## My Favorite Game, Social Media Style

*November 28, 2011 at 9:00 pm* *
10 comments *

Inspired by Planet Money’s Pick A Number contest, and buoyed by a story about how NCTM President Mike Shaughnessy recently used my favorite game with a group of students at Albuquerque Academy, I’ve decided to conduct an online experiment using a Google Docs form.

If you’ve got a minute and are willing to participate, read on.

The rules for my favorite game are as follows:

- On a piece of paper, everyone playing writes down a positive integer.
- Show your number to a neighbor (for verification purposes only).
- The winner is the person who wrote down
*the smallest integer not written by anyone else*.

In order for this psychological math strategy game to be any fun, you need one important piece of information — how many people are playing. If played as a solitaire game, you *should* win every time. But if played with a group of 50, well, some real thought will need to go into your choice. Consequently, I’m going to limit the game to 100 players. (Well, sort of. What I’m actually gonna do is break the total number of responses into groups of 100, and I’ll consider each set as a separate game. So it’s not exactly the same, but this should allow you to play using the same strategy as if you were playing with just 99 other people.)

For this online version, the second step of the rules — show your number to a neighbor — is unnecessary. So all you need to do to play is enter your number. (I’ve also asked for your name and email address, too, just so I can give you proper credit and contact you if you win. But those are optional. If you do supply your email address, cross my heart, there will be no spam or third‑party solicitations.)

**[Update]** This game was originally run for one week, Nov 28 – Dec 5, 2011. The results of that initial trial (based on 1,042 entries) are available at the link given below. That said, I see no reason to prevent others from participating and, from time to time, I will update the results page to reflect new data.

**https://mathjokes4mathyfolks.wordpress.com/2011/12/05/results-for-my-favorite-game/**

If you have difficulty accessing the form below, click this link.

Entry filed under: Uncategorized. Tags: docs, form, game, Google, number, postaweek2011, smallest.

1.Bon Crowder | November 30, 2011 at 3:32 pmI’m so nervous! Did I win? Probably not. No, really, the probability that I won is, well, quite low.

What IS the probability that someone wins this, anyway? 1/100? I’m guessing you can’t really tell because of the human factor – we’re all trying to think this through and figure out what others will do.

#ARG

2.venneblock | November 30, 2011 at 9:03 pmSorry, Bon, I should have mentioned that I’ll post results a week from the original post — which is next Monday, December 5. I want to give enough time for folks to pick a number.

3.Spiked Math | December 3, 2011 at 6:35 pmI’m pretty sure I won, so no one better be picking my number!!

4.SHiNKiROU (@ProjSHiNKiROU) | December 3, 2011 at 11:35 pmhttps://gist.github.com/1429134

I wrote a program to play that game in iteration.

There are 3 strategies:

– Adaptive: finds trend, randomizes data

– All One: always write 1

– Random

Here are the results for 1000 matches:

– 1 Adaptive, 1 All One, 48 Random: Adaptive wins

– 1 Ad, 48 A1, 1 R: Random wins (Adaptive second place)

– 48 Ad, 1 A1, 1 R: Random wins (Adaptive make each other lose)

An another strategy, Predictive is not yet programmed. It basically decides using n-grams, may be useful for matches between low amount of people.

Basically, if you found yourself in that game with full of inexperienced people, do Adaptive

5.Quantum Panda | December 4, 2011 at 1:07 amThinking about the strategies available to use in this game, I started considering the case of a two-player game. In that vein, I do not see any good strategy to use in a two-player game.

With only two players, there are only two cases: both players choose the same number, in which case no one wins, or they choose different numbers, in which case the lowest number chosen wins.

The logical play, in a two-player game, is to choose 1. If both choose 1, no one wins. If one player chooses a number greater than 1, then the other wins by choosing 1. I see no better strategy than choosing 1, as 1 loses only if both players choose the same number. Choosing any greater integer is a sign of overthinking it.

Somehow, I’m not comfortable with this analysis. Gut instinct suggests that a better strategy can be found with the right analysis. Is strategically analyzing the possibilities for two players second-guessing yourself, or is it something that can lead to a richer solution?

6.Jenny | December 4, 2011 at 2:26 pmIt’s definitely not 1/100, since there may not be a winner at all.

7.Martin Gerner | December 5, 2011 at 10:40 amWhen you announce the winner, could you also post a histogram of the distribution of the answers (both overall and limited to only the winning answers)? I’m curious to see what people entered.

8.venneblock | December 5, 2011 at 11:08 amAbsolutely! That’s part of the info I was planning to provide. I think it’ll be quite interesting.

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