You could create a shared Google Docs spreadsheet and enter this into one of the cells:
=ROUND(RAND())
Or...
=IF(ROUND(RAND()), "Joe", "Sally")
Every time you save (or rather Google Docs autosaves), the random number generator will generate a new number. So to do a coin toss just type a random character into any (other) cell and hit enter. Both users will see the same result.
Some not so simple but more interesting solutions...
You could try generating 2 random stock symbols:
CONCATENATE(
CHAR(RANDBETWEEN(65,90)),
CHAR(RANDBETWEEN(65,90)),
CHAR(RANDBETWEEN(65,90))
)
and use GoogleFinance(..., "price") to look up which is higher. Sort of a Wall Street high card draw...
However, do not combine both formulas in one cell, because this will cause an infinite loop: GoogleFinance() will fetch the stock price, changing the spreadsheet, causing the RANDBETWEEN() functions to recalculate, causing the stock symbol to be changed, causing GoogleFinance() to fetch a new value...
You can however, automate this process safely by using JavaScript (Google Apps Script) to generate the random letters.
You can also use Google Apps Script to track the number of times the random number generator has been run in the first solution to prevent cheating (or simply modify the formula to insert a neutral value as a simple binary counter).
Another solution would be to take a random word or string, add the CODE() value of each character, and select the least significant bit. If you're really paranoid, have one person pick the string, and have the other pick which bit position to use.
2How about a checkmark, or series of checkmarks, then divide by 23, multiply for 49, minus 4, convert to binary, take the 1's and 0's and put them into base ten, divide by 2.5, stand on one leg, and choose left or right mouse click? If it's even, it's heads, odd, it's tails – Canadian Luke – 2012-04-02T23:27:25.677
2Play any two-player game where the result is random as opposed to skill-based? – Tamara Wijsman – 2012-04-02T23:41:23.770
^ like card or dice online games and use first card, high card, or first roll etc – Psycogeek – 2012-04-02T23:59:18.457
3Depending on how long you are prepared to wait, you could use tomorrows lottery numbers. If the first ball is less then half the max value, player 1 wins, if it is greater than half, player 2 wins. – Paul – 2012-04-03T00:13:56.800