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In a game of cricket, it is not unusual for an experienced, high quality batter to be on strike, opposite a poor, tail-end player at the non-strike end. The player on-strike will usually try to score a single (or three runs) near the end of the over in order to be on-strike for the next over. This is done to prevent an inexperienced batter facing the bowler (and possibly getting out) and to provide more opportunities for the better player to score.

Supposing that the on-strike player hits the ball and one run is taken, then for some reason (an over-throw or a fielder fails to stop the ball) the ball goes to the boundary; the batting side is given four (or six) runs but can't rotate the strike when swapping ends may be of more value to them.

Is it possible for the batting side to decline the four/six runs in favour of the single run, and for the batters to change ends, with the experienced player ready to face the bowler at the start of the new over?

I've had a look The Laws of Cricket but can't find anything that covers this.

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    I do remember a test team kicking a ball that fell short of the boundary to the boundary once to get a player to remain on strike at the end of an over. The umpire decided to give it as overthrows and the captain got a warning for unsportsmanlike behavior
    – Neil Meyer
    Oct 11 at 11:04
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The simple answer is "no" - and this is exactly why towards the end of a first-class match if the bowling side is pushing for victory and the batting side has no chance of winning, you will see the field "come in" to prevent the single on the 5th or 6th ball of the over to keep the better batsman on strike, allowing the bowling team to bowl to the tailender in the next over. If the batsman scores a boundary, it's not going to affect the result of the match so the bowling side doesn't care.

The only exception to this is overthrows - if the batsman had crossed at the moment of the "overthrow or wilful act of a fielder" (Law 19.18), then the boundary counts in addition to the run already completed, so the batting team would score 5 and the batsmen would swap ends. This exception exists almost entirely to stop the kind of gamesmanship you suggest in your question.

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