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Choose the smallest number not chosen yet

amolas.dev

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Re: Choose the smallest number not chosen yet

#31

Post by londons_explore »

izietto wrote: post #16
alexmolas wrote: post #15

Earlier quoted context omitted.

hi! some people told me that they can access the site, but I've never knew why, and I'm not an expert on websites. Thanks for spotting it! How can I solve the problem? What does it mean to put a scheme in a cname?

> What does it mean to put a scheme in a cname? It means that https:// shouldn't be mentioned in the DSN records > How can I solve the problem? You should edit your DNS records and remove it

And the actual problem was probably that many browsers don't show the 'https://' in the URL bar, but do include it when copy-pasting.

So a user who copy pasted from the URL bar into the DNS records (probably following some guide) ended up with the wrong thing in there.

Re: Choose the smallest number not chosen yet

#32

Post by chii »

xnorswap wrote: post #5

This is used as a model for "reverse auctions" [1], which also then charges a fee for participation which essentially makes the whole thing a cross between a lottery and a scam. There were loads advertised on TV with misleading claims about people winning ipods for 37p, etc, which while technically might be true for the winner ignores the overall cost. I've not seen many advertised lately so either the practice itsel…

i thought these reverse auctions are more similar to penny auctions!

Re: Choose the smallest number not chosen yet

#33

Post by layer8 »

MauranKilom wrote: post #29

I read past four links in the text before it became clear that hyperlinks are visually indistinguishable from the rest of the text on this site. Who does this?

The links are dark blue with a very light grey underline. A bit hard to see, I agree, but not indistinguishable.

Re: Choose the smallest number not chosen yet

#34

Post by alexmolas »

wodenokoto wrote: post #20

So 3 players are following a strategy that leads them to wind just under a 3rd of the times on average. If they play thousands of times, what will the distribution of wins be?

that's an interesting question! I'll do the simulations later and add the plots to the post. Thanks for the suggestion :)

Re: Choose the smallest number not chosen yet

#35

Post by alexmolas »

planede wrote: post #26

What's super surprising if that I'm "dumb" and I play against two "smart" players then I can't have a bad strategy. Assuming that the "smart" players play the Nash-equilibrium mixed strategy then whatever strategy I execute, I have the same chance of winning.

oh, I didn't think about it!

It seems that it contradicts the principle of Nash equilibrium, since in Nash equilibrium you don't have any reason to change your strategy. However, if you change a "smart" strategy to a "dumb" strategy you're not increasing/decreasing your winning changes, so it still fulfills the Nash equilibrium principle.

Re: Choose the smallest number not chosen yet

#36

Post by planede »

alexmolas wrote: post #3
gus_massa wrote: post #2

If you have no played it, try this game with some friends. It's surprisingly fun. > To simplify the problem, let’s start with the simple scenario where you are competing against two other persons. > P(wining)~=0.296 Where does the other 11.2% go? Is the probability of a triple tie? Perhaps you can add it to the article.

I'll play it next time I see them :) Now I'm wondering which is the best strategy you can follow if the other players follow an unknown non-optimal strategy (like selecting 1,2 or 3 with p=1/3). Maybe it's a good scenario to try some reinforcement learning

> unknown non-optimal strategy

The hard part is to establish a prior for this "unknown". Otherwise you can't say anything.

Re: Choose the smallest number not chosen yet

#37

Post by lisper »

I must be missing something here.

> if we follow this strategy we’ll win a little bit less than one-third of the time.

That is not possible. If N players use the same strategy then by symmetry each of them must win on average 1 time in N. So against two other players we should win exactly one third of the time, not "a little bit less" than one third of the time.

Also, if all players use the same strategy then it doesn't matter what the strategy actually is. The only requirement is that it have some probabilistic element, otherwise all players would choose the same number every time.

Re: Choose the smallest number not chosen yet

#38

Post by [deleted] »

lisper wrote: post #37

I must be missing something here. > if we follow this strategy we’ll win a little bit less than one-third of the time. That is not possible. If N players use the same strategy then by symmetry each of them must win on average 1 time in N. So against two other players we should win exactly one third of the time, not "a little bit less" than one third of the time. Also, if all players use the same strategy then it does…

[deleted]

Re: Choose the smallest number not chosen yet

#39

Post by Revery42 »

planede wrote: post #26

What's super surprising if that I'm "dumb" and I play against two "smart" players then I can't have a bad strategy. Assuming that the "smart" players play the Nash-equilibrium mixed strategy then whatever strategy I execute, I have the same chance of winning.

This game seems to do weird things if you have a player able to disclose their choice in advance too. Stating that you will choose 42 is stronger than stating you will choose 1, assuming other players only maximize their own odds of winning. It's kind of like a convoluted game of chicken.

Re: Choose the smallest number not chosen yet

#40

Post by Jyaif »

lisper wrote: post #37

I must be missing something here. > if we follow this strategy we’ll win a little bit less than one-third of the time. That is not possible. If N players use the same strategy then by symmetry each of them must win on average 1 time in N. So against two other players we should win exactly one third of the time, not "a little bit less" than one third of the time. Also, if all players use the same strategy then it does…

sometimes all 3 players will choose the same number
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