Concept for a Macro to Win 49 Mines on Beginner

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Concept for a Macro to Win 49 Mines on Beginner

Postby EWQMinesweeper » Fri Mar 20, 2015 10:40 am

As of writing this Daniel Marden is the only person to have achieved a successfull solve on this board.

Over the years I have made a few attempts at finish such a game but I assume that altogether I have not played more than 50 000 boards. When keeping track of my progress I noticed that in about 1 in 10 games I got a second quare opened and in less than every 100th game a third square. Although I never got past 10 0r 11 opened squares, it seemed that with each opened square the chance to open another square increased slightly. Since using a macro to fake a (non-lucky) sub1 rt solve on beginner is relatively easy and should in theory take a comparatively small amount of time (short solving time and macro could discard many boards if first click is not an opening), I think it would be interesting to discuss whether it is feasible to use macros in density mode.

Below is a first very simple approach that tries to reduce the number of possible remaining outcomes for the rest of the board as its only priority. This approach however loses too much time moving the cursor around and discarding games based on conditions the board does not meet.

When evaluating an approach you should consider these aspects:
No 1 3BV boards
Moving the cursor and clicking takes some time
The solve should look like a normal game, thus making 15 clicks all over the board in 1.5s is not an option.

What are your thoughts and ideas for macros on 8*8/64?

first of, let's assume that we have pre-recorded a solve and thus are looking to find that particular board again. our macro starts every game with the same click and as soon as it becomes clear, that the current board is not the board we are looking for, our macro hits f2 and tries again. furthermore let's assume that our macro only takes 0.000001s to hit f2 and return to the starting position.

for 49 mines on 8*8 we have 159518999862720 possible different boards. (64C15)

now let's assume our first click is on (1,1) and we only continue playing on the condition, that this squares is an 8. (coordinates starting from top left corner and from (0,0))
having our first click there reduces the number of boards we need to consider to 37387265592825. (63C14)
the chance of this square being an 8 is 0.11644470. ((55C14)/(63C14))
from this point on we have 4353548972850 boards left to consider. (55C14)

for our second click we choose sqaure (1,4) three squares to the right and we take 1 second to get there and finish the click.
again, we only continue if this sqaure is an 8.
the chance of this is ((46C13)/(55C14))*(1/9) or 0.002597273 (fraction of remaining boards and ensuring that we don't hit a mine).
we now have only 101766230790 boards left to consider. (46C13)

our third click shall be (4,4) three squares below and like before we take 1 second to get there and finish the click.
we want this sqaure, too, to be an 8.
the chance of this is ((37C12)/(46C13))*(1/9) or 0.002022591.
this leaves us 1852482996 boards. (37C12)

our fourth click shall be (4, 1) three squares to the left with the same conditions as the previous two steps.
the chance of (4,1) being an 8 is ((28C11)/(37C12))*(1/9) or 0.001288012.
after these four clicks we have 21474180 boards left. (28C11)

to get this far our macro would need to play on average 1269213531 boards. (multiply the 4 probabilities and ^-1 it)
the enormous number of games in which the macro passes the first click and performs a second click accumulates to well over 4 years and 1 second per game. (first prob multiplied by average number of boards above)

thus, this approach of focussing primarily on eliminating as many squares as mines with as few clicks as possible does not seem to be a suitable approach for a macro.
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