The New Sudoku Players' Forum

[senecan]

This is a question about how to determine any particular Sudoku "play" as more difficult/rewarding than any other. Thanks for reading.

I'm in the final pre-beta testing stage of my Sudoku app that includes a multiplayer mode in real time, where up to 6 players can all throw guesses at the server and incur various penalties/bonuses if they get the play wrong/right. Right now each play incurs a score, and the winner is revealed only when the Sudoku grid is completed based on who accumulated the most points. But I realized I'm a bit conflicted as to which plays should be more rewarded than others.

So right now I am using these data to calculate a score, and various test algorithms with different outcomes:

1. Cell "vacancy": the total number of blanks in that given row/column and grid (where "grid" is the individual grouping of unique cells within the overall Sudoku).
2. Value "vacancy": the total number of that value remaining.
3. Candidates: the obvious potential candidates, from scanning only the row/col and grid and not applying any further logic.
4. Completions: the total features that were completed: from Row/Column/Grid/Value/Sudoku (the last meaning the final play, to complete the whole Sudoku).
5. Complexity: a skew based on the difficulty level, Sudoku size and Sudoku schema (the app supports jigsaw-style Sudokus too).

At first I thought to reward more Completions, but this ends in a rear-loaded game where the player that makes the final play gets a big bonus, since they completed all of the Row/Col/Value/Grid and Sudoku aspects. Then I thought to make it more Vacancy based (Cell and Value) with a small factor for Candidates, but this ends up with a front-loaded game where the big points are available with wild guesses at the beginning, and some players will withhold certain known plays so they can benefit from playing a higher vacancy one that depends on the withheld one. (Actually, this might even being a practice worthy of bigger score anyway).

So my question is ... what makes a "better" play than any other? Should I reward completions, or the more obtuse plays surrounded by more blank cells/fewer values used? Any opinion is good...!

Thanx
Sen

[denis_berthier]

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Hi Sen
Welcome to this forum.

My 2 cents.
I would say that the best play at any point in the resolution path is the play that results in eliminating the largest number of candidates after you have applied additional Singles after the user's play. And the score of this play could be precisely the number of candidates thus eliminated.
With a twist: at the end, this would imply a too large score. Perhaps the simplest way to correct this is to put an upper bound on positive scores.

About negative scores: any play that would lead to a contradiction could be assigned a negative score with a conventional value - to be set by you after experimenting which value is best. I think this value should be quite high in order to discourage plays based on guesses rather than logic.