Presentation on theme: "How To Chord by Fritz Löhr Written originally for the Facebook Minesweeper Fan Page Converted to Powerpoint and edited by Damien Moore (Aug 2010)"— Presentation transcript:
How To Chord by Fritz Löhr Written originally for the Facebook Minesweeper Fan Page Converted to Powerpoint and edited by Damien Moore (Aug 2010)
In the following pictures I will try to explain how you can use chording to improve your minesweeper times. I played this Intermediate board slowly to make sure that I can show you the immense advantage of using flags in the right places … so just ignore the timer in the following pictures! At first you need an opening in order to start solving. It is okay to do as many clicks as you need to get one, spreading your clicks around the board.
Now that we have an opening we can start solving the first patterns. In this picture the cursor is over a square that contains a 1, meaning that only 1 of the 8 squares it touches can be a mine. Only 1 square is still unopened so the green square must be a mine. Now look at the 1 that is two squares above the cursor. It also touches the green square, but the important aspect is that it also touches 2 more squares we have not yet clicked on. From this we know that the 2 purple squares are safe to click on.
Now we have two choices to uncover the two purple squares from the previous picture. We could do 2 clicks with the left mouse button, or we could use chording. First we mark the known mine with a flag, then we notice that the highlighted 1 now also has all the mines it touches marked.
Now we press both the right and left mouse buttons at the same time, on the 1 highlighted in the last picture. Notice that we have opened 2 squares with 2 clicks. So we did not waste any clicks by placing a flag! Even better, there is a chance that the square above the flag might also be a 1, in which case we can chord again and open another 3 squares. We will have opened 5 squares with only 3 clicks.
As you can see, we were lucky and got that 1.
Chording on this square will now uncover 3 more squares and still would be only our 3 rd click.
Here comes a part that might be hard to get used to, but not marking every mine can save clicks and result in a better score at the end. The 2 two squares right of the cursor touches only 2 squares, so they are both mines. The 1 by the cursor touches one of these mines, so the square above it must be empty. We could flag both of these mines, but it is quicker to just click once on the empty square.
So we clicked on the square, which was purple in the previous picture. Now we face a situation we can not solve: it is a 50/50 guess. The 2 under the cursor already touches a mine in the blue square, so the other mine is in one of the 2 purple squares. Normally it is better to take forced guesses as early as possible, because they cant be avoided and if you leave them unsolved until the end and guess wrong you have wasted your time. But in this tutorial I decided to leave the guess until later.
In this pattern we know that there must be mines under the flag and two squares below the flag. We know from the pattern that the mines must be beside the 1s. We could open the 2 purple squares in 2 clicks with the left mouse button, or we could place a flag beside the 1 and chord. Both options use 2 clicks, but we choose the second option because there is a chance we can use the flag to chord again and maybe save some clicks.
Right click to place the flag. Then move the cursor over the 1, which now has enough mines marked, and press both mouse buttons and release to open the squares.
Again it turns out it was useful to place a flag, because we can chord on the 1 that has just opened. This will uncover 2 more squares with only 1 click.
…But we can also place one more flag and then chord on the 2. This way we can uncover 3 squares with only 2 clicks.
In this picture all the purple and red squares are safe, while the green squares contain mines. As we know that the green squares are mines we now have to chord wisely. The best way would be to chord on the black 1 because this will open 3 squares, and if the red square is a 1 we would have a good chance to chord again soon.
By placing a flag here we can again open 3 squares in 2 clicks (1 to flag and 1 to chord).
Now we could either chord on this square or on the 1 above it. We choose this square because it opens 5 squares instead of only 3.
We hit an opening…
This flag I placed was not necessary because we cant use it to our advantage – the mine above the 1 two squares to the right would have been better.
So we placed a mine on the other 1 and missed our opportunity to save a click, because we could have only flagged this mine and chorded on the 1 to open 2 squares. However, the square between the two mines in the pattern is a 2 so we can chord it instead.
In this pattern we dont need to chord because the two red squares must be an opening, as from the 5 coloured squares we would open by chording on the 1, we know that the two red squares cant touch a mine. However we still should chord because the bottom purple square does not necessarily touch this opening.
The green squares have to be mines and the purple squares are safe. This pattern could be solved with no flags (NF) or by Flagging (FL). Both approaches should start with a left click on one of the purple squares. If the first square we open is a 1 we have another good chance to use chording.
And again there is a good spot for using a flag. With 3 clicks we now can uncover 5 squares.
Now, in this screenshot all the red and purple squares are safe. As the 3 red mines can not touch any mines they must be an opening. By clicking on a red square all 5 safe squares will open.
We now do a few more clicks where there is no use in placing a flag.
The purple squares on the left are 2 more left clicks where no flag is useful. The reason for the click on the red square is because it and the squares to the left and right of it must be safe. This square already has 1 mine (the green square) next to it, so if it turns out to be a 1 we could use chording to clear 6 squares.
We hit an opening. The 3 purple squares are two sets of 50/50 guesses … normally you should guess immediately so you dont solve the rest of the board only to blast at the end. In this example of solving a board I decided to leave them unsolved until the end for the sake of showing how to solve more patterns.
The purple squares were opened with left clicks, as in these patterns there was obviously no need for chording. As the 2 green squares are mines (due to the 3- on-the-wall pattern) the square under the cursor must be empty. From the surrounding patterns we can conclude this square is likely to be a 1, so we left click on it in the hope it will be a good spot for chording.
We had some luck and this square we clicked on turns out to be a 1. As we already know where the mine it touches is located, we flag it and can open 5 more squares with 1 chord.
Some more left clicks on the purple squares… Because the black 2 touches 1 known mine and another 2 squares, we can determine that the red squares touching the white 1 are empty. As there are no known mines next to them we have to left click on them instead of flagging.
We hit an opening with one of the left clicks from the last picture…
As the green square is known to be a mine, the red one is safe. As if often the case, no-flagging and chording are both equally efficient. NF would be 2 left clicks on the red square and the one below it. FL would be placing a flag on the green square and either chording on the 1 next to the red square or doing a left click on the red square.
As the square where we did the left click in the last picture turns out to be a 1, we can now chord again and open altogether 5 squares with 3 clicks in total.
Now back to the 50/50 guesses. There is no possibility to find out where the mine is but I can still give you advice – I always try to click on the square in the 50/50 guess which is closest to where I came from with the cursor. This saves some time, perhaps a few hundredths ;) However, in these places it comes down to luck…
If we were willing to win the board and ignore the timer, we could now count the mines that are known in this board, and if it turned out there is only 1 mine left this pattern would no longer be a guess, because the purple square under the 3 would be the mine. But there are 2 mines left so we have to guess anyways… However this is only 1 guess not 2, because if we get one of them right we will know the location of the other mine.
Again we were lucky on the forced guess and we won this Intermediate board. Notice that we have used only 10 flags and saved a lot of clicks. Thankyou for following this tutorial on how chording might improve your minesweeper gameplay. I hope you enjoyed it and that you learned something you might find useful when playing minesweeper yourself. P.S. Dont take the timer in this tutorial too seriously – my average time of 5200 Intermediate game on Arbiter is 22.68s (19.74s in 268 games won in 2009). When I played this game I was trying to involve as many tricks with chording as possible and actually my original plan was to make this a video tutorial…I think the pictures are easier to understand. Happy Sweeping and lots of Highscores Yours Truly, Fritz Löhr Admin of the Facebook Minesweeper Page (Tournaments)