Chess will never be solved, here's why - Chess Forums - Page 209

Elroch

Sep 26, 2022

0

#4161

MARattigan wrote:

But it's not a zero sum game without some changes to the FIDE rules.

Any FIDE rules that are not found in the pamphlet with a chess set that you might buy for a child are of no interest here.

It's about the legal moves and how a result is reached as a result of those moves. Those rules make the game finite and it can be assumed games are played to a finish. This is in common with the entire academic literature relating to this class of games ("combinatorial games" as @btickler reminded us they were called)

mpaetz

Sep 26, 2022

0

#4162

What you believe will not always prove to be true in the long run. You were the first to mention my supposed use of the term. I object to your putting words into my mouth and then chiding me for "saying" contradictory and/or incorrect statements, then publicly insinuating that I must be drunk, insane, or deviously deleting posts when I point out you are mistaken. However wonderful you think your memory may be, you are obviously wrong on this point.

And if things were "better left to rest", what was the point of reiterating your unfounded claim? You seem to need to always have the last word in order to convince yourself of your mythical greater intelligence and understanding.

Let's see if you can actually practice what you preach and let this drop.

DiogenesDue

Sep 26, 2022

0

#4163

Optimissed wrote:

Oh yes, so you're contesting what is told on account of the language used to tell it? I don't think that quite works, sadly for your assumption.

"Old bean" and "old thing" are completely extraneous to the discussion and only serve to deflect from the fact that you had no answer for my previous post. It's a common tactic...more common among the general public than claiming mental superiority, actually . Your use of "contesting what is told" is a contortion you chose to avoid saying "contesting my argument", because then this answer which I am giving now becomes blatantly obvious...it's not part of your argument.

Carry on.

Elroch

Sep 26, 2022

0

#4164

MARattigan wrote:

Elroch wrote:

MARattigan wrote:

Elroch wrote:

Optimissed wrote:

I was also going to explain why game theory cannot apply to the solving of chess... [snip]

Go on, give us a treat. Perhaps afterwards you can explain why number theory does not apply to the number 213276247234766621.

I think @Optimissed might be right this time.

Under FIDE laws possible yields include but are arguably not restricted to (win,loss), (loss,win), (draw,draw), (win+draw,loss+draw), (loss+draw,win+draw), (win,win), (win+draw,win+draw) and (arbiter determined) without any ordering specified. The objective is checkmate but that cannot be forced except from positions that are already checkmate.

What part of game theory would apply?

Still thinking about 213276247234766621; don't tell me. It's not prime but it has abnormally few factors.

While I understand that you are being light-hearted, you understand that "solving chess" refers unambiguously to the abstract game of chess (or, to be precise, a version of it defined by the relevant rule set), which has no time limits, nothing happening off the board, but may include well-defined rules such as the option (or obligation) to claim a draw in an n-times repeated position, or when the 50 move rule applies.

No arbiters ever the chance to get involved any more than they do in the solution of tic-tac-toe - the only laws involved are those that govern legal moving and results.

If I recall, the only appeal to game theory that has taken place in this forum was to a general theorem that applies to a class of games to which chess belongs. Given the definitions:

A (pure) strategy for a side is defined as a procedure that generates a move for any legal position (note that a mixed strategy is one where it may vary the chosen move in a position, but we don't need these).
The value of a strategy is the minimum of the values it achieves against all opposing strategies
An optimal strategy for a side is a strategy that achieves the maximum of the values of all strategies for a side

then there exists an optimal strategy for each side and these strategies achieve the same result.

I'd like this theorem to be trivial, but when trying to show it was, I convinced myself it is not quite! The theorem seems to rely on the fact that every game is finite, for example.

My point is that "chess" generally refers to one of the games defined in the FIDE laws.

No, not when SOLVING chess. This is about the abstract game.

Because they allow for resignation and agreed draws

Both completely irrelevant to solving chess, just ways to save time in real, imperfect games before the rules decide the result.

which occur asynchronoulsy with the moves and the results are are not prioritised in terms of win draw or loss either beteen themselves or with the results of completed moves, the possible results have no defined order. Is (win,win) for White better or worse than (win,draw) or (win,loss)?

There are exactly three results of a game

WIN > DRAW > LOSS

ok?

You say:

"1. A (pure) strategy for a side is defined as a procedure that generates a move for any legal position ..."

Where do claims come in? Those are part of chess.

To solving chess, you can assume all claims occur by the player they favour. Equivalently, you can assume an automatic result. It's not about competitive play.

A good strategy should generate a draw claim under the 50 move rule at some point if the opponent has a frustrated win. (It should also accept a draw offer in a losing position, but that would be extending the meaning of "solution".)

No, that would simply be part of the solution. A side aiming for a draw claims the draw when it occurs (or equivalently for solution, it is automatic).

2. The value of a strategy is the minimum of the values it achieves against all opposing strategies.

There can only be a minimum if the results are ordered. They're not under FIDE rules.

I have no idea what you are thinking about. WIN > DRAW > LOSS.

Ergo game theory doesn't apply to chess.

A false conclusion based on erroneous thinking I can't fathom.

It could as you say be applied to abstract version of "chess" that differ only marginally from the FIDE games.

That's the chess that is relevant to solving chess. It ain't about imperfect tournament and match play (FIDE's preserve)

But you define only a solution. If you want to propose finding a solution using existing software (as does @tygxc) the software will implement a concrete version of chess which also differs marginally from FIDE.

What you really mean is that FIDE differs from chess.

DiogenesDue

Sep 26, 2022

0

#4165

Optimissed wrote:

You could always approach btickler and see what he has to say on the matter. I tried that approach with him probably eight years ago. He made a series of answers to the effect that he dislikes people and has no intention of being friends with anyone. He denies that now but that's what he does and that was his answer. So have a word with him and tell him not to be such a troll, maybe. Coming from someone else it may help. The present feud he has with me is the result of me doing what you just tried to do now, when he was attacking someone else. Well, I basically told him to stop.

That narrative is a complete fiction, for the record. We have never had significant PMs of any kind. You used to, on occasion, try to rope me into teaming up with you on other posters, but once it became clear to you that I don't respond to such games, you stopped trying to ingratiate yourself with me and moved on to those with less integrity.

Optimissed lives in a world determined by his ego's best efforts to shield him from the truth of how he actually feels not about everybody else, but about himself. That's really the whole story right there. If you read his posts with this lens, you will never misunderstand his intentions, and everything he says will fall neatly into place.

DiogenesDue

Sep 26, 2022

0

#4166

Optimissed wrote:

Who said PMs? And not my games. Yours.

You did, the last half dozen times you tried to foist this fiction. Apparently your memory is slipping...

Your post then became (additions in bold):

"Who said PMs? And not my games. Yours. I am sure that all is not well with you and that you habitually project your own insecurities on others. Ultimately you always end up accusing THEM of projection. There isn't any doubt about it at all. Bonkers. Completely."

...and then that post became:

"Was that for the dishonest, refabricated, invented record?

Anyway, who said PMs? And not my games. Yours. I am sure that all is not well with you and that you habitually project your own insecurities on others. Ultimately you always end up accusing THEM of projection. There isn't any doubt about it at all. Bonkers. Completely."

Note that you can keep adding more aspersions and deflections to it...it's not going to help. It's kind of funny because I am prone to adding new points and clarifying things, but when you attempt to do the same you add gibberish and obfuscation. We default to different goals in our communications.

MARattigan

Sep 26, 2022

0

#4167

Elroch wrote:

MARattigan wrote:

Elroch wrote:

MARattigan wrote:

Elroch wrote:

Optimissed wrote:

I was also going to explain why game theory cannot apply to the solving of chess... [snip]

Go on, give us a treat. Perhaps afterwards you can explain why number theory does not apply to the number 213276247234766621.

I think @Optimissed might be right this time.

Under FIDE laws possible yields include but are arguably not restricted to (win,loss), (loss,win), (draw,draw), (win+draw,loss+draw), (loss+draw,win+draw), (win,win), (win+draw,win+draw) and (arbiter determined) without any ordering specified. The objective is checkmate but that cannot be forced except from positions that are already checkmate.

What part of game theory would apply?

Still thinking about 213276247234766621; don't tell me. It's not prime but it has abnormally few factors.

While I understand that you are being light-hearted, you understand that "solving chess" refers unambiguously to the abstract game of chess (or, to be precise, a version of it defined by the relevant rule set), which has no time limits, nothing happening off the board, but may include well-defined rules such as the option (or obligation) to claim a draw in an n-times repeated position, or when the 50 move rule applies.

No arbiters ever the chance to get involved any more than they do in the solution of tic-tac-toe - the only laws involved are those that govern legal moving and results.

If I recall, the only appeal to game theory that has taken place in this forum was to a general theorem that applies to a class of games to which chess belongs. Given the definitions:

A (pure) strategy for a side is defined as a procedure that generates a move for any legal position (note that a mixed strategy is one where it may vary the chosen move in a position, but we don't need these).
The value of a strategy is the minimum of the values it achieves against all opposing strategies
An optimal strategy for a side is a strategy that achieves the maximum of the values of all strategies for a side

then there exists an optimal strategy for each side and these strategies achieve the same result.

I'd like this theorem to be trivial, but when trying to show it was, I convinced myself it is not quite! The theorem seems to rely on the fact that every game is finite, for example.

My point is that "chess" generally refers to one of the games defined in the FIDE laws.

No, not when SOLVING chess. This is about the abstract game.

I believe that most of the contributors are referring to chess as defined in the FIDE laws, in which case I was pointing out the answer to OP's question is no; the FIDE game is insoluble.

No reference to the rules of an abstract game have been posted. Would it have a dead position rule for example? Tablebase adjudication ignoring the 50 move rule at 6 or 7 men or not at all?

Because they allow for resignation and agreed draws

Both completely irrelevant to solving chess, just ways to save time in real, imperfect games before the rules decide the result.

More than that; if both players simultaneously resign, for instance, they both win. The resignation rule in that case does decide the result.

which occur asynchronoulsy with the moves and the results are are not prioritised in terms of win draw or loss either beteen themselves or with the results of completed moves, the possible results have no defined order. Is (win,win) for White better or worse than (win,draw) or (win,loss)?

There are exactly three results of a game

WIN > DRAW > LOSS

ok?

Ok in your abstract game probably (depends on the rules).

In what I think most people are referring to as "chess", not ok. What's the result if your opponent resigns simultaneously with you moving into a dead position. That should have occurred in practice (e.g. in KNNKP). According to the FIDE rules you have won and the game is a draw.

You say:

"1. A (pure) strategy for a side is defined as a procedure that generates a move for any legal position ..."

Where do claims come in? Those are part of chess.

To solving chess, you can assume all claims occur by the player they favour. Equivalently, you can assume an automatic result. It's not about competitive play.

In the solution of your abstract game you can maybe assume that, but can you in solving? If you use a tablebase generation procedure the question is bypassed. If you use SF it only thinks it knows who is in favour and will repeat once whether or no if its evaluation for the position is better. So it could terminate a winning game in a draw.

So far as I understand it @tygxc's method may take that as proof of a draw. Admittedly it's not actually solving.

A good strategy should generate a draw claim under the 50 move rule at some point if the opponent has a frustrated win. (It should also accept a draw offer in a losing position, but that would be extending the meaning of "solution".)

No, that would simply be part of the solution. A side aiming for a draw claims the draw when it occurs (or equivalently for solution, it is automatic).

A solution for a player is a strategy for achieving the best result. If the best result is a draw and the recommended moves lead to a win for the opponent that is frustrated by the 50 move rule or triple repetition rule singly or in combination should the strategy not also prompt a draw claim to avoid a loss? (If that's what you mean by automatic, isn't it what I said?)

2. The value of a strategy is the minimum of the values it achieves against all opposing strategies.

There can only be a minimum if the results are ordered. They're not under FIDE rules.

I have no idea what you are thinking about. WIN > DRAW > LOSS.

I'm thinking about FIDE chess. If the players simultaneously resign both players WIN (read the rules). Is that better than WIN or worse?

Ergo game theory doesn't apply to chess.

A false conclusion based on erroneous thinking I can't fathom.

Not false. I'm using chess in the sense I think it's mostly used. Game theory doesn't apply to FIDE chess.

It could as you say be applied to abstract version of "chess" that differ only marginally from the FIDE games.

That's the chess that is relevant to solving chess. It ain't about imperfect tournament and match play (FIDE's preserve)

Agreed. But you still need to specify what's the chess.

But you define only a solution. If you want to propose finding a solution using existing software (as does @tygxc) the software will implement a concrete version of chess which also differs marginally from FIDE.

What you really mean is that FIDE differs from chess.

What I mean is that "chess" is being used in multiple senses and is a cause of some confusion. Some are taking it as FIDE competition rules, some as a to be defined abstract set of rules and some planning to use a GUI where you probably have to download the code to determine the rules. And all are different.

DiogenesDue

Sep 26, 2022

0

#4168

Optimissed wrote:

You edit your own posts continually so what point, if any, are you trying to make? And why don't you basically calm down and act more normally. Try to get on with others. This is a funny thread in not a particularly good way because it seems to attract people who are strange. I'm probably fairly strange too but I don't live in a delusory world.

You utterly do, not that you would be able to perceive that . The strangeness in this thread comes from two sources, both of whom have delusions that drive them. One driven by the need to be above everyone around them to feel secure and safe, and the other driven to turn the offhand comments of his deceased hero into reality.

DiogenesDue

Sep 26, 2022

0

#4169

speedupthesurfer wrote:

Will we ever known the EXACT number of sand grains on all the world's beaches???

No, but that is a fluctuating number, for multiple reasons . The analogy is not quite there.

DiogenesDue

Sep 26, 2022

0

#4170

speedupthesurfer wrote:

How is it fluctuating? Because people may take the sand home or it can blow onto the streets?

- The word "beach" is loosely defined and impossible to delineate for purposes of counting grains of sand.

- The word "sand" is also loosely defined.

- Sand particles are constantly being added to the world and making their way into beaches via erosion et al.

- Sand particles are constantly being removed from beaches in many ways.

Elroch

Sep 26, 2022

0

#4171

@MARattigan, the notion of solving chess is an abstract one, about the game as a mathematical object, an example of a combinatorial game. The precise drawing rule needs to be specified, but nothing that is not part of chess as a combinatorial game. There is no need for resignation or agreement of draws. While they could be added as optional actions they are superfluous to a solution.

The entire literature on solving combinatorial games deals with combinatorial games in the same way. (Eg that on the solution of checkers and a few modern popular games).

https://www.gamesver.com/is-connect-4-a-solved-game-what-does-that-even-mean/

Apparently Reversi/Othello remain unsolved, while 4x4 and 6x6 versions have been solved.

MARattigan

Sep 26, 2022

0

#4172

@Elroch. Agreed I don't think I said any thing to contradict that.

Except that if resignations and agreed draws are added they need to be prioritised with other game terminations or you don't have a zero sum game. Also you can't make the objective checkmate because that is never achievable against all opposition; if your opponent resigns you're stuffed.

The drawing rules for FIDE basic rules, FIDE competition rules, ICCF and TCEC are all different and would need different abstract games (TCEC could be very interesting). I'm not in any way convinced the solutions will be the same. They're all aiming toward different endpoints.

DiogenesDue

Sep 26, 2022

0

#4173

Optimissed wrote:

No, It's just because so many people here have disagreed with me over things I find obvious and clear, and when I challenge them there is usually no attempt to answer. People just sidestep. I know the chances of anyone having my IQ are vanishingly small and to you, conveniently, it's a delusion. The point is I know I'm clever and when Elroch or you fail to get the point of whatever it is, forever and forever, I'm obliged to put it down to that. I really am used to it. You, in your strange world of delusion, edit out uncomfortable facts but I have to admit that I am arguing here with a series of has-beens and never-wases because even at my age I'm still learning. You win a prize for guessing what I'm using it to learn.

It was good to see MAR finally getting the bit between his teeth. I think I commented a couple of months ago that I thought he was the only one here who has a good intellect. I'm not counting myself .... in a way I'm not here. That is, not accepted because I don't make the right grunts. Noises. MAR is finally taking on Elroch. I won my argument with E about game theory a dozen times and Elroch wasn't capable of even understanding that, let alone admitting it. So let's see how MAR does.

See, that's the only way your narrative holds up, if you are a 1 in a billion level genius, and everybody who disagrees with you are has-beens or never-have-beens. Now apply Occam's Razor and let the truth in...

What is it that makes you something more again? I'm not talking about IQ test scores or the psychic musings of long ago girlfriends...

You see, I don't really care if you want to have an opinion on everything and be stubborn about it. The problem is that you can't seem to do this without disparaging everyone around you. If you were one of those posters that ended with "well, I disagree, so I guess we're at an impasse", then I would not have much to say to you over time. I can only speak for myself, but I am guessing others feel similarly. I'm also guessing whatever you might have said that you deemed complimentary to Maratiggan might not have been taken as such. You have said similar things in the past about how felt about others... myself, Elroch, Tygxc, even CooloutAC, and how you "complimented" others' intelligence...by squarely placing it well below your own supposed but completely unproven level .

MARattigan

Sep 26, 2022

0

#4174

MARattigan wrote:

@Elroch. Agreed I don't think I said any thing to contradict that.

Except that if resignations and agreed draws are added they need to be prioritised with other game terminations or you don't have a zero sum game.

The drawing rules for FIDE basic rules, FIDE competition rules, ICCF and TCEC are all different and would need different abstract games (TCEC could be very interesting). I'm not in any way convinced the solutions will be the same. They're all aiming toward different endpoints.

@Elroch

Apologies.

On further reflection I have to retract the last point if you discount TCEC. I think you're right about the common weak solution to (versions of chess suitably abstracted from) all three.

Obviously the Sysygy construction if continued to 32 men would give such a solution.

The results could be different for different versions, but the moves would produce the correct results in each case.

MARattigan

Sep 26, 2022

0

#4175

Elroch wrote:

MARattigan wrote:

But it's not a zero sum game without some changes to the FIDE rules.

Any FIDE rules that are not found in the pamphlet with a chess set that you might buy for a child are of no interest here.

It's about the legal moves and how a result is reached as a result of those moves. Those rules make the game finite and it can be assumed games are played to a finish. This is in common with the entire academic literature relating to this class of games ("combinatorial games" as @btickler reminded us they were called)

But the child's pamphlet usually still contains a resignation rule and an agreed draw rule without any prioritisation of concurrent termination results that involve them, so it's still not a zero sum game. To solve you need to either drop them in your abstract game or prioritise concurrent terminations. I've not seen any suitable rules that do.

DiogenesDue

Sep 26, 2022

0

#4176

Optimissed wrote:

You keep saying "you see". I noticed it twice at the beginning of paragraphs. I also noticed that you don't really care. I haven't read the rest because it's so predictable. No point ... you aren't interesting. I gave my age specifically to see what you would do with it and sure enough, back came "old and bitter". A stereotype and it wouldn't be a very kind one if it were true. But I have a beautiful wife who looks 20 years younger than she is AND she's younger than me by 8 years, most things I need, my son is successful and a good person and I'm happy. I keep fit, do long walks, keep busy, have lots of interests. What do you do? Find people to try to upset. That's about what you seem to enjoy. I don't need to prove anything to you. Ability speaks for itself but only for people who know the language.

Lol. No, I didn't say a word about your age, or call you bitter, until after seeing you wax eloquent for years on end. I don't judge you or your life...*until* you judge others around you. Then I hold up the mirror. That's the ultimate issue. The things I know about you, by the way, are all things you have used in the past in attempts to show yourself as "better than" or to try and support dubious claims about others. Hoist with your own petard.

Speaking of ability, if you had the ability to exist here without having to put down everyone around you when you don't get your way, then the forums would be better off, and you would be far better off. Your life would be measurably better if you never talked about IQ or basically anything that implies nobody on whatever thread you happen to be infecting can hold a candle to you intellectually.

...and someone with an actual 160 IQ would have theoretically figured this out by the age of 70 , if IQ actually meant what you'd like it to mean.

adriazolaIvan

Sep 26, 2022

0

#4177

TheChessIntellectReturns wrote:

Imagine a chess position of X paradigms.

Now, a chess computer rated 3000 solves that position. All well and good.

Could another computer rated a zillion solve that position better than Rybka?

No, because not even chess computer zillion could solve the Ruy Lopez better than a sad FIDE master could.

the point is, there's chess positions with exact solutions. Either e4, or d4, or c4, etc.

nothing in the world can change that.

So if you are talking about chess as a competitive sport, then chess has already been solved by kasparov, heck, by capablanca.

If you are talking chess as a meaningless sequence of algorithms, where solving chess equates not to logical solutions of positional and tactical prowess, but as 'how many chess positions could ensure from this one?'' type of solutions, then, the solutions are infinite.

So can chess be solved? If it is as a competitive sport where one side must, win, then it has already been solved. Every possible BEST move in chess has been deduced long ago.

If chess is a meaningless set of moves, with no goal in sight, then sure, chess will never be solved.

your definitions arent correct, can chess be solved, I dont know, havent done the mah myself, but Im pretty sure you can, no one will waste his time doing it because the partial solution we have is more than enough and we get faster methods to get to solving chess every now and then, so starting a 10 years process right now doesnt make sense if you cansider that maybe if you start nex year it will only take 8 years, but im pretty sure they already know its posible and how much it would take them.

tygxc

Sep 26, 2022

0

#4178

@5352

"you can't use Stockfish in solving anyway, because it is incapable of evaluating perfect play"
++ You can use Stockfish. As calculated before: if you let the cloud engine run for 17 s (or a desktop for 17000 s = 4.7 h) in a legal position of between 32 and 7 men, then the table base perfect move will be among the top 4 engine moves except for 1 position in 10^20.
That is good enough as there are only 10^17 relevant positions.

"If you want to solve it going forwards, you have to handle repetitions/circular positions"
++ Yes, 3-fold repetition is a major drawing mechanism e.g. 16% of ICCF WC games.

"I wouldn't consider chess fully solved if the 50 move rule is applied"
++ The solution will not invoke the 50-moves rule as in the perfect ICCF WC games we have.
On the other hand if chess is solved without the 50-moves rule, then that same solution also applies to the case with the 50-moves rule. The 50-moves rule is a red herring.

DiogenesDue

Sep 26, 2022

0

#4179

tygxc wrote:

@5352

"you can't use Stockfish in solving anyway, because it is incapable of evaluating perfect play"
++ You can use Stockfish. As calculated before: if you let the cloud engine run for 17 s (or a desktop for 17000 s = 4.7 h) in a legal position of between 32 and 7 men, then the table base perfect move will be among the top 4 engine moves except for 1 position in 10^20.

Unproven outside of endgames.

That is good enough as there are only 10^17 relevant positions.

Also unproven. We've been through this before, and you've been through this before with so many other people...everyone on this thread (myself, Elroch, Maratiggan, Mpaetz, and even Optimiseed), as well as Pfren, BlueEmu, et al who also pointed out to you that this does not fly. The trump card is Tromp, who also disagrees with you even though you base your premise on his numbers before hacking away 27 orders of magnitude in ridiculous fashion.

tygxc

Sep 27, 2022

0

#4180

@5397

"you can't use Stockfish in solving anyway, because it is incapable of evaluating perfect play"
++ Yes we can use Stockfish. As calculated before: if the cloud engine runs for 17 s (or a desktop for 17000 s = 4.7 h) in a legal position of between 32 and 7 men, then the table base perfect move will be among the top 4 engine moves except for 1 position in 10^20.
Unproven outside of endgames."
++ Proof: calculated by extrapolation from the AlphaZero autoplay paper.
https://arxiv.org/pdf/2009.04374.pdf Figure 2.
1 s / move: 11.8% decisive, 88.2% draws
1 min / move: 2.1% decisive, 97.9% draws
Extrapolating:
1 h / move: 2.1% * 2.1 / 11.8% = 0.37% decisive, 99.63% draws
60 h / move: 0.37% * 2.1% / 11.8% = 0.07% decisive, 99.93% draws
60 h / move on the engine of the paper corresponds to 17 s / move on a 10^9 nodes/s cloud engine
0.07% decisive means 0.0007 errors / game means 10^-5 errors / position
Thus for 4 candidate moves: (10^-5)^4 = 10^-20 errors / position.
Thus in 1 position out of 10^20 the table base correct move is not among the engine top 4 with the cloud engine running for 17 s at 10^9 positions / s, or a desktop running for 4.7 h.

This is verifyable. Take a 7 men position KRPP vs. KRP. Let a desktop run for 4.7 h.
The table base correct move is among the top 4 engine moves.

"That is good enough as there are only 10^17 relevant positions.
Also unproven."
++ Proven in 2 ways.
1) top down: from the Tromp count 10^44 legal positions proven none can result from optimal play and the Gourion count 10^37 positions then applying analogy to the weak solution of Checkers 10^14 and Losing Chess 10^9: a weak solution requires less positions than a strong solution. That leaves 10^17 relevant positions. 1 e4 e5 2 Ba6? or 1 a4 are not relevant: no optimal play by both sides.
2) bottom up: forward calculation with width w = 4 (from the above argument) and depth d = 39 (average length of ICCF WC games, > 99% sure to be optimal play from Poisson distribution fit) .

An upper bound assuming no transpositions:
1 + w + w² + w³ + ... + w^d = (w^(d+1) - 1) / (w - 1) = (4^40 - 1) / (4 - 1) = 10^23
A lower bound assuming permutations of all white moves :
1 + w/1! + w²/2! + w³/3! + ... = e^w = e^4 = 55 regardless of depth d
Geometric mean of lower and upper bounds:
sqrt (55 * 10^23) = 10^12
Thus 10^17 is plausible.

"you've been through this before with so many other people...everyone on this thread"
++ So far nobody has come up with any argument leading to another figure than 10^17.
If somebody has a valid argument why it should be 10^18 or 10^16 I am all ear.

"myself" ++ You keep erroneously using the number 10^44 needed for strongly solving chess

"Elroch" ++ Keeps insisting that 1 e4 e5 2 Ba6? or 1 a4 win for white, that 1 d4 loses for white, refuses to accept that an endgame with opposite colored bishops is a draw
Keeps refusing to incorporate knowledge into the game solving, though Connect Four has been solved with knowledge: 9 rules.

"Maratiggan" ++ Keeps trolling with the 50-moves rule and other artificial constructs

"Mpaetz" ++ Has not stated anything on that matter as far as I remember

"Optimiseed" ++ Just expresses his liking for a magical evaluation algorithm instead of calculation and then divinely jumps to 5 million years out of nowhere

"Pfren, BlueEmu" ++ Have not stated anything on that matter as far as I remember,
only some emotional opinion no it cannot be done,
presumably out of dislike of the possible solution of the beloved game.
It is like "Never shall I be beaten by a machine!", Kasparov 1989

I am the only one who presents facts and figures,
and I back these up with peer-reviewed literature.