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The Shapley value is one way to distribute the total gains to the players, assuming that they all collaborate. It is a "fair" distribution in the sense that it is the only distribution with certain desirable properties listed below. According to the Shapley value, [5] the amount that player i is given in a coalitional game (,) is
In chess, a relative value (or point value) is a standard value conventionally assigned to each piece. Piece valuations have no role in the rules of chess but are useful as an aid to evaluating a position. The best-known system assigns 1 point to a pawn, 3 points to a knight or bishop, 5 points to a rook and 9 points to a queen. Valuation ...
This set has been used since 2000. Before that year, a slightly different configuration was used: Ź was worth 7 points, F was worth 4 points, and there were 2 F's, and 8 A's. Literaki, a Polish online Scrabble-based game, uses the same distribution, but the maximum number of points for a tile is 5. [37]
The game value is determined according to the rules described under "Bidding" at the Skat article. Outside of official tournaments, other rules may be agreed privately at the table that affect the game value enormously. Such variants can be found under "Alternative game values" at that article. Bidding values in Skat
Therefore, a 1.0 WAR value for a player signifies a contribution of roughly 10 more runs than a replacement-level player, over a specified period of time. A replacement-level player is defined by FanGraphs as contributing 17.5 runs fewer than a player of league-average performance, over 600 plate appearances. [ 4 ]
In duplicate bridge only, game and partial-game bonuses are awarded at the conclusion of each deal as follows: any partial contract, i.e. one scoring less than 100 contract points, scores a bonus of 50 points, and; any game contract, i.e. one scoring 100 or more points, scores a game bonus of 300 if not vulnerable and 500 if vulnerable.
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In the traditional Hong Kong scoring system or the Cantonese scoring system, scoring tends to be low due to the few criteria used. The general scoring modifiers apply (see above), with the point translation function being a piecewise function: a constant amount is given for scoreless hands, and the score is doubled for each point (that is, an exponential function).