24728

To reach a score of exactly 1000 points, you should take five viewings and then using the 1 to 10 side of the bar chart, start rounding the number of marbles to a whole integer. You may have to fiddle around with this a bit and recording the seperate results from each viewing will be helpful in case there are any anomalies. (Make sure your rounded numbers add up to ten!) then take a guess.
If you get it perfect each time it will take you five turns because five viewings is 50 points and you add 150 points for a perfect score so overall 100 is added to the scroe you had at the beginning of the round