move like a knight. This makes the queen very powerful, since she has the ability to administer mate without the assistance of any other pieces (for instance, an enhanced queen on h6 mates a king on h8, since Kg8 would still leave the king in check). Carrera considered this roughly equivalent to knight odds, although it varied depending on the players' strengths. Odds of the castled king: The odds-receiver begins the game with the positions of his king and one of his rooks interchanged (e.g., king on h8 or a8, and the displaced rook on the king's square). The first way (king on h8, rook on e8) is used unless otherwise specified before the game. Carrera thought this form of odds equivalent to the player with normally placed pieces giving a little less than two pawns, or a little less than a knight if the a8-rook and king are the ones interchanged. Staunton noted that Carrera's description and examples of these odds "are not adapted to our mode of castling" since the king and rook do not end up on the same squares they would normally occupy after castling. Staunton also mentioned the following unusual forms of odds not discussed by Carrera: Odds of the losing game: The odds-giver undertakes to force the odds-receiver to checkmate him. (See Paris–Marseilles, correspondence 1878, given below.) Additional pawns: The odds-giver permits the odds-receiver to begin the game with a specified number of extra pawns (for example, eight extra pawns). Unless specially agreed, the side with the extra pawns moves first. Odds of queen rook in exchange for the opponent's queen knight, or pawn and move, or pawn and two moves. Odds of queen knight in exchange for pawn and move, or in exchange for the first two moves. Rating equivalent Grandmaster Larry Kaufman wrote the following about the Elo rating equivalence of giving knight odds: [T]he Elo equivalent of a given handicap degrades as you go down the scale. A knight seems to be worth around a thousand points when the "weak" player is around IM level, but it drops as you go down. For example, I'm about 2400 and I've played tons of knight odds games with students, and I would put the break-even point (for untimed but reasonably quick games) with me at around 1800, so maybe a 600 value at this level. An 1800 can probably give knight odds to