来源 Source: https://docs.google.com/document/d/1Mh8bMPuKTWUpB2lbmPNwsrHYIS2nH-t9g835Xaen3x4/edit

标题 Title: What is a 50/50?

作者 Author: Scar

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What is a 50/50?

The term 50/50 is used to refer to a situation where there is a forced guess between cells, with a 50% chance of a mine being in one cell, and a 50% chance it is in the other. It applies to situations where this is certain - when no information will be able to differentiate between the two cells.

An example of the classic corner 50/50. There are two cells, with no way to know where the mine is.	It looks similar, but is not a 50/50. While the odds of each cell below the 13 having a mine is 50%, there is the possibility of outside information solving the situation.

There is not much that can be done about 50/50s, they are simply part of the game. If you encounter one, you have a 50% chance to lose, nothing can change that. What you can do however, is learn to recognize common 50/50 patterns, so you can guess them immediately. This has two benefits: It can save a lot of time, and it can improve your chances of winning - by giving more information on the board that may prevent you from needing to make another guess. If 50/50s really are a deal breaker for you, try out the NG (No Guessing) mode - it will never have a 50/50!

MYTH: A common reason given for not guessing 50/50s immediately is to get more experience. This is not true! Guessing a 50/50 may end the game, resulting in less experience for that particular game. However, if you start another game, for the same time spent playing you will get the same amount of experience.

50/50 Explained

Let us consider these two cells. Which cells provide information that differentiates between them?
Only the yellow cells give information that can be used to separate the blue cells. What if all the yellow cells did not provide information?
If all the yellow cells were mines, you would not be able to get any information about one blue cell that doesn’t also apply to the other. If only one of the blue cells is a mine, there would be no way to tell which cell it is, resulting in a forced guess, a 50/50. This is regardless of what numbers are in the green cells.

There are two things in the game that don’t give information: Mines, and the edges of the board. As such, the common patterns each have a few variations.

Common Patterns

For all images:

• If no further cells are shown, assume it is the edge of the board.
• All patterns will apply regardless of the state of the rest of the board - unless noted that minecount is relevant.

Pattern 1: (Red mines, blue contains 1 mine)

Full	Wall	Corner	Wall v2

Pattern 2: (Red mines, blue or yellow are mines)

Full	Wall	Corner

The corner variation is only a confirmed 50/50 if it must have 2 mines. If there are 1 or 3 mines remaining on the board, it can be solved via minecount.

Pattern 1 Extended: (Blue or yellow are mines)

	This pattern is tricky to spot. It is an extended version of pattern 1. While it may look like further information will be able to solve this situation, no matter what numbers are in the bottom row no further information will be gained.
	None of the cells below will differentiate between the two pairs. Even the central cell (highlighted yellow) cannot give information that will be useful - both pairs are still possible.

6 Cell 50/50:

This setup is a 50/50 regardless of how many mines are left.

Either yellow or blue are mines, creating a 50/50. The two floating cells cannot provide information that differentiates between the cells.

2 Enclosed area 50/50 (Requires minecount)

This is another example of how a 50/50 can occur. As this pattern requires minecount to confirm there is only 1 mine remaining, it is generally not useful.

Large area 50/50

That is all one giant 50/50! If you place the mines, there are only 2 possible combinations.

Linked 50/50

In some situations there are what looks like multiple 50/50s. However, one guess resolves the situation, the other ends in another 50/50.

Here are some examples, guess one of the highlighted cells to solve the board. Guessing the other cells would result in a second 50/50.

(The last variation requires minecount to confirm there are 4 mines)

Methods for guessing

While there is nothing that will increase the odds of success, there are a few things to consider, or ways to go about guessing.

Confirm it is a 50/50 before guessing. It sounds silly, but when you guess next to a 4 that looked like a 50/50, but was actually both mines… it hurts.

Make sure there is no linked 50/50 (see above for details), where guessing one cell may resolve a second 50/50.

If you struggle to decide which cell to guess and often waste time, or agonize over the decision, make a rule. My rule was: Top left. I would guess the top left most cell of the 50/50. Having a rule like this can save time, and helps remove the sensation of “if only I guessed the other cell”. A common tactic on WoM is to guess the cell that would be a higher number. The reason for this is to have a higher chance of getting an arena ticket. If you have the same chance either way, why not?

If you are playing for speed: Guess the cell closest to your mouse. Naturally most players wait to see the result, train yourself to look ahead and keep playing without any pause.

Other Forced Guesses

66/33 and 33/66 are also a common term used for situations where there is a forced guess with a 66% or 33% chance of survival.

66/33
	The yellow cells have a 66% chance of being safe. For further information, see the Probability Calculation guide.(There are 3 possible combinations for the remaining mines. In two of those combinations, the yellow cells are safe)
	Guess either cell on the outside not the center. If you guess the center, you just made yourself a 50/50.

33/66
	There is no correct cell to guess, good luck.

Pseudo 50/50

This is an advanced technique. Pseudo 50/50s are situations where a cell is either safe, or a 50/50. In both situations it makes sense to click, so you should guess pseudo 50/50s immediately.

Example 1

The cell highlighted yellow is the cell to guess. In all possible variations it is either safe, or a 50/50.

If the mine is above the 3, the cells to the left are safe. (Red mine, green safe)

If above the 3 is safe, you get no further information and it becomes a 50/50 (Green is safe, blue and yellow are a 50/50)

Example 2

The cell highlighted yellow is the cell to guess. In all possible variations it is either safe, or a 50/50.

Due to the three, there can only be 1 mine above the 4. If the mine is in either cell above the 4, to the left becomes a 50/50. (Red mine, green safe, blue and yellow is a 50/50)

If both mines are to the left of the 4, the corner cell is still safe. (Red mine, green safe)

Example 3

The cell highlighted yellow is the cell to guess. In all possible variations it is either safe, or a 50/50.

If the mine is in either cell below the 3, the cells to the left are safe. (Red mine, green safe)

If below the 3 is safe, we get a common 50/50 pattern. (Green safe, blue 1 mine)

It is also possible to find pseudo 50/50 via minecount. The picture below has two pseudo 50/50s. Yellow is a pseudo 50/50 using the same logic as the third example above. Blue is a pseudo 50/50 via minecount: There are 5 mines remaining. The rest of the board uses at least 4 mines, leaving at most 1 mine in the floating cells.

Collection of 50/50s

If you find an interesting 50/50 send a screenshot to me and I’ll add it to the collection.

66/33