Dice Binning Calculator for Post-Election Audits

Joseph Lorenzo Hall (joehall@berkeley.edu), UC Berkeley School of Information

To increase the transparency of the 1% manual tally process, a few California counties have begun to use 10-sided dice to produce publicly-verifiable random numbers (See Cordero, Wagner and Dill 2006). Unfortunately, using 10-sided dice to 1) select from only a few precincts or 2) to select from many precincts can require a lot of re-rolling of the dice. To increase the efficiency of the process, Cordero et al. suggest "binning" the dice rolls so that each precinct has a range of corresponding values, of equal width, that allow a higher percentage of dice rolls to "hit". This calculator implements this idea. It can also output the binning data in a form that is easily pasteable into a spreadsheet. Please click here for source code and licensing information.


Number of dice:
Number of precincts:
(By default, it starts with 2 dice and 13 precincts.)


Here are the steps necessary to paste the bins below into a column of a spreadsheet (We need to insert a new column, format that column and then copy and paste the data below.):

  1. Open the spreadsheet.
  2. In your spreadsheet, click on the column header for the column to the right of where you want the new column.
  3. In the spreadsheet menu, select "Insert" -> "Columns". This will insert a new column.
  4. With the new column selected, choose "Format" -> "Cells...". In the number tab select "Text" and click "OK". (We're text-formatting this column because some spreadsheet programs interpret numers like "7-13" as dates.)
  5. With your mouse, select all the bins below on this page. Copy the selection (Ctrl-C on Windows PCs or Cmd-C on Macs).
  6. In the spreadsheet again, click on the first cell of the column you just created. Paste the selection (Ctrl-V on Windows PCs or Cmd-V on Macs).
91-99 -> reroll