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Here, I've read through the famous Réti endgame study. However, there is a possibility that both sides can get a queen. For example, take a look at this variation.

[FEN "7K/8/k1P5/7p/8/8/8/8 w - - 0 1"]

1.Kg7 h4 2.Kf6 h3 3.Ke7 h2 4.c7 h1=Q 5.c8=Q+ *

I've consulted another Wikipedia page, entitled "Pawnless chess endgame", and it says "Queen versus queen: usually a draw, but the side to move first wins in 41.75% of the positions." You can also see the table from the "Tables" section, under the "Common pawnless endgames" subsection. It basically states the same thing. In queen vs. queen, the longest win is in 10 moves and the winning percentage is 42%.

I am really not very good at chess, but is the Wiki article totally correct? If it's correct, then, considering my 41.75 percent winning chance, how do I have to play in order to defeat my opponent if he/she and I both get a queen?

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considering my 41.75 per cent winning chance, how do I have to play in order to defeat my opponent if he/she and I both get a queen?

First of all you need to understand what is meant by "41.75% winning chance". It does NOT mean that your chances of winning are 41.75%. What it means is that in 41.75% of the games considered the game ended in a win and in the other 58.25% it ended in a draw.

Before heading for such an endgame you should first calculate what the result will be because it is pretty hard and fast unless one side blunders.

Basically (provided no blunders) it is always a draw unless one of two conditions apply:

  1. The side on move has a forced sequence of moves leading to checkmate
  2. The side on move has a forced sequence of moves leading to win of the opponent's queen

The problem is that if the side on move is not in check then they usually have the possibility of an almost endless series of checks on the opponent's king.

Here black is in check and can force an immediate draw by blocking the check with the queen and simultaneously giving check with Qb7+.

However even if black played Kb6 there is no forced checkmate for white and provided black doesn't blunder (by putting the king on the a8-h1 diagonal, the back rank or the h file allowing a skewer check) there is no chance of losing the queen. So it is going to be a draw.

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    Note that there's an important corner case where KQ beats KQ when the defending Queen is in the corner and the attacker finishes with a quiet King move. This is a common conclusion of King and pawn vs. King and Rook-pawn. For example, White to move starting Ke6+Pe5 vs. Kb2+a7 wins starting with 1 Kd5! and probably ending with Kb3+Qd2(e2) vs. Kb1+Qa1 where Black to move has no good checks and soon gets mated. To be sure this doesn't affect the Réti ending. Mar 3 at 4:29
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"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.

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In this specific position, there is nothing better than to force a queen trade (and the draw) by playing ... Qb7+.

Most good players would have agreed tp a draw no later than the 3rd move as they know that this position will end with in a draw with just reasonable moves. There are examples of both sides queening, but one sides wins due to an immediate checkmate or winning skewer. With lower rated players or maybe if time is really low, there's a chance for a mistake which would explain the absurdly high win percentage.

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