Guess a Number Game Results

Chad DeShon

A few months ago we ran an interesting online game.

The game asked everyone to pick a number. Any number you want. And the winner would be the player who pick a number that was

bigger than 2/3s of the numbers picked and smaller than 1/3 of the numbers picked.

You can get a little dizzy if you think about this. The strategy is simple. Think of the average number everyone else is going to pick, and then pick a number that is a decent bit bigger than that. Of course, everyone else is doing the same thing. So they are going to be inclined to be a bigger number than normal. No problem. You'll just pick an even bigger number. But they know you are going to do that. So that are going to pick an even bigger number. And on and on and on.

It seems like if everyone is thinking it through, then the numbers will approach infinity. But you have to choose a real number to type into the box. How far do you go before you decide the number is big enough?

I have the answer.2,281 people played. And the winning numbers were...

(drum roll)

57,000 (picked by two people)

Now we are going to go off into the weeds about this game that I find completely weird and fascinating. If the intersection of big numbers and human sociology isn't interesting to you, then you should stop reading here.

Here's how the distribution of guesses broke down.


First, why were there 4 winners? You'd think that since 2281 - 1 is divisible by 3 there would only be one winner with 760 people having picked a larger number and 1520 people having picked a smaller one. The problem is, the person in that spot picked 57,000, which was also picked by another person, meaning that were only 759 larger guesses. So we have to expand to 4 winners before there were exactly twice as many guesses smaller than the winner as there were larger than the winner.

Here are my observations:
    • As you might guess, the answers formed kind of a bell curve. The winner was on the right side of the curve, but not out in the long tail.
      • The winner was closer to the peak of the curve than I expected. I think that is because the left side of the curve is steeper than the right side.
        • The median answer was 6,666. 6 people guessed exactly that. There were many guesses with repeating sixes. 2/3 seemed to make people gravitate toward repeating 6s.
          • The smallest guess was -5.387. It was the only negative number guessed.
          • One person guessed 0.
            • 9,999,999,999,999,9999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999 was the largest guess.
              • I am guessing that anyone who picked a number less than 10 didn't read the rules carefully or didn't understand them.
                • 25 people didn't guess a whole number.
                  • One person guessed a fraction. Their guess was 3 1/3. The other 24 stuck to decimals.
                    • Average is a completely useless statistic in a set like this. The average was approximately
                    • 43,840,713,137,512,700,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. This was larger than every guess but one.
                    • The most popular numbers picked were:
                      • Answer to the Ultimate Question of Life, the Universe, and Everything (19 times)
                      • The Sign of the Beast (16 times)
                      • The luckiest number in western cultures (15 times)
                      • Jenny Jenny's number (15 times)
                      • The unluckiest number in western cultures (13 times)
                      • 9 (11 times)
                      • two-thirds of one-hundred, rounded to the nearest whole number (11 times)
                      • 75 (10 times)
                      • four nines (10 times)
                      • Sequential digits one through nine (10 times)

                    We're going to play the game again!

                    Same rules as last time. Try to guess a number that is going to be higher than 2/3 of the numbers that everyone else guesses.

                    I'm really curious to see how publishing the results from last time affects the answers in this round.

                    The winner(s) will receive both games from our current Kickstarter.

                    << Click here to play! >>

                    Happy gaming,

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