For a round of Golf, the net score for a player is their gross score minus their handicap. The net score for one hole is the gross for the hole, minus the strokes allowed for the hole. The stroke index for the hole and the players handicap is used to determine how many strokes you get, and on which holes.
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Net stroke match play is the same as normal matchplay with the difference being there is a handicap allowance. If a player gets a shot on a hole and makes 5 and his partner makes 4, his stroke reduces his score to 4 and the hole is halved. It is a way of making the game fairer and ensuring that all players play on a level playing field.