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Kelly Can't Fail

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389 points jmount | 4 comments | | HN request time: 0.598s | source
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PaulHoule ◴[] No.42470752[source]
When I was a teen I discovered that I could always guess more than half the cards right using card counting to determine what color is more common in the deck. I programmed my

https://en.wikipedia.org/wiki/TRS-80_Model_100

to simulate it and it never failed. Recently I thought about it again and wrote a Python script that tried it 30 million times and... it never failed.

I've been thinking about what to do with it and came up with the options of (i) a prop bet and (ii) a magic trick, neither of which seemed that promising.

As a prop bet I can offer $1000 to somebody's $10 which is not the route to great prop bet profits, also I worry that if I make a mistake or get cheated somehow I could be out a lot of money. (Now that I think of it maybe it is better if I re-organize it as a parlay bet)

As a magic trick it is just too slow paced. I developed a patter to the effect that "Parapsychologists were never able to reliably demonstrate precognition with their fancy Zener cards, but I just developed a protocol where you can prove it every time!" but came to the conclusion that it was not entertaining enough. It takes a while to go through a deck which doesn't seem like a miracle, you will have to do it 7 times in a row to exclude the null hypothesis at p=0.01. Maybe somebody with more showmanship could do it but I gave up.

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1. jdhwosnhw ◴[] No.42473121[source]
That reminds me of my favorite algorithm, which can find the majority element in a list with any number of distinct entries while using O(N) time and O(1) space (provided a majority element exists). I sometimes pose deriving this algorithm as a puzzle for people, no one has ever solved it (nor could I).

https://en.m.wikipedia.org/wiki/Boyer%E2%80%93Moore_majority...

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2. barapa ◴[] No.42473561[source]
That is really cool
3. lupire ◴[] No.42475175[source]
What's great about that is that the assumption (or O(n) check) that the majority exists is incredibly powerful, enabling the algorithm, which is nearly the dumbest possible algorithm, to work.

The one flaw in the magic is that "2nd pass to verify" is a significant cost, transforming the algorithm from online streaming O(1) space to O(n) collection-storage space.

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4. jdhwosnhw ◴[] No.42480680[source]
Ah shoot I never thought of that. I wonder if there’s a sneaky way around it? You’re right, that definitely impacts the utility of the algorithm.