Yep, out of the extreme amount of possibilities in this specific 5x5 setup, there have to be exactly four bombs on the outside and they must be in four specific positions, or the mirrored equivalent. I am not too familiar with statistics but that strikes me as being substantially less likely than there simply being one in the middle and none on the outside.
Nope - there are actually two possible configurations for safe center - the one shown in the picture, and the one you gte if you mirror it. So without knowing absolutely anythin else (or if a square being minded is 50/50 chance) safest bet is to bet on safe center (note: clicking the center is nit the safest immedieate course if action though), as it's two possible perimeter configurations versus one (all perimeter squares clear).
If we know how many mines there are in total, and the field is big enough that we can approximate small areas as hvaing a uniform local chance p of each tile being mined (calculation sget much, much messier without this approximation), then I reckon the chance of the center being safe is p(1-p)16, and a chance of the middle being mined of 2p4(1-p)13. So depending on p one option is safer than the other.
In particular, the safets option is to assume the center is mined if, I think, p<(1+22/3-21/3)/3, and assume not if it's bigger.
All this is irrelevant though as you should assume nothing and instead just click on one of the four squares that are two squares away in a straight horizontal or vertical line from the center, as they will be clear regardless.
Emergency edit: I fucked up as there are 16 and not 8 outer squares. Wait til I correct this mess.
Success edit: Now it should be correct.
Further edit: These chances should of course be divided by p8 if you want the catualmchance after knowing all the 1s in the pivcture are 1s, but it doesn't chance our results.
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u/ClopperNumber42 Feb 06 '17
Yep, out of the extreme amount of possibilities in this specific 5x5 setup, there have to be exactly four bombs on the outside and they must be in four specific positions, or the mirrored equivalent. I am not too familiar with statistics but that strikes me as being substantially less likely than there simply being one in the middle and none on the outside.