Here's an example of Bayesian probability.
The proposition is:
47127418247124127428012420880848921392173297412972983482691264127966916284263432862841268461298642198461298461298461249812649126428682687 is prime
I don't know if this is true or false. The number was generated as a sequence of (quite) random digits. I checked the last one wasn't 5 or even, but nothing else.
@tygxc would say there are only two values of this proposition, so you have to either take the view it is true or it is false. This is wrong.
The appropriate Bayesian probability - a quantification of belief - would be the one that makes you neutral about the betting odds. To explain that, if the probability of an outcome is p, the fair odds on that outcome is (1-p) to p. i.e. if you stake p and the proposition is true, you get 1-p profit. If it is not you lose p. To put it another way, if you stake 1 that the number is prime you get (1-p)/p profit for being right and lose 1 for being wrong.
Your Bayesian probability is the one where you are indifferent whether you bet that the proposition is true (with odds (1-p)/p to 1) or false (with odds (p/(1-p) to 1).
Anyhow, back to that possibly prime number.
One approach would be to remember than the density of primes at N is about 1/log(N). So if you worked out the natural log of that number (easy to do approximately) and inverted it, that would be a probability you could use.
But you could improve on that. The last number not being a 5 or even increases the chance it is a prime (all the primes are in the other 4/10 numbers., so you increase p by a factor of 10/4=2.5 ). Then you could add all the digits up to see if the number is divisible by 3. If it is, bingo, you can make p=0! If not, p has increased again, but a factor of 3/2 this time.
An interesting point is that, as a betting game, the person who does a better job of estimating the probability is in a good position. If someone else offers different odds, he believes he knows which side is profitable. This is true even though both he and the other person might have worse estimates of probability than someone with better knowledge.
The best knowledge of all would be to have worked out that the number is prime or composite (This might be too hard for the players, but they would be told later).
"a weak solve means only the games derived from perfect play are known"
No perfect game of chess has ever been established to have ever happened.
Ever.
And regarding Elroch's post and 'magic step'
is claiming 'know more than all of you here' that 'magic step'?
Somebody here (not I and not Elroch) has emphatically so claimed.
We know who it is. Does it explain all his posts?
Very very possibly if not probably. More like probably.
------------------------------
History of the forum:
1) There was a gigantic claim by the 'knows more' person that the basic top speeds of computers in a chess context 'don't matter'.
That one didn't sell very well. Most people would know better. Do know better.
2) Same 'knows more than all' person tried to claim 'taking the square root' of the number of possible legal positions is 'OK'.
Anybody who knows anything about exponents knows its not.
That one didn't 'sell big' either.
3) But then some engines kept drawing each other.
That filled our 'knows more than everyone' friend with Much Hope.
Is now his Main Push. Along with the ++ stuff.
With the tactical references back to the failed #1 and #2 when needed so he can keep circling back to Main Push.
4) But various much better informed posters and posters much more free of illogic (big overlap there) then bring out the real information and logic while exposing and refuting the postings of the 'knows more' person and the discussion becomes informative instead of disinformational.
5) A moderator coming in helping the quality of discussion.