Double on split A's

Speaking of Little River's rule of being able to double on split aces (they call it buying one card), anyone have index #'s when to double or just stand. You cannot hit or resplit, you have to either stand or "buy" the one card. You also dont have to buy it for the full bet amount if its over table minimum. Here is what I asked the Wizardofodds:

While in northern Michigan I came across a new blackjack rule on splitting aces. Instead of resplitting you still only receive one card but you may double on it if you like. Can you tell me the effect of this rule?

I've never heard of this rule before. According to my analysis, being allowed to double after splitting aces decreases the house edge by 0.08%. However not allowing resplitting any pair, compared to resplitting to four hands, increases the house edge by 0.06%. So the combination of the two rules decreases the house edge by 0.02%. Following is the basic strategy of when to double after splitting aces, assuming 4 to 8 decks and the dealer stands on soft 17:
Soft 12 to soft 16: double against anything
Soft 17: double against 2 to 9
Soft 18: double against 3 to 6
Soft 19 to 21: never double May 30, 2004

Rules are as follows:
6 decks, S17, DOA, DAS, resplit to 3 hands except aces, no resplit aces but can double on them, no surrender.

Now lets say my bet was $20 and the table min is $5 and I split my A's against a 9 and catch a 2. Now I have A,2 vs 9. He says to double. In this instance would I double for the full $20 or just the $5 minimum. So I am asking for index numbers for all potential hands versus all the possible up cards. Also when to "buy" for the full amount or just the table minimum as well. Some will be obvious as in an A,6 vs 6, double for full of course, but some like the A,2 vs 9 senario are more difficult.

Quite an interesting option. I will take a stab at it and let's see how close my guess is. My response is italicized. I would like to see what the math guru's have to say.

Assuming the count is zero on the scenarios below:

Double with a minimum bet if not within BS index.

Soft 12 to soft 16: double against anything
Soft 17: double against 2 to 9 (wondering about 10 & A too)

Make play as is stated but with full amout double.

Soft 18: double against 3 to 6
Soft 19 to 21: never double

This type of play option would cause me to bet larger than the typical idex would provide when there are a considerable amout of "more than average" number of aces left in the pack. Be cool to have max bet down and catch a pair. But then if the next card is outside of BS for a double, the double down could be a minimum bet.

Ibeatyouraces,

Now lets say my bet was $20 and the table min is $5 and I split my A's against a 9 and catch a 2. Now I have A,2 vs 9.

Ok, to find the new B.S. (we'll get back to Index Numbers in a bit) whip out your copy of BJA3 and consult Table A58, page 451, which contains EV's vs. a dealer's 9 for 6D, S17. With A-2 vs. 9, we see that the EV's for Standing, Hitting, and Doubling are -0.539111 (Stand), -0.034089 (Hit), and -0.443187 (Double), respectively. Since the largest (in this case, least negative) of these is -0.034089, we see that Hitting is the B.S. play.

Note that the Double value is for doubling for the full amount, and is in units of your original bet (not the total bet).

In your case, after splitting aces and receiving a deuce on the first ace, Hitting is no longer an option, so now you have to choose among Standing, Doubling for the Full Amount, or Doubling for the Table Min.

If you Stand, your EV is $20*(-0.539111) = -$10.78.

If you Double for the Full Amount, your EV is $20*(-0.443187) = -$8.86.

Finally, if you Double for the Table Min, your EV is ($20+$5)*(1/2)*(-0.443187) = -$5.54. Here, the ($20+$5)*(1/2) term means that, if you double for $5, then your new total bet is $25, which has the same EV as if your original bet were $12.50 and you doubled for full.

Here, the highest EV (in this case, the least negative) choice is Doubling for Table Min.

Now, just run all the other cases to find the new B.S.

To get index numbers, you need to have the Stand and Double EV's at each TC, then perform the same type of calculations to find the point at which your strategy should change. If you have CVData, you can use it to generate Index Numbers for your game, request detailed output, and get these Stand and Double EV's for each TC.

Hope this helps!

Dog Hand

I dont have BJA3 hence this is why I asked so I guess I'll have to pick it up. Also I used the $20 figure an an example only. I am guessing anything over table minimum would give the same results, but then again maybe not depending on the up card. I would guess that it would be a full double down in any situation where regular BS would dictate as in my A,6 vs 6 senario but if it isnt, like the A,2 vs 9, then to double for just the table minimum. Better to buy a card for $5 then to be stuck with trash. It's a nice rule and casino but since the Kewadins have surrender, I prefer to go there when traveling to northern Michigan. But the figures are nice to know when hitting this joint. And also wanted to know if there would be index number on whether to stand or double on those plays.

PS: Detroit BJ still blows!!

would be when you catch another ace on one which has already been split. I have never seen anywhere any BS as to double on it or for which up card to double on, other then what the Wizard says. I would suppose against a 6 you would double for full but what would one do say against a 3 or 4 and what would be the correct index # where you would double for the full amount or just table min. It sucks to split aces against a 3 with a max bet out, then catch another ace and not know whether to double for the full amount or just the minimum.

Has the info you are looking for. He has a BS table for doubling for less after splitting aces. He does not list count based index plays though. You can buy his book right off this website.

Heres a link