Guesses & Statistical Probabilities

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Guesses & Statistical Probabilities

Postby LittleReg1 » Sat Jan 01, 2011 11:50 pm

To All:

For the past year or so, I've been conducting a series of experiments with Minesweeper to try and see if there are any hidden patterns in the distribution of the mines that I'm simply not seeing which might account for some significant statistical anomalies that I've encountered in playing.

A little background...I'm one of those 'casual' players, someone who doesn't use the ? markers all that often to solve for possibilities, nor do I take the logic very deep when aware of the choices. I'll simply attempt to 'restart' the game somewhere else on the board and hope that I can get enough of a fresh opening to continue. That said, I've reached the point where I very rarely 'blunder,' that is, click on a square which was obviously a mine - in other words, I may not be highly skilled on the analytical side of the game, but I've acquired a baseline discipline. Currently, my winning percentage is running a bit over 19% for the Advanced Level (don't laugh, please!).

The reason the above is important is to engage the following question: are there 'patterns' which have been built into the mine distribution on the basis of some sort of psychological preferences of the players, i.e., numerical or 'shape' symmetry vs. random, corners vs. lines, etc.?

Once I acquired the 'no-blunder' discipline, I set out to conduct an series of experiments based upon some bizarre early observations about frequency of wrong guesses. While I could accept that an overall winning percentage would be down significantly due to the lack of desire to engage deeper analysis and the overall number of outright guesses associated with the Advanced Level, what has been bothering me is how low my successful guess rate is. One would think that guessing between two possibilities would result in ~50% success rate, but this is not the case with me. After 5,886 games (after my 'discipline' period), my successful guess rate is hovering slightly above 20% - quite a gap! Again, this rate is for the two-square guesses only.

Statistically, after this many games, this kind of guess success rate is rather curious, wouldn't we believe? Yet, after each guess, I record the result in a spreadsheet just to see if I'm going batty, but I'm not. While I'll let that simmer, I've noticed other curiosities which suggest that there is something else going on other than random occurrence.

First, I've noticed that the Windows 7 version of the game almost always opens a window, even if small. I have an old copy of the Windows 3.1 version on another machine and ran a test on 200 games on each version. In the Windows 3.1 game, I 'blew up' on the first click slightly less than 10% of the time; in the Win7 version, the immediate end occurred in less than 1 in 20 games! How does the Win7 version 'know' to provide the user with a 'non-bomb' for the first click? This suggests to me that the new version of the game has some sort of 'intelligence' built into it to allow users to be able to at least start a game without blowing themselves up all the time.

Another thing I noticed about the Win7 version is that I have a >60% 'success' rate of clicking on a mine square when attempting to navigate 'walls.' This flies in the face of my atrocious success rate in guessing the two-square patterns. After I 'explode,' I analyze the distributed mines and have noticed that there seem to almost always be 'clumps' of mines positioned in key places along the wall where users might want to click for the highest rate of return information.

I've noticed this about corners, as well. Whenever I'm presented with four unclicked squares in a corner surrounded by either mines or numbers or both, there is a >50% instance that there is only one mine left in those four squares and it is nearly always under the square which is diagonally placed away from the exact corner square.

Is there anyone who belongs to this forum who has encountered similar anomalies? I'd like to know once and for all if there are indeed psychological patterns built into the mine distribution or if I am simply imagining things and am simply the victim of a bizarre (and still unresolved) statistical imbalance.

Thanks,

Greg
LittleReg1
 
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Re: Guesses & Statistical Probabilities

Postby KamilSaper » Sun Jan 02, 2011 10:12 am

" In the Windows 3.1 game, I 'blew up' on the first click slightly less than 10% of the time; in the Win7 version, the immediate end occurred in less than 1 in 20 games! How does the Win7 version 'know' to provide the user with a 'non-bomb' for the first click?" -> I didn't know u can blast in the 1st click :o
0.49 - 7.03 - 31.13
NF: 0.49 - 7.03 - 31.51
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Re: Guesses & Statistical Probabilities

Postby EWQMinesweeper » Sun Jan 02, 2011 4:40 pm

few notes to you greg:

*welcome to msinfo and this forum
*9 paragraphs? yikes! :P
*vistamine and win7mine are crap! winning percentage is useless, since the mine distribution is random, which might lead to forced guesses


1st paragraph of yours: there should be no 'statistical anomalies' at all in minesweeper.

2nd one: you very rarely 'blunder' - i assume this means that you still do not recognise all solvable patterns and in consequence have to guess a bit more often than actually needed.

3rd one: huh? mines are randomly distributed. patterns are patterns. 3 on a wall - they're all mines.

4th: 50-50 guesses are 50-50. everything else is subjective. are you sure those were all really 50-50 guesses? amount of remaining squares and numbers often does have a slight impact on the actual probabilities. again, win percentage means nothing. it's about how many games you win per hour and how fast. on beginner and intermediate i used to play for exactly that: completing 100 beg or 25 int games in the shortest time and on both levels over 95% of the time was actually spent on solving and completing boards.

5th: doubt it!

6th: you can't blast on the first click on winmine. in no winmine version. never. if your first click would be on a mine the game moves that mine to another sqaure.

7th: forget that! learn how to actually play minesweeper. sorry if i sound rude, but your paragraph sugeest that you haven't understodd the game yet.

8th: same as 7th

9th: you're making things up. learn how to play minesweeper and you'll see that your post was a waste of time.

happy sweeping and a happy new year.
„Das perlt jetzt aber richtig über, ma sagn. Mach ma' noch'n Bier! Wie heißt das? Biddä! Bidddää! Biddddäää! Reiner Weltladen!“
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Re: Guesses & Statistical Probabilities

Postby LittleReg1 » Sun Jan 02, 2011 5:57 pm

Judging from your repsonse, it was obvious that you didn't read my post very carefully. The main error you made in your replies was mixing the concepts of 'winning' and 'guessing' as usedin my original post.

I've already admitted that I do not play to win to the last degree - it was never the intent of my post to ask for 'help' in this respect. Instead, I was asking if there were any hidden aspects to the distribution of mines which I was missing so that when I've uncovered 99 mines and am faced with two squares left with one mine remaining, my guess success rate should be ~50%. I know enough about the game to know when I've encountered one of these conditions even before I reach the 99-mine state on the board, too.

Furthermore, I admitted in my post that there very well could be things that I am missing, such as, "If there is a mine in the 123rd square, then when making a guess as to the last mine, it will rarely be on the border, but instead, one row in." Your reply infers that there are indeed no 'hidden' patterns to this effect, but this doesn't explain my low success rate with guesses.

I stated that I did not include in my survey of play the types of guesses that experts like you consider simply rash pokes. For example, I know that when I'm facing what I consider to be a wall, most of you more advanced players go through and figure out the correct choices. The only thing I noted here was that there are parts of a wall which seem more 'attractive' in a sense because a successful click would mean the revealing of squares with more than one piece of information to use (such as clicking next to 3 or 4 collected identified mines), and I noted that when I select such squares, I again have a result rate that is considerably different than 50%.

I misspoke about the first-click mine. What I had meant to say in that piece of the post was concerning a random second-click mine when the opening window reveals a condition requiring more than one logical step to solve (IF this, THEN this). If we use the two-possibility condition as a guideline, and just count the 'open' squares as evidence, Win7 seems to permit the user to begin with far more open spaces than the older version. You may think this is crazy, but you admitted that no game opens with a mine, right? Well, this means that the mines are not distributed *prior* to the first click, but *after* the first click. This means that the game has the capability of configuring itself based upon mouse clicks and it NOT operating from a fixed grid.

Well, why couldn't this kind of thing occur *throughout* a game?

Thanks for your remarks.

Greg
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Re: Guesses & Statistical Probabilities

Postby EWQMinesweeper » Sun Jan 02, 2011 6:31 pm

geez, could you please stop the babbling and keep your posts short?

i certainly did read your posts carefully enough. you obviously didn't understand why i brought in winning games. despite real forced guesses being the same for all sweepers it is still possible to win a lot of games. if you claim that your success rate on forced guesses is lower than it should be, the reason must be that you don't know the patterns well enough. if it is a 50-50 guess and you blast, accept it. there is no point in claiming that some mean minesweeper programmer has added a piece of code to the game that decreases your success rate on those occasions. the short answer is: learn your patterns and learn to accept that you can lose on forced guesses.

in winmine the mines are spread over the board after you press f2 or otherwise start a new game. if your first click is on a mine, said mine is moved to another sqaure!

"Well, why couldn't this kind of thing occur *throughout* a game?" - NO!

"...but this doesn't explain my low success rate with guesses." - you want an explanation? here you go: maybe you haven't understood the game yet.
„Das perlt jetzt aber richtig über, ma sagn. Mach ma' noch'n Bier! Wie heißt das? Biddä! Bidddää! Biddddäää! Reiner Weltladen!“
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