Pencil and Paper Games

EluZions.com Games Paper :

These are games you can play anywhere, with just pencil and paper. Pencil and paper games are among the oldest and most popular, especially with children. The rules are usually very simple, but still the games are challenging and entertaining. Most of them are best for just two players, but sometimes can be played by more.

Boxes (aka Dots)

Draw a grid of dots, e.g. 10 x 10. Take turns to draw a line between two neighboring dots, vertically or horizontally. If this completes one or more square boxes, write your initial(s) in it (or them) and take another turn. Play continues until no more dots remain unconnected. The one who has made the greatest number of squares is the winner.

Hangman

One person thinks of a dictionary word, and draws a series of dashes, one for each letter in the word. The other person takes guesses at letters in the word. When a guess is correct, the first person writes the letter above each corresponding dash; when a guess is wrong (the letter isn't in the word) then another line in the gallows and stick figure is drawn (starting with the lowermost 'ground' line). The first person is the winner if the 'man' is hung before the second player can guess the word.

Optimal Strategy

It's best to start with the commonest letters: E T A O I N S H R D L U, starting with E, the commonest letter in English words. You can memorise the sequence by the 'words' Etaoin shrdlu.

Nim

This is an ancient game with numerous variations. Most simply, place some objects (e.g. matchsticks or counters) into separate heaps, or draw rows of short lines on paper. Typical numbers of objects in the rows or heaps are 1, 2, 3, 4, 5 or 1, 3, 5, 7. Players take turns to remove any number (>0) from any heap. The player who is forced to take the remaining object loses. One variant is that the player who takes the las object wins. Another: Draw 5 sticks in a row (or place real sticks in a row). Draw 4 sticks in another row, then 3, then 2, then 1. Take turns to strike out (or remove) consecutive sticks in any one row (i.e. the sticks are neighbors in the row). The last one to take a stick is the loser.

Winning Strategy

Write the number of objects in each heap in binary, then sum the columns modulo 2 (i.e. count the number of 1's and divide by 2; take the remainder). Alternatively, determine if the number of 1's is odd or even; if odd write 1, else write 0. If the sum is all zeros then this is a winning position; whatever your opponent does, you can always restore the sum to zeros. Example: suppose the heaps contain 3, 2, and 1 objects; this is 11, 10, and 1 in binary. The number of 1's in each column is even and so your opponent cannot win unless you make a mistake. Suppose he takes all 3 objects from the first heap - then you take all 2 from the second. I leave you to analyse the other possibilities :)

At first, this looks like hard work, especially if you're not a math whiz. But with a little practice and experience you can soon learn to recognise winning patterns, for example, pairs of heaps having the same number of objects, or 3 heaps with (1, 2, 3), (1, 4, 5), (1, 6, 7), (2, 4, 6), (2, 5, 7), or (3, 4, 7) objects. Combinations of winning patterns are also winning patterns, e.g. 1, 2, 3, 4, 4. : TacTix online Java game, an 'upgrade' to Nim.

Sprouts

Draw a small number of dots. Take turns to connect any two dots so long as neither of the dots has more than 3 lines into it (a straight-through line counts as two). Place a new dot in the middle of the new line. The last one who can draw a line is the winner.