J. A. Nairn false claims about first to calculate split evs for finite decks

[lij45o6]

To clarify, the tradeoff is between simplicity and *optimality*, not accuracy (at least in the sense of our ability to compute the exact EV corresponding to any of CDZ-, CDP1, CDP, or CDPN).

Got it!

And beyond this is what as far as I know only ICountNTrack has computed, the truly optimal overall expected value by playing *perfect* (EV-maximizing) strategy... where strategy within a split is allowed to vary depending on the *exact composition of all cards in all hands previously split*.

In short, I agree with what I think is Don's point in his comment: when we talk about "basic" strategy, basic is in the eye of the beholder, and a CDP player requires a better memory than a CDZ player (which in turn needs a better memory than a TDZ player-- and there are intermediate possibilities in between, such as that outlined in BJA3).

E

Yeah, in hindsight, I did ask a stupid question here!

I think I have a better understanding of what is going on here. CDZ* is much like CDZ-, except there are specific 'relaxation of the rules' governing CDZ-. As a consequence, such relaxation results in developing 'exceptions' much like [2 6] vs 5 as per the given example. This is akin to taking the TD strategy and saying: "Follow this strategy, except for +3-Card Hard 16 vs T; Stand." If I am not mistaken standing on all multi-card hard 16's vs a Ten results in a small improvement for the basic strategist, no? But, even then! Not all multi-card hard 16's are to result in standing. Some are still hit! What's nice is, we can delineate each of these exceptions and see how much gain in EV they offer us each. We can choose which ones to use and which to ignore. Much like post-split strategy, we can choose to include doubling [2 6] vs 5 or not!

With that said, it seems (correct me if I am *still* wrong) that what you are trying to look for is what post-split exceptions you want to include that maximizes EV for our zero-memory CD strategy. The issue is you don't know which ones to use as there may be multiple such strategies (hence CDZ*) and a full combinatorial analysis would be too much work to find out.

No updates. Nairn is saying he got it but the fact is that Cacarulo and I got it years before he did. We were first and it was based on my questions and ideas. Period. Even Eric's mini-paper was out before his (which again was based on my ideas even if a different hand order was used, and I have the emails to prove it, but Eric updated this). The fact that he assumes he's correct means he needed reference numbers. We provided those in the forums and Cacarulo provided them in Don's book. We got our initial couple of verifications from brute force calcs from Ken Smith. Nairn knows he's taking credit for other's work but Eric mentioned he talked to him before so if I go after him it'll have to be through his department and that risks his job. If he tries to actually publish it and not just arxiv it I'll have to bring it up. Hopefully he gets some sense before he pushes it further for publication.

I initially used Eric's dealer prob calcs and modified them slightly for splits but not that much. They are very fast.

I also save them all and re-use them for the various shoe states. Dealer probs for any player hand with 2 or more of the same card can be used for post-split calculations. You just change the player total accordingly. You can see how I do that in my CA. Since there are only a few thousand player hands total, it doesn't take long at all.

Storing/caching dealer probabilities is definitely an optimization technique that is to be used. (I know Eric caches his, and now I know you do to! )

With that said, I have been pondering if we can even speed up further on our computation of dealer probabilities. What I noticed is that there were some instances where some CA recomputes specific probabilities multiple times over for different dealer probability subsets and that the next optimization would be to store/cache pre-computed shoe subset probabilities.

A question I asked Eric a while back:

The genesis thought is this: There is a corresponding collection of dealer and player hand subsets that exists for some fixed deck set. That is, for an infinite deck, there are many probable dealer hand subsets for player hand [T6] and player hand [AA245] alike. Now, let's assume that there are a total of 3072 unique player hand subsets and 2200 unique dealer(S17) hand subsets. The product of these two is 6.76*10^6 unique evaluations. Now, does there remain certain evaluations that repeat? Let's say that we are evaluating player hand [66] vs dealer[T]. We will see dealer hands like [7T], [8T], [9T], [TT], and [AT]. Now, there same hands can be seen with player hand [56], [44], [23], ..., etc. So far, we have reduced this to less than 6.76*10^6 by a few less evaluations. Can we go further?"

The first thing that came to mind is that what is the connection between player hand subsets and dealer hand subsets when computing standing expectation? Well, it is the given deck subset! Right? Instead of recalculating all 2200 dealer hand probabilities 3072 times over, it is possible to reduce that to a much lower number, say, less than 10^6?

I speculate that "yes we can." How much of an improvement is up for debate.

[MGP]

Got it!

Storing/caching dealer probabilities is definitely an optimization technique that is to be used. (I know Eric caches his, and now I know you do to! )

With that said, I have been pondering if we can even speed up further on our computation of dealer probabilities. What I noticed is that there were some instances where some CA recomputes specific probabilities multiple times over for different dealer probability subsets and that the next optimization would be to store/cache pre-computed shoe subset probabilities.

A question I asked Eric a while back:

I speculate that "yes we can." How much of an improvement is up for debate.

Yes, the dealer probs are based on the shoe state... That's how I can re-use them. I started with Eric's method and fine-tuned for my CA and splits.

[iCountNTrack]

Thanks, Eric. Lovely post. Again, I've always had a problem calling CDP1, CDP, and beyond "basic" strategy, because, well, they're really just a form of card counting. None can deny that we're reckoning all the cards we see. How can that suddenly become anyone's definition of "basic" strategy? Finally, what sense does it really make to permit the reckoning of every card in four split hands (maybe even 20 cards) in what we will call basic strategy but not permitting the reckoning of our neighbor's two cards while we play our two-card holding? The former is "permitted" within the realm of someone's definition of "basic" strategy but the latter is not? It's a purely arbitrary convention that I simply cannot abide.

Don

I have been away from Blackjack jargon for a long time and last time i read BJA3 was in 2009 . But my understanding of basic strategy is that its a EV maximizing strategy based solely on the player's hand, dealer's up card, number of decks in the shoe and game rules. Basic strategy has two flavors : composition dependent and total dependent, We would agree that total dependent basic strategy is by far the most used/known because of it's simplicity and effectiveness for shoe games ( i remember though seeing once at a 2D table a guy with a giant composition dependent handwritten cheat sheet ). Also probably note mentioning that total dependent basic strategy is not exactly pure total because it differentiates soft hands and pairs which are really composition dependent, but i digress...

That being said, all methodologies for computing EV for a split hand offer a means to generate the "Basic Strategy" (which could have been generated using CVData through a sim). My split calculation algorithm where the playing strategy is recomputed at every split hand based on the cards on all the other split hands. While my methodology for computing the expectation value of a split hand offers the perfect play EV maximizing strategy (call it CDO), while EV(CDO) will always be greater or equal to (CDZ, CDP etc...), for current blackjack rules the difference is usually in the 4th decimal and will not result in a discrepancy of a playing decision.

But suppose we have a game called Blackqueen with some weird rules that results in an optimum playing decision discrepancy between fixed split strategy and re-computed split strategy. A "Basic Strategy" player for Blackqueen will be at a disadvantage playing if he adopted the playing strategy from the fixed split strategy and not really using a "EV maximizing strategy" as defined in the first paragraph.

Also please note that while during the process of generating the basic strategy, playing strategies are recomputed based on composition of the split hands, for the player using that generated Basic Strategy that's not the case since his decision is always only based on the split hand being played and dealer up card.

[ericfarmer]

Anyways, I am not misunderstanding you. The example you give is a good one. It does give a higher overall EV. But what I am saying is that I don't think it's a matter of methodology missing local minima that needs something really special to find them. I will restate that a fully CDZ+ strategy is ONLY dependent on the shoe states I shared above and if you take all the CDP/CDN hands and play those out optimally then you will have a complete and full CDZ+ strategy. So in order to get a fully CDZ+ strategy I am saying you simply do the same kind of calculation but use the pair hand options in the calc, go through it again if there is a strategy change to make sure and that is enough.

I'm afraid I need someone to help me understand this. First, what does "CDZ+" mean (since I haven't seen that mentioned in this thread yet)? I've tried to be precise about what we mean by CDZ, and CDZ-, and CDZ* as a temporary notation for a "local/single-step" modification of CDZ- strategy to marginally improve EV. What is "fully CDZ+"?

And how does CDP or CDPN factor into the determination of an optimal *zero-memory* strategy (where we must make the same decision ignorant of whether we are even *in* a pair split), other than by providing a set of *candidate* modifications to CDZ-? That is, what does "take all the CDP/CDN hands and play those out optimally" mean?

[ericfarmer]

No updates. Nairn is saying he got it but the fact is that Cacarulo and I got it years before he did. We were first and it was based on my questions and ideas. Period. Even Eric's mini-paper was out before his (which again was based on my ideas even if a different hand order was used, and I have the emails to prove it, but Eric updated this). The fact that he assumes he's correct means he needed reference numbers. We provided those in the forums and Cacarulo provided them in Don's book. We got our initial couple of verifications from brute force calcs from Ken Smith. Nairn knows he's taking credit for other's work but Eric mentioned he talked to him before so if I go after him it'll have to be through his department and that risks his job. If he tries to actually publish it and not just arxiv it I'll have to bring it up. Hopefully he gets some sense before he pushes it further for publication.

"We were first and it was based on my questions and ideas. Period." I think we should all take a deep breath here. I don't see how you can possibly claim this. As I said before, as just one potential example, Max Berger was providing CA numbers in rgb discussions in the late 90s; how do you know he had not solved this problem well before you, and simply hasn't bothered to let anyone know about it, let alone publish algorithms or results? How do we know someone else with even less online presence hasn't solved this problem quietly on their own, and simply been, as Cacarulo was at the time, "not 100% comfortable about it being available publicly" (an attitude my opinion of which has been made repeatedly and painfully clear )?

To be clear, I'm not defending Nairn. If you've contacted him and pointed him to credible dated online sources of exact values demonstrating that he's late to the party, then he should acknowledge as such. But that acknowledgment should be of the form, "MGP and Cacarulo have computed these values *before me*." This is different from saying "MGP and Cacarulo computed these values *before anyone*."

[MGP]

I'm afraid I need someone to help me understand this. First, what does "CDZ+" mean (since I haven't seen that mentioned in this thread yet)? I've tried to be precise about what we mean by CDZ, and CDZ-, and CDZ* as a temporary notation for a "local/single-step" modification of CDZ- strategy to marginally improve EV. What is "fully CDZ+"?


And how does CDP or CDPN factor into the determination of an optimal *zero-memory* strategy (where we must make the same decision ignorant of whether we are even *in* a pair split), other than by providing a set of *candidate* modifications to CDZ-? That is, what does "take all the CDP/CDN hands and play those out optimally" mean?

My bad, I meant just a fully CDZ calc where you include post split hands (I said CDZ+ to indicate post-split hands are included but it's redundant).


Let's step back a second and make sure we are talking about the same thing. To me:


1) We are talking about strategies from the top of the deck.


2) A fully CD strategy means each hand uses its best strategy


3) A hand does not include the upcard or split cards - i.e. a split into 2 hands means just that.


4) Whether the other cards in the other hands are used or not for the calculation is what differentiates the different CD type strategies.


5) CDZ means you play the hand the same way pre or post-split but take into account all used pre- and post-split hands in the calculation. CDZ- means you take into account only pre-split hands when determining the strategy.


6) After a split the calculations require that you take into account the order of hand creation. P cards are second or third pair cards that result in a new hand. N cards are non-pair cards that don't branch.


7) A CDZ strategy that takes into account post-split hands needs to weigh the net strategy for post-split hands that are reached into the EVs for the given hand to determine the overall strategy for that hand.


8) CDP means you can play hands after P cards removed differently than the pre-split hands. CDPN means you can play any of the types of hands taking into account the P and N cards that are remvoed.


What I am saying is basically what you have said in the past. You have pointed out that the hands after a pair have the same EV and I agree (putting aside that there is an equivalent calculation based on effects of removal that is more accurate with Australian rules).


I believe if you want a true CDZ strategy that looks for all exceptions like the one you found, it is enough to weigh in all CDPN type hands into the calculation and you will get the best strategy. But I do think you need to cycle through at least twice. Yes there may be a possible hand that is effected by other hands, but keep in mind that any CD strategy is built going upstream (i.e. start with hard 21 and work your way backwards) so other than by including pairs there isn't a way to come up with a higher EV play by changing things downstream that I can think of.

[MGP]

"This is different from saying "MGP and Cacarulo computed these values *before anyone*."

There may be a Newton (who calculated the orbits of the planets before Kepler) out there, but aside from that possibility I am very comfortable saying we were first and the first to share the values with the community, even if initially that community was private in the BJ Math private forum.

[exwannabe]

MGP. Regardless of who was first, I hope your method of calculating the exact number was more accurate than his.

Per the software he posts on github, his method of handling the dealer peek issue is wrong. He assigns zero probability to the dealer blackjack (correct), but then normalizes the remaining odds only locally for that leaf. It must be global. He should have passed up the normalizing factor (weighted and summed at each level) and applied the total to the final result.