D&D 5E Title / Subject - or probabilities are hard

[clearstream]

Assuming you meant 1-2 is 1, 3-4 is 2, 5-6 is 3.

Oops! Thanks, I did.

Sort of interesting. Uniform random choice among the three sites is a better strategy than always sticking with the one you picked originally, but worse than always switching to one of the others. (6:24, 8:24, 9:24)

That's what I thought. What I found interesting is that obeying uniform random choice seems to overwrite the known odds. That seems identical to the naive error frequently made when first assessing the Monty Hall dilemma (to guess that odds are equal between the chosen door and the remaining door).

I'm familiar with the Monty Hall game, that's why I suggested it in this thread as a possible route for @CapnZapp to take. Using the original framing (because it is clearer) we can make a very simple statement like

1. There are 3 doors, one hides a prize
2. We get to pick one door
3. Given we had no other information, the door we picked has a 1:3 chance to have the prize
4. There is a 2:3 chance that the prize is behind one of the other doors
5. One of those other doors, that is certainly empty, is revealed: that doesn't change the probability distributed among them so the last door has a 2:3 of being correct

Say the contestant says "Hold on a minute here Monty, your conundrum is far too clever for me! I'll just flip this here nickel that I have in my pocket." It should be clear to all observers that the chance of that nickel picking the door that has the prize is 50/50.

That was intended to be ironic. And funny. Ironically funny.

I'll get my coat...

 

[CapnZapp]

The best part is that in a fantasy game like D&D you can frame this in magical terms: "when Monta tells you there's no gold at site 2, you feel the Probability Spirit escaping to site 3, doubling the chances of finding the statue there..."

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[clearstream]

The best part is that in a fantasy game like D&D you can frame this in magical terms: "when Monta tells you there's no gold at site 2, you feel the Probability Spirit escaping to site 3, doubling the chances of finding the statue there..."

That is one of the very, very neat things about games

 

[CapnZapp]

If I'm ever gonna roll up a Statistician character, it definitely will not be in one of these games...

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