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Comment by gameswithgo | Hacker News Reader

I recall this happening as a high school kid. I couldn't tell from the arguments who was right or wrong, so I wrote a simulation, which was fairly easy, and proved her right. I found it interesting that writing an simple program in this case could confirm the right answer easily whereas having a PHD in math was no guarantee that you would reason it out correctly

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I wrote a simulation as an exercise (not to convince myself, just to illuminate the logic). I recall becoming extra-convinced when I spotted an optimization that would have been paradoxical if the correct solution hadn't been correct. I don't remember exactly what it was; I think it had something to do with collapsing nested if() into a single if() based on p vs. (1 - p) for the original door choice.

edit: the more I think about it, the more I suspect that the actual optimization was not randomizing both the door choice and the location of the car, which then allowed simplifying the win logic. If door 0 is always considered the door with the car, then the whole loop body can be collapsed down to:

    if (rand() / (RAND_MAX / 3) == 0) noswitch_wins++;

No threat of a paradox as I was thinking before, but a fairly clear statement that the odds of winning by not switching are 1 in 3.

This is actually a good example for a problem where simulation does exceedingly help in gaining insight. I once did a webpage [1] comprising both logic and simulation to sort out a dispute. (The debating parties each had a PHD in philosophy, implying some courses in logic absolved – which apparently didn't help much with the specific problem.)

[1] https://www.masswerk.at/misc/montyhall/

The key aspect, I think, is in writing the simulation oneself. At one point, I was attempting to explain the Monty Hall problem, and wrote a simulation out of frustration. It failed to convince the other person, who accused me of subverting the simulation such that it would give the answer that I wanted.

I'm wondering if gambling would be a good way to go about it. Start with $10 each, and alternate who plays the "host" of Monty Hall. One person is only allowed to switch, and another is only allowed to stay. For each correct answer, take $1 from the other person.

Hmm, maybe to sweeten the deal, the person who switches gets $2 for a win, but the person who stays gets $3. That way, it would show that even with 50% better payout, it doesn't overcome the 2x difference in odds.

Don't sweeten the deal. With the regular odds, after 12 games you will only be ahead ~61% of the time. You have to play a larger number of games to be relatively sure you win and the other accepts they must be wrong. The number of games increases by quite a bit if you sweeten the deal.

This is certainly true, if you're able to do the simulation on your own, you may also play with parameters, remodel the problem, etc.

Another problem which is best explained by simulation is the random distribution of wealth [1]. (I played a bit with this one, introducing further parameters like liminal damage, debt, asymmetric amounts depending on investors trust, etc, to see how basic economic assumptions would reshape the model. Answer: only to the worse.)

[1] http://www.decisionsciencenews.com/2017/06/19/counterintuiti...

That is true, if is only convincing for people who can understand the code.

I don't think I'm a sociopath, but often I use monte-carlo or agent based simulations to help me understand what happens, because writing and running the code is simpler (for me) than closed form analytic solutions. IF I then need to convince others, I guess I can do the closed-form solution (based on the prior intuition), but since I don't really care whether anyone agrees with me or not (I go develop 'engines' in my corner of "the system"), I guess their opinion is immaterial to my/group/company progress?

Do you think that agent-based computational simulations (say of micro-economics bubbling into creating emergent macro-economics) are ever used in debates?

I specifically changed my mind when one of the writers-in said they wrote a simulation and it matched what Vos Savant said.

That made me realize: code is a better way to describe problems than human text.

And I have written a simulation which proves her wrong, doesn't matter. I mean, when we deal with ambiguous questions like this a simulation doesn't really help since you had to add information not originally stated in order to write it. It just happens that most people make assumptions which aligns with this answer, but you could just as well make other assumptions and get another answer.

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