Double Down on Soft 12

[Cacarulo]

Another back-track for me on this. Further investigation of my algorithm shows that my software indeed only examined A,A vs ? as the initial hand. Because playing split aces is not allowed by the rules, examination of A; A,A ? never occurred.

Somehow Cac knew this psychically.

You made me laugh about my psychic powers
One thing you could try without modifying the code, is to remove an ace from the 6 deck pack, count it, and then recalculate AAv3. I think that would fix the problem.

Sincerely,
Cac

[Gronbog]

One thing you could try without modifying the code, is to remove an ace from the 6 deck pack, count it, and then recalculate AAv3. I think that would fix the problem.

Your psychic powers have failed you this time

Each time the hand A,A vs ? is examined during the simulation for this game, anywhere from zero to 22 other aces may have been removed. This is the same as things occur during actual play of the game and the results for playing A,A vs ? are the amalgamation of these results. So the contribution of A; A,A vs ? is actually represented (a back-back-track or re-track on my part?) along with all of the other possibilities. Removing an ace from the shoe would mean that anywhere from zero to 21 other aces may have been removed, which does not represent any useful situation.

Just curious. How do the CA algorithms handle the possibility that different numbers of aces may have actually been removed when playing this hand? In general, how do they handle the vast number of remaining deck compositions which are possible when playing any hand?

[k_c]

Your psychic powers have failed you this time

Each time the hand A,A vs ? is examined during the simulation for this game, anywhere from zero to 22 other aces may have been removed. This is the same as things occur during actual play of the game and the results for playing A,A vs ? are the amalgamation of these results. So the contribution of A; A,A vs ? is actually represented (a back-back-track or re-track on my part?) along with all of the other possibilities. Removing an ace from the shoe would mean that anywhere from zero to 21 other aces may have been removed, which does not represent any useful situation.

Computing splits efficiently requires using a fixed strategy. Computing every possible strategy decision encountered in the course of splitting a pair can result in an enormous number of iterations, each of which requires calculating dealer probabilities.

The split strategy known as CDZ- ignores computing post-split strategies altogether by applying pre-split strategies to split hands.
CD means composition dependent
Z means zero memory optimal strategy accounting for cards that have been played
- means pre-splt

I came up with a strategy which Eric Farmer calls CDP1. CDP1 uses the optimal strategy of the first split hand and applies it to all subsequent split hands. It is a fixed strategy because all split hands employ the same strategy. I think what Cacarulo is suggesting is something like this where split strategy indexes could potentially differ from indexes using pre-split strategy for splits. For a lot of decks there probably wouldn't be much difference.

Just curious. How do the CA algorithms handle the possibility that different numbers of aces may have actually been removed when playing this hand? In general, how do they handle the vast number of remaining deck compositions which are possible when playing any hand?

In the course of splitting varying number of pair cards are removed. A fixed strategy allows a very accurate estimate of split EV using a relatively small number of shoe states rather than having to consider all of the possible iterations.

The first split algorithm I came up with was recursive and continuously removes pair cards until no more splits are allowed. The theory was that hand1 and hand2 of a split would have equal EV if each could be resplit the same number of times. I proceed as if hand1 EV = hand2 EV and the repair the erroneous EV.

http://www.bjstrat.net/splitAlgorithm.html