Here are some historical data showing uses of the Buffon Needle simulation to estimate pi.

The table gives the name of the investigator, the year of their investigation, the sample size (number of throws), and the estimate of pi, which we call pi-hat.

Name        Year       n        pi-hat
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Wolf        1850       5000     3.1596
Smith       1855       3204     3.1553
DeMorgan    1860        600     3.137
Fox         1864       1030     3.1595
Lazzermini  1901       3408     3.1415929
Reina       1925       2520     3.1795

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Actual pi is approximately 3.1415927.
From a paper by Gridgeman, 1960.