split aces, but you can double, when is doubling better than hitting if at all? dealer 5 and 6?
assume just basic strategy.
If you can't split aces, but you can double, when is doubling better than hitting if at all? dealer 5 and 6?
assume just basic strategy.
yumyumgeeitsfun,
Since you didn't specify the house rules, I assumed a 6D, S17, DAS game. The output below is from Eric Farmer's Blackjack Strategy Calculator. The options are listed from most favorable to least favorable, with upper-case letters indicating +EV options. As you can see, if you cannot split, the next-best option is to Hit against every upcard except a 6. As you can see, when hitting you are the underdog against a 9, X, or A.
.
Pair | Dealer's up card
hand | 2 3 4 5 6 7 8 9 10 A
-----------------------------------------------------------
A- A | PH PH PH PH PDH PH PH Ph Ph Ph
you got 1D, S17 DAS?
thanks.
yumyumgeeitsfun,
I've provided the entire output for you. As you can see, with A-A vs. 5, if you cannot split, next best is to double.
I fondly recall playing this game when I first started playing!
.
1 deck, S17, DOA, DAS
Hard | Dealer's up card
hand | 2 3 4 5 6 7 8 9 10 A
-----------------------------------------------------------
10- 9 | S S S S S S S S S S
|
10- 8 | S S S S S S S s s s
|
10- 7 | s s s s s s s s s s
9- 8 | s s s s s s s s s s
|
10- 6 | s s s s s h h h h h
9- 7 | s s s s s h h h h h
|
10- 5 | s s s s s h h h h h
9- 6 | s s s s s h h h h h
8- 7 | s s s s s h h h h h
|
10- 4 | s s s s s h h h h h
9- 5 | s s s s s h h h h h
8- 6 | s s s s s h h h h h
|
10- 3 | h s s s s h h h h h
9- 4 | s s s s s h h h h h
8- 5 | s s s s s h h h h h
7- 6 | s s s s s h h h h h
|
10- 2 | h h h s h h h h h h
9- 3 | h h s s s h h h h h
8- 4 | h s s s s h h h h h
7- 5 | h s s s s h h h h h
|
9- 2 | DH DH DH DH DH DH DH DH DH DH
8- 3 | DH DH DH DH DH DH DH DH DH DH
7- 4 | DH DH DH DH DH DH DH DH DH DH
6- 5 | DH DH DH DH DH DH DH DH DH DH
|
8- 2 | DH DH DH DH DH DH DH DH H H
7- 3 | DH DH DH DH DH DH DH DH H H
6- 4 | DH DH DH DH DH DH DH DH H H
|
7- 2 | DH DH DH DH DH H H h h h
6- 3 | DH DH DH DH DH H H h h h
5- 4 | DH DH DH DH DH H H h h h
|
6- 2 | h H H H H H h h h h
5- 3 | h H H DH DH H h h h h
|
5- 2 | h h h H H h h h h h
4- 3 | h h h H H h h h h h
|
4- 2 | h h h H H h h h h h
|
3- 2 | h h h H H h h h h h
|
Soft | Dealer's up card
hand | 2 3 4 5 6 7 8 9 10 A
-----------------------------------------------------------
A- 9 | S S S S S S S S S S
A- 8 | S S S S DS S S S S S
A- 7 | S DS DS DS DS S S h h s
A- 6 | DH DH DH DH DH H h h h h
A- 5 | h h DH DH DH h h h h h
A- 4 | h H DH DH DH H h h h h
A- 3 | H H DH DH DH H H h h h
A- 2 | H H DH DH DH H H h h h
Pair | Dealer's up card
hand | 2 3 4 5 6 7 8 9 10 A
-----------------------------------------------------------
A- A | PH PH PH PDH PDH PH PH Ph Ph Ph
10-10 | S S S S S S S S S S
9- 9 | PS PS PS PS PS S PS ps s s
8- 8 | Ps Ps Ps Ps Ps Ph ph ph ph ph
7- 7 | ps Ps Ps Ps Ps ph ph h s h
6- 6 | ph Ps Ps Ps Ps ph h h h h
5- 5 | DH DH DH DH DH DH DH DH H H
4- 4 | h H PH PDH PDH H h h h h
3- 3 | ph ph Ph PH PH ph ph h h h
2- 2 | ph Ph Ph PH PH Ph h h h h
-----------------------------------------------------------
S = Stand
H = Hit
D = Double down
P = Split
Uppercase indicates action is favorable for the player
Lowercase indicates action is favorable for the house
When more than one option is listed, options are listed from left to right in order of preference.
Up |
card | Overall expected value (%)
---------------------------------
2 | 10.207280001
3 | 13.869479692
4 | 18.573267564
5 | 23.852284019
6 | 24.375344289
7 | 14.695151167
8 | 5.480406657
9 | -4.366775083
10 | -17.072310820
A | -36.019565788
---------------------------------
Total | 0.182894557
Up | Probability of outcome of dealer's hand
card | Bust | 17 | 18 | 19 | 20 | 21 |Blackjack
-------------------------------------------------------------------------------
2 | 0.35297 | 0.13898 | 0.13176 | 0.13182 | 0.12395 | 0.12053 | 0.00000
3 | 0.37559 | 0.13031 | 0.13095 | 0.12376 | 0.12334 | 0.11605 | 0.00000
4 | 0.40280 | 0.13097 | 0.11416 | 0.12068 | 0.11629 | 0.11510 | 0.00000
5 | 0.42891 | 0.11969 | 0.12348 | 0.11691 | 0.10469 | 0.10632 | 0.00000
6 | 0.42082 | 0.16695 | 0.10645 | 0.10719 | 0.10070 | 0.09788 | 0.00000
7 | 0.25985 | 0.37234 | 0.13858 | 0.07733 | 0.07890 | 0.07299 | 0.00000
8 | 0.23863 | 0.13086 | 0.36299 | 0.12944 | 0.06829 | 0.06979 | 0.00000
9 | 0.23344 | 0.12189 | 0.10392 | 0.35739 | 0.12225 | 0.06111 | 0.00000
10 | 0.21426 | 0.11442 | 0.11288 | 0.11466 | 0.32888 | 0.03647 | 0.07843
A | 0.11654 | 0.12613 | 0.13100 | 0.12949 | 0.13155 | 0.05156 | 0.31373
-------------------------------------------------------------------------------
Total | 0.28359 | 0.14583 | 0.13806 | 0.13482 | 0.17581 | 0.07363 | 0.04827
You went beyond the call, well done. I haven't played this game in a while, but it's all comming back fast.
I have some doubts that doubling soft12 against 6 is better than hitting and my infinite deck program actually favours the latter slightly. After all, in 5 out of 13 cases one would like to hit again.
Francis Salmon
Francis Salmon,
Don Schlesinger's Blackjack Attack 3, Table A55 (6D S17: Dealer's Upcard 6), page 448, gives the EV's for A,A vs. 6 as -0.145699 for Stand, 0.187974 for Hit, 0.190709 for Double, 0.682366 for Spl1, 0.796424 for Spl2, 0.815037 for Spl3.
Eric Farmer's program for 6D, S17, DA2, DAS, gives -14.56985770% for Stand, 18.797352079% for Hit, 19.070859754% for Double, and 68.236641601% for Spl1 (since I input "no RSA").
Hope this helps!
Dog Hand
My infinite deck program gives an advantage of 0.6% for hitting over doubling but after checking effects of removal I realize that the two missing aces increase the dealer bust rate by 0.4% - just enough to tip the balance in favor of doubling.The dealer bust is of course essential in soft doubling since in most cases you end up with no total.
The perfect identity of Farmer's and Schlesinger's data is of course astonishing ...and since Don didn't mention Eric Farmer in his book, I assume they got their results independently.
Francis Salmon
"The perfect identity of Farmer's and Schlesinger's data is of course astonishing ...and since Don didn't mention Eric Farmer in his book, I assume they got their results independently."
Yes, for sure. But, as everyone knows, because I have plastered his name all over the Appendix, "my" results were generated by the one and only Cacarulo. :-)
Don
