# The maths of parkrun Bingo

1. How many parkruns should it take me to get a Full House?
2. How does my performance at parkrun Bingo compare with other parkrunners and some parkrun celebrities?
3. If every single person on the planet tried to complete parkrun Bingo, what is the fewest (and the greatest) number of parkruns in which people would complete a full house?
1. I could sandbag as I approach the line to try to target one of my missing times. This is not easy because of the difficulty in matching your desired finishing time to the one recorded the stopwatch. However, if I only required one number to complete my Bingo card, it would take me much less than the (on average) 60 attempts required by relying on probability alone.
2. I could go into WebFMS (the parkrun results system) and manually edit the seconds part of a few of my runs.
1. I wrote a computer program to simulate 7.44 billion parkrunners trying to complete parkrun Bingo (yes that’s everyone in the whole world).
2. I solved the problem analytically using probability theory.
1. By the time they join the 50 Club: no-one will have completed Bingo (obviously)
2. By the time they join the 100 Club: 1 in 12 million parkrunners will have completed Bingo
3. By the time they join the 250 Club: 39.3% of parkrunners will have completed Bingo
4. By the time they join the 500 Club: 98.7% of parkrunners will have completed Bingo
5. By the time they join the (as yet non-existent) 1000 Club: 99.9997% of parkrunners will have completed Bingo

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## More from Stephen Ferguson

Mayor of St Neots, Cambridgeshire County Councillor & parkrun Event Director

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## Stephen Ferguson

Mayor of St Neots, Cambridgeshire County Councillor & parkrun Event Director