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cameron-martin / tsumego

An app for playing tsumego puzzles

Home Page:https://tsumego.app/

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Change puzzle win probability

cameron-martin opened this issue · comments

commented

#15 picks puzzles with 50% chance of solving. We must come up with a way of setting this probability to something different.

The following properties must hold:

  • The probability of the user solving puzzles given to them should be a fixed value. This arises from the notion that "puzzles should be of the correct difficulty" by just defining difficulty as the probability of the user solving a puzzle.
  • Every puzzle should have a non-zero probability of being shown to a user. This ensures that all puzzles will eventually get some games, and therefore have an opportunity to be rated.
  • Users should not be shown the same puzzle "too often". This is a bit of vague requirement currently.
  • The probability of a puzzle being chosen only depends on the rating and rating deviation.

Let be the probability that puzzle i is shown to the user. This is the distribution that we must sample from when showing the user a puzzle, but currently I do not know how to compute this distribution.

Let be the probability that the user wins. We want this to be a fixed value.

is the probability that a user wins given the puzzle is puzzle i. This is a known value and can be computed as shown in the glicko paper.

The relationship between these values is as follows:

commented

It should be explicit that the probability puzzle is shown to the user depends on the score and rating deviation of both the puzzle and user, i.e. that the function is .

I think the best way forward is to assert a form for and optimise its parameters such that is relatively constant (within an interval?) over representative values of and for all . We may be able to source this from chess data - it seems reasonable to assume that the distribution of user/puzzle ratings and rating deviations is similar.

The obvious choice of form is polynomials of increasing degree, or, in the extreme, an artificial neural network.

Edit: I hadn't appreciated that depends on all puzzles ...

commented

Alternatively, given a value of for a user and all puzzles (which we could recompute each rating period?), we could select puzzles such that the distribution of is approximately a chosen bounded domain distribution on [0, 1].