"41.75% win" seems even worsely misleading. The value is technically true for a random position: some stats, but based on the immensely high probability that QxQ or a skewer wins on the spot. In a "neutral" position the chances are more like 0.4175% - if you can't capture or skewer the Q immediately, the only longer win is the Polerio ending. Thus, in the position after queening, you can almost make random moves as long as you don't hang your Q.

"41.75% win" seems even worsely misleading. The value is technically true for a random position: some stats, but based on the immensely high probability that QxQ or a skewer wins on the spot. (35%, minus K protects his Q, for the capture alone, see below.) In a "neutral" position the chances are far lower - if you can't capture or skewer the Q immediately, the only longer win is the Polerio ending. (Most illuminating here would be a stats of number of won positions vs. win length, this has been done, but I can't find a reference offhand.) Thus, in the position after queening, you can almost make random moves as long as you don't hang your Q.