RE: Hardest percentage of mine density

Records for the 5 standard levels are 49, 42, 95, 161 and 225 mines -
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Joined: Sun Aug 21, 2011 1:43 pm

RE: Hardest percentage of mine density

Post by DMarden » Wed Dec 12, 2012 11:26 am

qqwref wrote:
wylx wrote:...I've always wondered what the optimally hardest percentage of mine density is, or if it varies across board sizes. Just to pick a nice number, I'll conjecture that it moves toward 1/sqrt2 as board sizes become larger. I don't see a need to limit ourselves to Intermediate and Expert densities, which are pretty arbitrary, and it'd be interesting to see, for example, the record for largest board on which 50% density is achieved.
For high densities you can look at the custom rankings - once about 1/3 of the board is filled the chance of being able to solve patterns using logic drops substantially. The 16x30 custom WR has a density of 33.5%, and the 24x30 custom WR has one of 31.3%. After that point, even on small boards, you are more or less constantly relying on guesswork - higher densities (anything up to one or two squares unfilled, basically) are more or less unplayable even on a beginner board. Int and Exp density is good for large board records because you're mostly still going through realistic patterns, but your suggested 50% density event would basically be a contest of pure patience and luck, like asking people how many heads they can get in a row while flipping a coin.
I've moved this over from a different thread because, being a density player, it took my interest. I would agree with qqwref that 50% is a very tough density regardless of the board size and is practically the crowning achievement of any player.
I would argue, however, that 50% is more realistic on the smaller grids of 8x8 and 9x9 since there is more chance of having a grouping of mines (with no empty squares separating them) in a corner or along one of the walls. Of course, this wouldn't guarantee a winning game since there would still no doubt be at least one instance of 50-50 or 33-33-33 guessing, and you would have to play a lot of games until such a board came up.

I've been trying to beat my PBs on the two largest boards, but decided to take a break last week and switch back to going for 38 on 9x9, so I thought I'd just conclude with a brief description of my approach to the two smallest grids. I start in the center with two clicks (one above the other) and whichever square contains the higher number, I click in the opposite direction, especially for obvious openings such as 14, 25, 36, 47. This can lead to some nice openings. I've been using this strategy for a couple of hours a day this past week and I've come within 5 to 6 mines a few times. Fingers crossed, I'll get it one day.

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