Are dots and boxes solved?

Are dots and boxes solved?

Dots-And-Boxes is a well-known and widely-played combi- natorial game. Using these tech- niques, we have determined for the first time that Dots-And- Boxes on a board of 4 × 5 boxes is a tie given optimal play; this is the largest game solved to date.

How do you get more points on dots?

Make squares Drawing a square of like-colored dots eliminates all dots of that color from the board. It’s the fastest way to rack up points and the only way to get your score into the stratosphere. That’s because squares beget squares: Make one, and you’re setting yourself up for many more.

What is a good score on the dots?

The highest score ever is 800 so 600 or 700 is quite good. Even 500 is a huge milestone. Huge. If you’re in the 400 range or lower, don’t worry.

How do you clear all blue dots?

Drawing a square with four or more circle dots clears the entire board. It seems like a great idea, but it’s usually not: random dots are worse than whatever your planned next move is.

What is Dot formula?

Given that the vectors are all of length one, the dot products are i⋅i=j⋅j=k⋅k=1.

What is the point of Dots and Boxes?

Dots and boxes is a simple game with a simple goal: whoever “owns” the most boxes at the end of the game wins. You and your opponent take turns drawing horizontal or vertical lines to connect the boxes.

What’s the best way to win the Dot Game?

Loop: A loop is any string of 4 or more boxes that begins and ends in the same place. A loop counts as “2”. Y-Chain: See below for the value of a Y-Chain. Play this on any odd (or non-square odd-by-even) board size (such as those found in the Dot Game (3×3, 5×5, 7×7).

What happens when you sacrifice two boxes in dot?

If your opponent forgets to sacrifice the two boxes at the end, the count will drop by 1 which can sometimes result in victory if your sacrifice did not give away too many boxes. To avoid excessive sacrifices, pick the smallest chains to sacrifice. Y-Chains are complicated as there is more than one branch that can be considered a chain.

When do you encounter a Y loop in dot?

When you encounter a Y-Loop, the loop is always the base and branch which counts as “2” followed by the count of the chains that branch off of it. Similar to the Y-Chain, if there are 2 or more chains branching off of it, there is a possibility of cutting the Y-Loop by sacrificing 1 or 2 boxes within the loop and creating one large chain.