Tag: love

• THE PRISONER’S DILEMMA-a core situation of game theory and probability

  The Prisoner’s Dilemma is considered as one of the greatest situations in game theory, and like many problems it seems very simple yet the math and logic behind it is very interseting. The situation simply goes:
  Two partners in crime are arrested. The police put them in separate rooms and offer them the same deal:
  If you both betray each other, you both get 2 years.
  If you betray your partner and they stay silent, you go free and they get 3 years.
  If you both stay silent, you both get only 1 year on a minor charge.
  
  So what do you do? Now you would think that a huge part of this has to do with your relation to the other person and how strong your bond and loyalty is. While this does play a factor if you were entirely focused on a shorter sentence this social aspect is irrelevant.
  
  Let E(silent) be the expected value of prison sentence if you stay silent, and let E(betray) be the expected value of prison sentence if you betray your partner.
  Also let P(this is the variable, depending on the other person’s loyalty) be the probability that your partner stays silent, meaning 1-P is the probability that they betray you.
  Now let’s split into cases on if you stay silent or if you betray:

  Case 1: You stay silent–> if they stay silent as well you get 1 year, if they betray you get 3 years
  E(silent)=1*(P)+3*(1-P)=3-2P (if you are confused where this formula is coming from, it is simply just multiplying the outcome by the probability of it happening, this is the most straightforward way of calculating expected value)
  Sentence for you: 3-2P years
  
  Case 2: You betray–> if they stay silent you get 0 years, if they also betray you get 2 years
  E(betray)=0*(P)+2*(1-P)=2-2P
  Sentence for you: 2-2P years

  Conclusion: E(silent) is 3-2P years, while E(betray) is 2-2P years. As you can see you will always get 1 year less on your sentence if you betray!
  
  So the moral of the story is to never lie to police(and always betray your friend, just kidding), but like always don’t blame the math!

  2026.07.24

• 7/17/25-repeatable things

  Everyone has that one thing. The most basic, yet oddly fun stress reliever. Something that is so random, something that everyone else would question. Something that just passes time. For me this happens to be throwing a foam ball off walls. Yes, I know, throwing something off of something seems like the most boring thing in the world but it’s just fun for me. My dad listens to a lot of podcasts and sometimes when I listen to a bit of them, a huge theme in many is that repeatable things result in repeatable outcomes, like if something is working, why change it? For me I do this throwing thing almost any time I have nothing to do, it just fills up the boredom, or “nothingness” and is something so mindless I can think of something completely different while doing this. To illustrate to you how much I do this, let me give you the exact details. It’s summer break for me, and it can’t be everyday that you meet a friend, or have a class, meaning much of the day is doing assignments and courses, You obviously can’t do this all the time(at least if you want to keep your brain from frying), so I have adequate breaks. During these breaks I read or throw my ball around. The total time I throw around is probably around an hour a day if not more. The walls in my room literally have black marks in the shape of circles from how much I throw. It’s just so easy, so oddly satisfying, and I’m sure that you have something like this, or you just haven’t discovered it yet. So next time you are bored think about what is something basic that makes you happy. 🙂

  Question: Do you have one of these “repeatable things” if so what is it? Comment your answer down below!

  ~aaroosh

  2025.07.17