Claps!

In an earlier post, I wrote about how children intuitively make use of probability in games. Here, I further explore that premise by taking a specific example called 'Claps!' which my friends and I frequently used to make decisions in our games. I would recommend reading the earlier post since I make references to it in this post.

I was reminded of the claps method by a reader of the blog who recalled using it as a child! 😃 It looked something like this...

Source: https://www.istockphoto.com/in/video/multicultural-kids-group-hands-on-top-of-each-other-outside-gm819959134-135028361

The idea was simple - players would come together and each would put out one of their hands towards the centre of the group until we ended up with a pile of hands. On the count of three, we would all raise our hands and bring them back down away from the centre in one of two ways - palm facing up or palm facing down.

     

Based on the distribution of the two different orientations in the group, we would either pick an odd one out or make teams of players with the same orientation depending on the need.

Here, I will explore the case of picking an odd one out...

To pick an odd one out (three players)

The possible outcomes when three players are involved is shown in Figure 1. The rows boxed in green indicate the cases where it is possible to pick an odd one out. In each green row, the odd one out is marked with a red dot.

Figure 1

Evidently, in 6 out of 8 cases (or 75% of the time), the method of claps is successful in picking an odd one out. Perhaps, this is why we gravitated towards using it when we had three players among which we needed to pick/exclude one.

Also, note the symmetry and fairness - the 6 cases are equally distributed among the 3 players.

The logical next question - will the claps method to pick an odd one out work equally well (or better? or worse?) for 4 players? How about for 5 players? 6 players? What happens as the number of players increases?

To pick an odd one out (four players)

The possible outcomes when four players are involved is shown in Figure 2. The green boxes and red dots are used in the same sense again. Here, the 'P' denotes 'player'.

Figure 2

We can see that, in 8 out of 16 cases (or 50% of the time), the method of claps is successful in picking an odd one out. Decent, but not as good as when there were only three players.

Again, note the symmetry and fairness - the 8 cases are equally distributed among the 4 players.

To pick an odd one out (five or more players)

Following a similar logic:
  • if there were 5 players, the method of claps would be successful in 10 out of 32 cases (or ~ 31% of the time). For simplicity, only the 10 successful cases are shown in Figure 3 with the odd one out indicated by a red dot. In the remaining 22 cases, either all 5 hands are in the same orientation OR 3 hands are in one orientation and 2 hands are in the other orientation - either way, picking an odd one out directly was not possible in those cases.
Figure 3
  • if there were 6 players, it would work in 12 out of 64 cases (or ~19% of the time)
  • if there were 7 players, it would only work in 14 out of 128 cases (or ~11% of the time)
Are you seeing a pattern emerging?

Is there a link between the number of successful cases and the number of players?

What about the number of players and the total number of cases - is there a link there?

A key point here is that there is a steep decline in the effectiveness of the claps method for picking an odd one out as the number of players increases.

We children had an intuitive sense of this - I cannot recall a single scenario in which we tried to use the claps method for picking an odd one out when there were more than 4 players. We resorted to the strategy we used in Kings (see this post) or picked a person arbitrarily so that we could get the game started!

A hidden social element

I will conclude by highlighting something I found interesting and common to both the method used to start Kings and the claps method described above. In both cases, players come together to get the game started before dispersing when the den or the odd one is picked out. I found this act subtle but possibly integral to the inherent social element present in many games.

Standing around in a circle in close proximity or having one's hand a part of a pile of hands perhaps, subconsciously, makes each player feel a part of a group that is invested, for however short a time, in making the game a fun experience for all players. 😀

Comments

  1. Hello Bhaiya !!
    Thank you for sharing me the post. Reading the post I was remembering the sweet memories and I don't remember last time the I used this technique. When we used to use this method we would work on majority. We all would say that "MAJORITY WIN". When the numbers increases it was easy for us to pick the person(Criminal). Concluding, I admire the way you are demonstrating the application of maths.
    Once again Thank you !!

    ReplyDelete
    Replies
    1. Hi Adnan,

      Yes, the majority method is useful when we do claps in stages. As I wrote in the fourth paragraph, making teams is also something that can be done with claps. Maybe, that will be my next post! :-)

      Delete
  2. I see the patience in this post, chalking out the probability for each case scenario. Thanks for reminding of the claps we have played and now I see my daughter playing and presenting this way

    ReplyDelete
    Replies
    1. Thanks, Arpan!

      Glad it brought back some childhood memories for you and it is heartwarming to know that your little girl does this in school today too!

      Delete
  3. This was such a great throwback! Another point about probability - The probability definitely trends with what we used clap for. As the probability for odd one out got lower with increased number of players, we used it more and more for dividing players into two teams for which the probabilities trend higher. Great that you have analyzed this in a wholly mathematical manner, with an icing of philosophy too, loved reading it.

    ReplyDelete
    Replies
    1. Thanks, Kartik!

      Take a look at the fourth paragraph - you'll see that I mentioned how we used claps to make teams as well. In fact, I am thinking about writing that as the next post... let's see! I am sure if I do the basic analysis for making teams, it will reveal higher probabilities which is possibly why we used it. :-)

      Nice phrase - "icing of philosophy" :-)

      Delete
  4. Loved this post! Such fond memories. From what I understand this method is universally used around the country (maybe even elsewhere) and actually goes by different names. Growing up in Manali, HP, we called this 'pugata'. What's interesting to me is that as kids, like you mentioned, though we didn't understand the inner workings of probability, we did intuitively know that the method is less effective with more participants.

    I think it goes to show how important it is to respect that intuition that children possess and the experiences children have already had, before we proceed to 'impart' something 'new' to them.

    ReplyDelete
    Replies
    1. Hi,

      I am really glad that you brought up the point on respecting children's intuitions and experiences. Often, teachers can fall prey to thinking of them as empty vessels into which knowledge and skills need to be poured - that is far from the truth! Thank you for highlighting that. :-)

      Interesting to note how this method goes by different names in different parts of the world. :-)

      Delete
  5. Great analysis and amazing efforts to pictorially represent the concept :D

    ReplyDelete
    Replies
    1. Thanks, Shaunak.

      Yes, pictures are often more powerful than words and very helpful in breaking down for the purposes of analysis. Something I have had to do a lot as a teacher! :-)

      Delete
  6. A beautiful read.
    "We children had an intuitive sense of this - I cannot recall a single scenario in which we tried to use the claps method for picking an odd one out when there were more than 4 players" --> Well actually. Similar to what someone has mentioned the comment above, what we used to do as children were that, if there are 5 or 6 members, we would eliminate one or 2 member with this. That way, with 5 members, it is super effective as 30 out of 32 cases you will find either 1 or 2 person who could be eliminated. With 6 members also, 42 out of 64 cases you can eliminate 1 or 2 members.

    ReplyDelete
    Replies
    1. Thanks, Gaurav.

      Yeah, we did that too in school too. In this post, I was focusing on the first iteration of the process and its connection to probability. :-)

      In the fourth paragraph, you'll see that I mentioned how we used claps to make teams as well. This works out similar to what you've written in your comment wherein we would opt for a 3-2 split (in the case of 5 people) or a 3-3 split (in the case of 6 people) for making teams. We can build on that idea by using it for elimination instead of making teams (as you've written here).

      Might be a future post - who knows?!

      Delete

Post a Comment