Double Down on Soft 12

[Cacarulo]

Apparently this thread is talking about two different sets of rules, one of which is clear and the other is not.

1) The OP states that the rules are as follows: 6D,S17,DOA,DAS,SPA1,NS and the decks are shuffled after each hand.
As can be deduced from the photo of the basic strategy, it is possible to DD with soft-12, that is, after splitting a pair of aces and receiving
another ace in one of the hands (or in both).
Under this scenario it is only possible to count cards if there are multiple players at the table. Obviously the bets will be flat.
If the player is not counting cards the basic strategy is the one mentioned by k_c.
Therefore, the basic strategy would be:
6D, S17 (or H17)
AAv6 ==> DD
AAv5 ==> H
AAv4 ==> H
(Even removing three or four aces is still the same)
The expected values can be verified in BJA3.

2) The second set of rules has not been specified. If we assume that there is no shuffling after each hand, counting cards would make more sense in this case.
Gronbog assumes 6D (S17 or H17) and Hi-Lo as the counting system.
The indices are fine, but there is a little detail that was overlooked in their generation. For example:
AAv6 assumes that two aces and a six were removed from the pack and this implies that when you receive that hand you are NOT able to split the pair of aces.
What would have to be done is to remove three aces and a six to make the calculation since the soft-12 appears after splitting the first pair.
What is the difference? Let's see:

a) S17
AAv6 ==> DD if TC >= 0 (two aces and a six removed)
AAv6 ==> DD if TC >= -1 (three aces and a six removed)

b) H17
AAv6 ==> DD if TC >= -1 (two aces and a six removed)
AAv6 ==> DD if TC >= -2 (three aces and a six removed)

Sincerely,
Cac

[Gronbog]

The indices are fine, but there is a little detail that was overlooked in their generation. For example:
AAv6 assumes that two aces and a six were removed from the pack and this implies that when you receive that hand you are NOT able to split the pair of aces.
What would have to be done is to remove three aces and a six to make the calculation since the soft-12 appears after splitting the first pair.

No such detail was overlooked in my generation of these indices. The indices were computed using simulation and therefore the data were collected across a wide variety of naturally occurring hand compositions, remaining deck compositions and penetrations. No attempt was made to construct representative instances of the possible situations.

[Zenfighter]

No attempt was made to construct representative instances of the possible situations.

Let´s try then, with the aid of exact 6dks EoR´s (checksum = -2.46109 e -13) plus combinatorial analysis, I get the following results:

S (17) doubling A, A vs 6

Removing a, a, 6.

Db if TC > - 0.355349

removing a, a, a, 6

Db if TC > - 0.837136

H (17) doubling A, A vs 6

Removing a, a, 6

Db if TC > -1. 32251

removing a, a, a, 6

Db if TC > -1,73297

That every derived index has a certain element of faith in its generation, no matter if it is with Monte Carlo simulated runs, and/ or with the aid of exact combinatorial, is still a valid assumption, that Griffin foresaw, almost now, 43 years ago. Here the discrepancies between your figures and mine, and specially for the h17 ones, speak for themselves. A matter of faith, then? I will agree for close decisions mainly, but not for this case of doubling with the H17 rule in effect. The full -deck favorability for carry on the action, namely, to double down equals:

m (6) = 0,971026

And thus, your h17 index can´t be equal to zero, no matter how naturally it has occurred in your sims. It must be lower, then. Think about it, Gronbog. An “Old-Timer” advice, btw.

Zenfighter

[Cacarulo]

No such detail was overlooked in my generation of these indices. The indices were computed using simulation and therefore the data were collected across a wide variety of naturally occurring hand compositions, remaining deck compositions and penetrations. No attempt was made to construct representative instances of the possible situations.

Ok, I understand what you are doing. Would you mind checking AAv3 again (S17 and H17)? I got +7 for both cases. We also have a discrepancy in AAv6. For S17 I got -1 and for H17 I got -2.
Maybe it has to do with penetration, I don't know. I am using 4.5/6.

Sincerely,
Cac

[Gronbog]

Quote Originally Posted by Gronbog View Post
No such detail was overlooked in my generation of these indices. The indices were computed using simulation and therefore the data were collected across a wide variety of naturally occurring hand compositions, remaining deck compositions and penetrations. No attempt was made to construct representative instances of the possible situations.

Ok, I understand what you are doing. Would you mind checking AAv3 again (S17 and H17)? I got +7 for both cases. We also have a discrepancy in AAv6. For S17 I got -1 and for H17 I got -2.
Maybe it has to do with penetration, I don't know. I am using 4.5/6.

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.

[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

[Gronbog]

The indices are fine, but there is a little detail that was overlooked in their generation. For example:
AAv6 assumes that two aces and a six were removed from the pack and this implies that when you receive that hand you are NOT able to split the pair of aces.
What would have to be done is to remove three aces and a six to make the calculation since the soft-12 appears after splitting the first pair.

In the mean time, until I can find time to digest what has been posted with respect to methodology, it might be reasonable to run this experiment.

Rather than removing an ace, I think the equivalent adjustment for my software would be to discard and count an ace at the start of each shoe (after the burn card). This would place all instances of A,A vs ? into a context where at least three aces have been observed and counted just they would be when playing A,A after splitting.

Does this sound reasonable?

[Cacarulo]

In the mean time, until I can find time to digest what has been posted with respect to methodology, it might be reasonable to run this experiment.

Rather than removing an ace, I think the equivalent adjustment for my software would be to discard and count an ace at the start of each shoe (after the burn card). This would place all instances of A,A vs ? into a context where at least three aces have been observed and counted just they would be when playing A,A after splitting.

Does this sound reasonable?

Perfectly reasonable. That is what I suggested in a previous post. I think there's a semantic issue about removing an ace, but it's exactly what you're proposing. That's why we're counting it.
In my program I don't burn any cards although I don't think that affects the results.

Sincerely,
Cac

[Gronbog]

it might be reasonable to run this experiment.

Rather than removing an ace, I think the equivalent adjustment for my software would be to discard and count an ace at the start of each shoe (after the burn card). This would place all instances of A,A vs ? into a context where at least three aces have been observed and counted just they would be when playing A,A after splitting.

Does this sound reasonable?

Perfectly reasonable. That is what I suggested in a previous post. I think there's a semantic issue about removing an ace, but it's exactly what you're proposing. That's why we're counting it.
In my program I don't burn any cards although I don't think that affects the results.

I didn't forget about this experiment. It just took some time for me to get to it.

Under the conditions suggested above, for doubling over hitting A,A vs 3 I now get +8 as the index S17 (was +9). This matches Cac's simulation result. However, I'm still getting +8 for H17 where Cac's simulation result is +7.

Some suggestions regarding the H17 difference:

1. Encountering this hand with at least three aces and a 3 removed at +7 and +8 is a rare event occurring only 122,878 and 98,232 times respectively over the course of 100 billion rounds I simulated. As such, the EVs that were computed are separated by only 0.5 standard deviations (the standard deviation of the difference in the EVs) giving a probability of about 30.85% that doubling might be correct at +7.
2. My software never computes indices in isolation. It always includes the effects of other related index plays. It does this automatically and I've never found a practical reason to prevent it. In the case of A,A vs 3 at +8, the only relevant index play which can also be triggered downstream would be 12 vs 3 (stand) at +2 (there are others but their indices are too negative for them to be relevant in this situation). I would be interested to see what index Cac and others get for this situation (A,A vs 3, at least 3 aces removed, H17) when 12 vs 3 is also enabled. This would tend to increase the value of hitting and therefore tend to make the index for doubling higher.

[Cacarulo]

I didn't forget about this experiment. It just took some time for me to get to it.

Under the conditions suggested above, for doubling over hitting A,A vs 3 I now get +8 as the index S17 (was +9). This matches Cac's simulation result. However, I'm still getting +8 for H17 where Cac's simulation result is +7.

Some suggestions regarding the H17 difference:

1. Encountering this hand with at least three aces and a 3 removed at +7 and +8 is a rare event occurring only 122,878 and 98,232 times respectively over the course of 100 billion rounds I simulated. As such, the EVs that were computed are separated by only 0.5 standard deviations (the standard deviation of the difference in the EVs) giving a probability of about 30.85% that doubling might be correct at +7.
2. My software never computes indices in isolation. It always includes the effects of other related index plays. It does this automatically and I've never found a practical reason to prevent it. In the case of A,A vs 3 at +8, the only relevant index play which can also be triggered downstream would be 12 vs 3 (stand) at +2 (there are others but their indices are too negative for them to be relevant in this situation). I would be interested to see what index Cac and others get for this situation (A,A vs 3, at least 3 aces removed, H17) when 12 vs 3 is also enabled. This would tend to increase the value of hitting and therefore tend to make the index for doubling higher.

In the index obtained by simulation I've also included other related plays like 14v3, 13v3 and 12v3.

For S17: 14v3 = -5, 13v3 = -2 and 12v3 = +2
For H17: 14v3 = -6, 13v3 = -3 and 12v3 = +1

I think the difference we have is in 12v3. Check that index.
Note also that in these indices the difference between S17 and H17 is one less, which is also true in AA(A)v3.

Sincerely,
Cac

[Gronbog]

In the index obtained by simulation I've also included other related plays like 14v3, 13v3 and 12v3.

For S17: 14v3 = -5, 13v3 = -2 and 12v3 = +2
For H17: 14v3 = -6, 13v3 = -3 and 12v3 = +1

I think the difference we have is in 12v3. Check that index.

Good call to also check the index numbers above with the extra ace removed. I had not bothered to check but, with the extra ace removed, my sim agrees with all of the indices above. I think that the negative indices are too far removed from A,A vs 3 at +7 and +8 to kick in downstream and have any effect with the 4.5/6 penetration we are using.

Are you saying that your H17 index for A,A vs 3 with the extra ace removed is still +7 even with these indices enabled?