Change centipawn fallback to account for sharper WDL with high WDLCal…

…ibrationElo (#2075)

* half eval fallback formula 

With WDL sharpening at 3600 Elo (most commonly used value e.g. in TCEC both for playing and for kibitzing), the old centipawn calibration is off by about a factor 2 compared to Stockfish and generally takes over too quickly around +2.00 while it should only take over around +4.00 since up to there, `WDL_mu` behaves well enough.

With lower calibration Elo (e.g. for analysis of human games / openings), the takeover point is significantly later due to lower Q from broader WDL, so this change doesn't affect anything.

Doesn't yet fix the jumpy eval behavior in draws with very low W or L but substantial L resp. W remaining.

* changed factor to +128 convention

initial oversight: in a +1 position we want to display +128, that shouldn't change

src/mcts/search.cc

@@ -338,7 +338,7 @@ void Search::SendUciInfo() REQUIRES(nodes_mutex_) REQUIRES(counters_mutex_) {
       // Reports the WDL mu value whenever it is reasonable, and defaults to
       // centipawn otherwise.
       const float centipawn_fallback_threshold = 0.996f;
-      float centipawn_score = 90 * tan(1.5637541897 * wl);
+      float centipawn_score = 45 * tan(1.56728071628 * wl);
       uci_info.score =
           network_->GetCapabilities().has_wdl() && mu_uci != 0.0f &&
                   std::abs(wl) + d < centipawn_fallback_threshold &&