Choose the smallest number not chosen yet
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Re: Choose the smallest number not chosen yet
#2If 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.
Re: Choose the smallest number not chosen yet
#3If 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
Re: Choose the smallest number not chosen yet
#4If 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
There is a nice strategy that is playing always 1, and claiming it.
Everyone else should not play 1 because otherwise they would not win. But if no one else plays 1, you win. So they must take turns to lose and make you lose. It's a good strategy to not meet them again ever :)
Re: Choose the smallest number not chosen yet
#5This 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 itself or the advertising of it was cracked down on.
[1] https://www.gamblingcommission.gov.uk/public-and-players/gui...
Re: Choose the smallest number not chosen yet
#6Interesting problem and I appreciate the author bringing it to our attention. That said, I have to admit I found the Math Overflow post he took the solution from much clearer: https://math.stackexchange.com/a/80743/
For one thing, the Math Overflow post is correct, whereas the blog post states a crucial inequality in the wrong direction. This confuses the whole argument, since the surrounding text isn't clear enough for the reader to easily self-correct the typo.
The other factor is the flow of the exposition. For example, the blog post attempts to define Q before using it, but the definition is too vague and ends up being less useful than the "define in the course of the argument" approach used in the Math Overflow post.
Re: Choose the smallest number not chosen yet
#7Interesting problem and I appreciate the author bringing it to our attention. That said, I have to admit I found the Math Overflow post he took the solution from much clearer: https://math.stackexchange.com/a/80743/ For one thing, the Math Overflow post is correct, whereas the blog post states a crucial inequality in the wrong direction. This confuses the whole argument, since the surrounding text isn't clear enough…
hi! thanks for your comment. which inequality is the wrong direction?
Re: Choose the smallest number not chosen yet
#8Interesting problem and I appreciate the author bringing it to our attention. That said, I have to admit I found the Math Overflow post he took the solution from much clearer: https://math.stackexchange.com/a/80743/ For one thing, the Math Overflow post is correct, whereas the blog post states a crucial inequality in the wrong direction. This confuses the whole argument, since the surrounding text isn't clear enough…
hi! thanks for your comment. which inequality is the wrong direction?
> Since we’re looking for the Nash equilibrium we’ve Q_i >= Q_P, this is, the best winning strategy you have is to follow the strategy P.
Re: Choose the smallest number not chosen yet
#9Earlier quoted context omitted.
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
There is a nice strategy that is playing always 1, and claiming it. Everyone else should not play 1 because otherwise they would not win. But if no one else plays 1, you win. So they must take turns to lose and make you lose. It's a good strategy to not meet them again ever :)
The other players then always pick 1 and 2, making the latter the winner, and you always the loser.
But in this case you lose no matter what strategy you use; you only get to decide which of the other players wins. That's why the article analyses the case where the other players use the same strategy.
Re: Choose the smallest number not chosen yet
#10If 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.
Yes, the only case in which there's no winner is if all 3 pick the same number.
Which is why the author skips the case of two players. Because then picking 1 always is a dominating strategy in which neither player wins.