She Loves me…She Loves me not
Now, I’d like to present my thoughts on how biased/unbiased this “Love me-Love me not” game is. Let me go through the protocol in detail for readers who’ve been blessed with the fortune of not committing this grave error (a waste of time), or for those who’ve not heard of this “event”.
- Pluck a daisy from your garden (or from your friend’s)
- Sit on a bench
- Feel anxious to know whether he/she loves you or he/she doesn’t.
- Start with one of the two phrases. “He/She loves me” or “He/She Loves me not” [Friendly Tip: Start this game with an auspicious phrase, preferably “He/She loves me”]
- As you pluck a petal*, alternate between the two phrases.
*Try not to Litter.
Now, coming to some simple math. Most daisies have a Fibonacci** number of petals. Why? The fibonacci numbers are linked to the golden ratio, which is intimately linked to the spiral forms of many types of shells. So, this gives us a finite list of numbers to work with. [0,1,1,2,3,5,8…]
** Fibonacci numbers were discovered by Leonardo Fibonacci in the early 1200’s, but Indian Scholar Hemachandra discovered this series centuries before Fibonacci (early 1100’s). I’m going to refer to Fibonacci numbers as the Hemachandra numbers from now on.
Given the number of petals is a hemachandra number, we have to determine whether this number is even or odd. There are 2 ways to determine this probability:
- 1. We know that hemachandra numbers follows this sequence (order): E,O,O,E,O,O,E,O,O,E… ie for every even number, there are 2 odd numbers. This simplifies our calculation, giving us probability of getting an odd number (2/3 = ~0.67) and getting an even number (1/3=~0.33). [E-even; O-odd]
Not convinced? Let’s try another method.
- 2. As, I’m a fan of the monte-carlo method for determining probabilities, I’ve written a simple python script to determine the probability of picking an odd hemachandra, and of picking an even hemachandra number. (Script attached)
This result clearly shows that the probability of getting a “She Loves me” result is significantly higher (~70%). As it isn’t a 50-50 (equal probability) event, I conclude this game is inherently biased.
All “Lovers” out there, plucking petals to know if she loves you, take advantage of this inherent defect and start this game with “She loves me” to get a desirable result 😉