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How to score this situation step by step?
No runners. Batter makes a bunt to the first base. Pitcher pick up the ball and throws it too high to 1B. Batter advances to third.
I have to score bunt and advances to third on error OR error (1) and the batter advances to third?
In what case I have to use in play->bunt?

In Play -> Bunt would only be used for a bunt single.

In this case, you would use In Play -> Error, error on pitcher, asks what happened to batter that is now on first, Safe, Third, Error, Pitcher.

If you believe that the batter would have beaten the throw without the error, then I agree bunt single and then error to get the batter to third. If the overthrow was the only reason the batter was not out at first, then batter reaches on error, no bunt single.