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If you have ever played a card game where you have to guess if the next card is going to be higher or lower than another card, this should not be a surprising r
by deckar01 7y ago
If you have ever played a card game where you have to guess if the next card is going to be higher or lower than another card, this should not be a surprising result. You should always assume the next card will be the average of all possible cards. What makes these kinds of games fun is having to recalculate the average card in you head based on the cards that you can see.
- lonelappde 7y agoThis is a different problem. Cards are finite. The OP problem is infinite.
- deckar01 7y agoThe set of real numbers used in the simulation is finite, but it doesn't prevent the result from being approximately the same. Using a small number of cards is no different. The best solution should be obvious, but was not presented in the cited paper, and was glossed over in this example. The more interesting result to me is that there is no difference between choosing the larger of two finite sets and choosing the more probable of two infinite sets. I think the whole pick a random number and modulate the choice based on it is rather trivial. Knowing that you are starting with a 75% success rate with the optimal strategy, you should be able to produce a strategy with an arbitrary success rate P=[0.25, 0.75] with one very simple extra rule: X% of the time, choose the non-optimal option. P = 0.75 - 0.5*X. If you want to construct a 66% strategy, choose sub-optimally 0.166% of the time.