How do we have the number of legal chess positions?
Tromp has the most accurate estimate here.
But it's only for basic rules (no account of 50 move rule or triple repetition rules).
Nobody has attempted an answer for competition rules, but it's VASTLY bigger (vastly bigger also than the number of ways of shuffling a deck of 52 playing cards).
@tygxc finds it more convenient to overlook the difference.
As a detached discussion of the facts, that remains valid. But it also remains true that it is very likely irrelevant to the weak solution of chess - the topic of this forum.
If it were feasible, the first variant of chess to solve would be one without any 50 move rule. All the two strategies to achieve this have to do is avoid a basic rules loss. This would achieved a la Schaeffer by constructing a complete proof tree with all leaf nodes being tablebase wins or draws (and many loops back to positions already covered).
The proof would not explicitly use a 3-fold repetition rule either, but games played according to one of the strategies will be guaranteed to reach one by the pigeon hole principle (if another satisfactory terminator is not reached).
The point is that if such a solution is a draw it will be fully adequate for FIDE rules too. The only thing that would change is some games ending earlier with 50 move draws.
[Note that pedantically we don't know the value of basic rules chess and we don't know that this form of chess has the same value as chess with some drawing rules, but it seems extremely likely that both have the same value because of the empirical rarity of positions requiring a relaxation of the 50 move rule].
. You are agreeing with "the trolls", just gnash your teeth and accept it.
And here is another example of @tygxc stating a falsehood that has already been pointed out.
He starts by suggesting ignoring 1999 out of 2000 positions with 3 or more promotions to pieces not previously captured can be ignored. This is absurd given that such positions even occur in the tiny master game database comprising less than 1 billion positions, a minuscule fraction of his own underestimate of the positions needed to solve chess.
So not only is the reduction absurd based on the data, it forgets that you don't find extremes in a tiny sample (like a billion positions). I feel here, @tygxc is genuinely deluded, confusing the fact that small samples can be good for estimating averages and not understanding that this does not extend to extremes (because extremes occur in such a small fraction of the data - there could even be just one example!) that they are not going to be visible in small samples at all.
And then, having wrongly argued for a 2000-fold reduction in the number of positions, he says to ignore 1999 in each 1000 of those positions by ignoring his previous reduction and using a position count for a game like chess where promotion to pieces not previously captured (an entirely arbitrary restriction on legal moves with no logical basis) is entirely illegal.
Counting is important. Being honest is too. Improvement is needed on both.